Interval Specificity Table

[Paul Morris]

Our recent discussions reminded me of an "interval specificity" table I made a few years ago.  I'm attaching a version of it as an HTML file that you can open in a web browser.  (I tried putting it on the wiki but the ability to format the table wasn't as good as with HTML.)

It... "shows the types of intervals it is possible to represent  in traditional notation and in a chromatic staff notation. It illustrates how the addition of key signatures and accidental symbols each allow for greater specificity in the representation of (enharmonic) intervals."

This shows how:

"A chromatic staff notation system that has alternative key signatures and accidental signs (that allow for differentiation between enharmonically equivalent notes like C# and Db) can represent the same set of interval types that are found in traditional notation."

Being able to differentiate between enharmonic intervals allows an alternative notation system to remain compatible with traditional music theory (the part dealing with intervals).  All that's required is alternative key signatures and accidentals that indicate a particular name for enharmonic equivalent notes (like G# and Ab).  If you can differentiate between enharmonically equivalent notes, then you can also differentiate between enharmonically equivalent intervals, and continue to use traditional music theory.

If an alternative notation system uses a new chromatic note-naming system (with 12 note names per octave), that does not differentiate between enharmonically equivalent notes (like A# and Bb), then there's no way to differentiate between enharmonic intervals like a major third and a diminished fourth, as in traditional notation.  You then have 12 (or maybe 13?) interval types per octave, rather than 26 (but maybe that's enough...).

Whether these distinctions between enharmonic intervals are beneficial or not, or whether they are adding unnecessary complexity, whether we need 13 interval types per octave or 26, are open questions. 

(With TwinNote I did not want to limit it to only those on one side or the other in this debate.  I want to make it possible to use TwinNote with either the traditional note names, interval names, and music theory, or an alternative approach to these things.)

Cheers,
-Paul

[Doug Keislar]

Hi Paul,

Thanks for sending the table of interval specificity.  This seems like a very useful analysis.

I have some questions.  First, how does adding a key signature increase the number of interval types?  The key of Gb, for example, has the same number of intervals as the key of C.  There is something I fail to understand about what you mean.  Second, are the "interval types" referring just to intervals from the tonic, or all intervals between any pair of notes in the key?  (I think the latter, but still I fail to see how a key signature changes the total.)  Third, is an octave considered a different "interval type" from a unison?  In one sense, it should be considered the same, just as a tenth is considered equivalent to third, etc.

In any case, it seems there are some errors or inconsistencies in the table row that lists the numbers of interval types.  For example, the second column says "12 interval types" but there are 13 rows below it; and the third column says 13 although there are 14 rows below it; but in the case of the first column the number (8) does reflect the number of rows below it.

Probably illustrations of TN and a chromatic AN would clarify what you mean in some cases.

Doug

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[Paul Morris]

Hi Doug,
Thanks for the feedback.  See below...

Doug Keislar wrote:

I have some questions.  First, how does adding a key signature increase the number of interval types?  The key of Gb, for example, has the same number of intervals as the key of C.  There is something I fail to understand about what you mean. 

So, for example, in TMN, without knowing the key signature, you can tell whether an interval is a third or a second, but not whether it is a major or minor third (or second).  So adding the key signature makes it possible to be more specific about what kind of interval you are seeing on the staff. 

This is a little confusing since in a sense the TMN staff always has a key signature of C major / A minor by default (unless there is a different key signature instead), since those are the notes of the lines and spaces of the staff.  But if someone were to cover up the beginning of the staff with a sheet of paper so you couldn't see what the key signature was, and then asked you whether a third was major or minor, you wouldn't be able to say for sure without knowing the key signature.

Unless I'm mistaken, for a chromatic staff system, adding a key signature would only help to differentiate between a diminished 5th and an augmented 4th.  This is the only real difference between the second and third columns in the table.  So for a chromatic staff system, a key signature doesn't do much as far as interval identities are concerned, especially since there's only one augmented 4th and one diminished 5th in each key that you might want to differentiate.  (But this is not the only reason one might want to have a key signature.)

Second, are the "interval types" referring just to intervals from the tonic, or all intervals between any pair of notes in the key?  (I think the latter, but still I fail to see how a key signature changes the total.) 

The latter, any two pairs of notes from the key.  For example, in the key of C, there is a diminished 5th from B up to F, and an augmented 4th from F up to B.  (And there is no diminished 5th or augmented 4th starting from the tonic C.)  

Third, is an octave considered a different "interval type" from a unison?  In one sense, it should be considered the same, just as a tenth is considered equivalent to third, etc.

Good point, I guess to be consistent they should be counted as one "type" of interval. 

In any case, it seems there are some errors or inconsistencies in the table row that lists the numbers of interval types.  For example, the second column says "12 interval types" but there are 13 rows below it; and the third column says 13 although there are 14 rows below it; but in the case of the first column the number (8) does reflect the number of rows below it.

Hmmm...  good catch.  I think if we count (perfect) unisons as the same type as (perfect) octaves, then the interval types row should be:

7, 12, 13, 25

With each number being one fewer than the number of rows below it.  (There would need to be a note about counting unisons and octaves as the same type.)

Probably illustrations of TN and a chromatic AN would clarify what you mean in some cases.

Agreed that this would help. 

Cheers,
-Paul

[Doug Keislar]

Hi Paul,

Thanks, I get it now.  "No key signature" doesn't mean "no sharps or flats in the key signature" (as one might mistakenly think); instead, it means "Unknown key signature."

Besides "covering up" the beginning of the staff to disguise the key signature, you could also omit the clef sign.  In the case of the key of C (A minor),  I think this loss of information probably has the same effect as "covering up" the key signature: namely, reducing TN to the 7 interval types in your first column (or 8 if you consider the octave as distinct from the unison).  (For other key signatures, you can figure out the clef by looking at the vertical positions of the sharps or flats in the key signature.)

Doug

[Peter Jackson]

Hi Paul and friends,

my own book Learning the Intervals is a free download from the website www.klavarmusic.org  It is a severely practical book the aim of which is to improve people's sight  reading and mastery (ownership) over  the intervals of the  piano for the purpose of playing music written in  the Klavar notation. It also adds a new, enjoyable, dimension to   reading the music.  Intervals are presented in mirror images, each image has an accompanying cartoon character up to Major 6ths. All the minor thirds are cute birds for example;inversions of minor 3rds are     major sixths which feature the same birds associated with weapons of war (the tanks are particularly impressive) etc. I am not sure if you would find it of interest but it I think it   is worth a look.

All the best

Peter

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[John Keller]

Hi Paul,

 

It occured to me that in the last column, there should be a few more possible intervals (including some negative intervals such as E# "up" to Fb - a doubly diminished 2nd  = -1 S!)

 

The ones I first thought of were the doubly diminished 3rd  eg E# up to Gb (= 1 S), the doubly augmented 2nd eg Gb up to A# (= 4 S), and their inversions.

 

Not sure of there are any more. (I know these are probably not useful in practice.)

 

cheers, John K 

[Paul Morris]

Hi John,
Good call.  I didn't think of those.  I guess there are probably these kinds of intervals missing for each of the intervals listed in column 3. 

So since each note can have 3 values according to its accidental sign (sharp, flat, natural), that means you can increase or decrease the number of semitones in the interval by -2, -1, 0, +1, or +2,  so that each interval has 5 possible variants / numbers of semitones.

So for the basic intervals (before accidental signs):

Minor intervals:
    doubly-diminished (-2)
    diminished (-1)
    minor (+0)
    major (+1)
    augmented (+2)

Major intervals:
    diminished (-2)
    minor (-1)
    major (+0)
    augmented (+1)
    doubly-augmented (+2)

Perfect intervals:
    doubly-diminished (-2)
    diminished (-1)
    perfect (+0)
    augmented (+1)
    doubly-augmented (+2)


So with a little spreadsheet work (attached), the 4th column should include all of those listed below.  Basically about 3 possible variants for each number of semitones, for 39 total possibilities (if you count unisons and octaves as the same type).  Of course, many of these you probably would not see very often, if ever...

(Hmmm... I guess this includes using double-sharps and double-flats for notes that are already sharp or flat based on the key signature.  But doesn't include even more intervals that would be possible if those accidental signs were used in general.)

Cheers,
-Paul

Interval "Number"	Interval "Quality"	Semitones
Unison	2xDim	-2
Unison	Dim	-1
Second	2xDim	-1
Unison	Perfect	0
Second	Dim	0
Unison	Aug	1
Second	Minor	1
Third	2xDim	1
Unison	2xAug	2
Second	Major	2
Third	Dim	2
Second	Aug	3
Third	Minor	3
Fourth	2xDim	3
Second	2xAug	4
Third	Major	4
Fourth	Dim	4
Third	Aug	5
Fourth	Perfect	5
Fifth	2xDim	5
Third	2xAug	6
Fourth	Aug	6
Fifth	Dim	6
Sixth	2xDim	6
Fourth	2xAug	7
Fifth	Perfect	7
Sixth	Dim	7
Fifth	Aug	8
Sixth	Minor	8
Seventh	2xDim	8
Fifth	2xAug	9
Sixth	Major	9
Seventh	Dim	9
Sixth	Aug	10
Seventh	Minor	10
Octave	2xDim	10
Sixth	2xAug	11
Seventh	Major	11
Octave	Dim	11
Seventh	Aug	12
Octave	Perfect	12
Seventh	2xAug	13
Octave	Aug	13
Octave	2xAug	14

 




John Keller wrote:

[John Keller]

Hmmm,

 

There are actually two more possible intervals using only sharps, flats and naturals !

 

- the TRIPLY augmented 4th from Fb up to B# (=8S),

 

and its inversion:

- the triply diminished 5th from B# up to Fb (=4S).

 

Now could these be legitimately used in practice?

 

Yes I think they could.

 

Take the chord of the augmented 6th, in the key of Ab major. It contains a bass note of F flat up to a melody note of D natural.

Now decorate the D natural with a lower apoggiatura (a "leaning" note) of C#, which itself is decorated with a lower acciacatura (a "crushed" note) of B#.

At this point, the interval from the bass note up to the melody, Fb up to B#, is a triply augmented 4th!

 

Cheers, john K

 

----- Original Message -----

[Nextstep Musical System]

On Thu, Apr 26, 2012 at 4:43 PM, John Keller <jko...@bigpond.net.au> wrote:

Hmmm,

 

There are actually two more possible intervals using only sharps, flats and naturals !

 

- the TRIPLY augmented 4th from Fb up to B# (=8S),

 

and its inversion:

- the triply diminished 5th from B# up to Fb (=4S).

 

 

John, never heard of such name but coming from you I asked Google, and in the entire web found only one reference to the "triply diminished 5th" and is not to explain it, but to call it an absurdity.

http://books.google.com/books?id=xcgvuHlAgmgC&pg=PA195&dq=%22triply+diminished+fifth%22&hl=en&sa=X&ei=4cuZT9WwAoig2AWBjbX8Bg&ved=0CDAQ6AEwAA#v=onepage&q=%22triply%20diminished%20fifth%22&f=false

 

I think there is no need of complicating what is already complex.

B.R.

Enrique.

 

[Bob Stuckey]

I'd just like to add a diagram which I use to teach standard interval theory. I set it out on a fretted neck because equal temperament stemmed from the fretted instruments around 1550.

One puzzle is why the perfect intervals should be less elastic than the imperfect intervals.

bob

--

[Doug Keislar]

Hi John,

That is ingenious.  But I wonder whether we might be talking about how many angels can dance on a pinhead.  I doubt most composers would use a B# in the scenario you describe; they'd more likely use a C.  They might also use a Db instead of the C#.  Although the C# is possible (because composers like to see sharps in an ascending chromatic scale), Db is already in the key.   Also, since the augmented sixth chord is often considered an alteration of the subdominant or supertonic (both of which would contain Db in this key), I think the Db spelling is likely.  In other words, although you are considering the C# to be an unstable embellishment leading chromatically up to the D, it might more likely be heard as a stable tone in the key leading up to an unstable tone (D) which is an alteration of the stable tone (just as the augmented sixth is an alteration of the subdominant or supertonic).

Doug

[John Keller]

Well what would you call the interval from Fb up to B# if given the question in a traditional music theory exam???

 

F to B is an augmented 4th.

F  to B#   = ?

Fb to  B#  = ?

 

john K

 

----- Original Message -----

From: Nextstep Musical System

To: musicn...@googlegroups.com

Sent: Friday, April 27, 2012 8:45 AM

Subject: Re: [MNP] Interval Specificity Table

--

[dominique.waller]

Great job. Thanks Paul !

 

---- Original Message -----

--

[John Keller]

Its a bit like having an A# in C minor. The key signature has Bb but the leading note B natural is common, so if you decorate B with a lower mordent, you would write B A# B.

 

When i have a minute i'll write the example in Finale : )

[Nextstep Musical System]

On Thu, Apr 26, 2012 at 7:01 PM, Bob Stuckey <bobst...@gmail.com> wrote:
> I'd just like to add a diagram which I use to teach standard interval
> theory. I set it out on a fretted neck because equal temperament stemmed
> from the fretted instruments around 1550.
>

Thanks Bob, nice and elegant.

B.R.
Enrique.

[Doug Keislar]

Agreed about the mordent (which has both a descending and an ascending minor second).  But the scenario you had described earlier was (I think) just an ascending chromatic scale.  I'm not sure it's analogous.

Doug

[Joseph Austin]

Bob, 

I too like your diagram.  The even/odd separation/comparison puts the intervals in a perspective that is obscured by the names.

As to your puzzle, I'm not sure exactly what you mean by "elasticity", but I assume it relates to: why don't the fifths have major and minor like the thirds?

I'll speculate it comes from the way scales are formed.

The two methods I'm familiar with derive scales from either:

- incomplete circle of fifths (2:3 intervals in just intonation), e.g. F C G D A E B  (or just the inner 5 for the pentatonic scale)

- what I call the "Tonnetz torus" of thirds, by dividing the "fifth" (2:3) into 4:5 + 5:6, giving a major (M) and a minor (m) interval.

Then, beginning with the subdominant, you take MmMmMmm and you're back (near) to the beginning with the notes of the diatonic major scale and related modes, e.g. F A C E G B D (F).

If you want to modulate into other keys, you will need to "augment" or "diminish" one or more of the scale intervals of the home key to get the same interval pattern in the foreign key.

Of course, in just intonation, neither sequence is mathematically closed, but in equal temperament, forcing F# = Gb in the circle of fifths, and equalizing all the intermediate intervals gives us: 4 semitones (major third) + 3 semitones (minor third) = 7 semitones (perfect fifth) and it all comes out even in a sequence of 12 semitones.

But accepting the anomaly of the extra m at the end, the "circle of thirds" method, in equal temperament, is a "closed" path.

This suggests to me a reason why the traditional scales stop with 7 notes.

From a mathematical perspective, a "fifth" is seven semitones; to divide that in "half" would give 3.5 semitones, or 7 quarter tones (quartertone = a ratio of  1:[24th root of 2]).

But if we don't want to go to quarter-tone intervals, we have to "compromise" and alternate between 3 and 4 semitones!

The choice of taking the larger or smaller interval first may then account for the "elasticity" you refer to.

Jazz, of course, introduces "blue" notes and scales with adjacent semitone intervals.  

Now I haven't studied jazz theory, but to me, these seem to arise as a "combination" of the major and tonic minor scales.

Perhaps they arises when modulation becomes so frequent that the "foreign" tones merge into the scale itself.

Or maybe, as I recall some have suggested, the jazz scales may have arisen from a culture that actually did divide the 2:3 in half, 

and our jazz scales are an attempt to recover the lost quartertones within a semitone scale.

-----

Stepping back to the larger issue of the names of notes and intervals,

i think part of the problem is we tend to confuse absolute and relative measurements.

Notes are absolute pitches, which must be qualified by a physical unit of measurement: frequency, for example.

Intervals are ratios of pitches, and as such are pure numbers, which should be the same regardless of the unit of measurement of the pitches.

Now the confusion arises when we start referring to notes as intervals relative to some fixed note, such as the tonic.

Then the note "quantification" also appears to be a pure number.

But that is only a convenience (or an obfuscation); the note must ultimately have an actual pitch.

So our attempts to notate and name both pitch (absolute) and interval (relative) with the same staff or note names or interval terminology lead to these lively discussions!

BTW, the same kind of confusion arises in rhythm.  I believe we confuse the notation of rhythm patterns by notating timing as duration between notes instead of time position within the measure.

In fact, IMHO, we do both backwards:  we attempt to notate melody and harmony, which are intervalic, with absolute (pitch) positons,

and we attempt to notate rhythm, which is positional, with relative durations.

No wonder we have such a hard time learning and an even harder time explaining!

Joe Austin

DrTechDaddy.com

For more options, visit this group at http://groups.google.com/group/musicnotation?hl=en<table of intervals (2).jpg>

[John Keller]

Here is an example of what I consider a well notated harmonic progression showing the triply augmented 4th Fb to B# between the bass and melody in bar 6 beat 2.5.

 

Comments?

[Doug Keislar]

You win!

Doug

[Nextstep Musical System]

could not download the file.

[Doug Keislar]

You need some version of Finale to open the .MUS file.  Then you can see and hear John's convincing little composition.

Free download of Finale NotePad here:
http://www.finalemusic.com/Notepad/FreeDownload.aspx

Doug

[Nextstep Musical System]

Thanks Doug but is the file that I cannot download. It should be because I raised the security settings.

[John Keller]

Hi Doug,

 

Thanks for the Finale 2012 link. I had not realised that once again Finale NotePad is free.

 

I downloaded it and tried an Express Stave file. Unfortunately this version does not show the notes on the correct side of the stems. They have corrected the anomoly that had let me override the stemside rules in the 2006 version.

 

What I had discovered was that by simply copying a blank ES staffstyle over music, the notes stemside did not change until you played the file with the playback control. Then while scrolling, the notes flipped to the "correct" side according to whether they were in the same or adjacent line or space positions. But in ES I do not want this because the ES "space" is equivalent to two TN spaces.

 

Then I happened to find that if I applied a "human playback" plugin, then on playback the notes no longer flipped. All this was simply trial and error and relied on Finale's rather haphazard design.

 

I suppose that down the track I would have to employ a finale codewriter if want a fully functional ES transnotation to work with the latest version. But for the moment, Finale 2006 works very well, so I just stick to that.

 

I have a private link for Finale Notepad 2006 if anyone wants it. I suppose the older versions of Finale NotePad are not available from the official site, but havent checked this. (They had taken them off when they decided to charge $ for NotePad. I dont know when they made it free again.)

[Nextstep Musical System]

On Fri, Apr 27, 2012 at 11:15 AM, John Keller <jko...@bigpond.net.au> wrote:

Here is an example of what I consider a well notated harmonic progression showing the triply augmented 4th Fb to B# between the bass and melody in bar 6 beat 2.5.

 

Comments?

 

John K

 

John, I saved your examp as MIDI and opened it in all major score writers I have, there is some little discrepancy on how to notate some notes, except for bar 6 where they all agree to eradicate the practice you propose, and instead do this.

 

Enrique.

[Paul Morris]

Joseph Austin wrote:
> Stepping back to the larger issue of the names of notes and intervals,
> i think part of the problem is we tend to confuse absolute and
> relative measurements.
>
> Notes are absolute pitches, which must be qualified by a physical unit
> of measurement: frequency, for example.
>
> Intervals are ratios of pitches, and as such are pure numbers, which
> should be the same regardless of the unit of measurement of the pitches.
>
> Now the confusion arises when we start referring to notes as intervals
> relative to some fixed note, such as the tonic.
> Then the note "quantification" also appears to be a pure number.
> But that is only a convenience (or an obfuscation); the note must
> ultimately have an actual pitch.

Hi Joe, This is a good point you raise. You have to be clear on
whether you're talking about a note's position within the current
key/scale, or the interval between any two notes. I like to think of
three ways of "parsing" notes:

1. absolute pitches/notes (A, B, C, etc.)
2. relative interval relationships (5th, Maj 3rd, etc.)
3. relative position within the key/scale (movable-Do, Re, Mi... Shape
note, Nashville numbering system, or chord names: I, IV, V, etc.)

I see these as complimentary to each other -- you just have to be clear
about which one you're talking about. That's easier if you have
separate naming schemes/conventions for each one. (Something to keep in
mind when re-thinking naming along with music notation.) Also, since
TMN doesn't really do #2 that well, the chromatic staff approach has a
lot to offer by improving on #2 as well as #1.

(I have a draft of a tutorial that discusses this -- that there are two
ways of reading music, either by individual notes/pitches, or by
interval relationships. Notation systems can support both of these
types of reading to one degree or another and both should be considered.)

> So our attempts to notate and name both pitch (absolute) and interval
> (relative) with the same staff or note names or interval terminology
> lead to these lively discussions!

Agreed that you need separate terminology for these things, but I think
you can represent both on the staff without any confusion. A note has
both an absolute (pitch) value and an interval relationship to
surrounding notes, and both can be portrayed clearly at the same time on
a chromatic staff.

> BTW, the same kind of confusion arises in rhythm. I believe we
> confuse the notation of rhythm patterns by notating timing as duration
> between notes instead of time position within the measure.

That's interesting. I haven't thought of rhythm in the same terms, but
it makes sense. But here as well I think the two ways of understanding
rhythm can be complimentary, since they are two ways of looking at the
same pattern. But it would be interesting to see proposals for how you
could better support both in notation.

> In fact, IMHO, we do both backwards: we attempt to notate melody and
> harmony, which are intervalic, with absolute (pitch) positons, and we
> attempt to notate rhythm, which is positional, with relative durations.
> No wonder we have such a hard time learning and an even harder time
> explaining!

Maybe so, although I would tend to see these as complementary cases of
both/and rather than cases of either/or. For me a good notation system
would support both ways, for example, both reading notes as individual
pitches and in terms of their interval relationships.

Cheers,
-Paul

[Paul Morris]

Bob,
I also like your interval chart -- showing it with frets is a nice way to illustrate the enharmonic overlap.

John and Doug,
I guess we'll have to add 3xAugmented 4th and 3xDiminished 5th to the table!  The main point (after we're done counting the number of angels on the head of a pin... :-)   ), is that, whether by accident or design, TMN and traditional theory includes all of these "enharmonic" interval names.  And you can make it possible to keep using them in a chromatic staff system by providing alternative accidental signs and key signatures.

So the question is whether it makes sense to simplify these 41 interval types down to 12 (or 13), or whether to (make it possible to) use the traditional note and interval names and theory by providing alternative accidental signs and key signatures.  Would we miss these distinctions if we didn't have them?  Could we just infer from the context what they indicate more explicitly -- in terms of a note's or an interval's function in a piece of music? 

John,
Looks like NotePad becoming free again just happened in February 2012.  Glad they realized that charging for it was a bad idea, especially with competition from the free MuseScore heating up.  Here's a comparison between MuseScore and NotePad:

http://musescore.org/en/comparing-musescore-and-finale-notepad-feature-feature

I searched Finale's site for downloads of older versions of NotePad, and did not see any:
http://www.finalemusic.com/Downloads/Default.aspx

Before you pay someone to customize Finale, take a look at MuseScore.  :-)  

Cheers,
-Paul

[Nextstep Musical System]

On Sat, Apr 28, 2012 at 11:49 AM, Paul Morris <pa...@paulwmorris.com> wrote:
>
> (I have a draft of a tutorial that discusses this -- that there are two ways
> of reading music, either by individual notes/pitches, or by interval
> relationships.  Notation systems can support both of these types of reading
> to one degree or another and both should be considered.)
>
>

Paul, you may have also a draft of a tutorial about when we apply fire
to a vase with water it turns hot.

It results shocking (and somehow insulting to me) that after more than
two years trying to take the MNP out of its little world, basically
limited to notation and anachronic criteria you subtlety and slowly
are changing your talk as though you were getting to some novel
conclusions.

It is true, everything I have exposed here has not made a dent on the
MNP official website presentation, which I think remains wrongly
focused on the isolated notation of music, I feel it has caused
reflection, mostly perceived through silence and afterward comments.

The sun cannot be covered with a finger and eventually there will be
people with other values that put everything within context in a truly
professional way, you guys had the chance but I think missed it.

I intended to be patient but there is a limit and I think I am wasting my time.

Regards
Enrique Prieto.

[John Keller]

Hi Enrique,

 

Thanks for looking into this. It is interesting (but to be expected) that ALL the score writers would have the 6th bar beat 2.0 top note as a Db, rather than a C#. This is because Db is in the key, the 4th degree of Ab major.

 

But with this notation, most piano players reading it would then assume the bottom note of that right hand chord was also meant to be a Db! 

 

To counter this, the bottom D note should have a courtesy natural sign, perhaps in brackets. Of course midi files converted into score will never do niceties like that.

 

The C# is more correct in my opinion. Players will not then play the wrong note at the bottom of the chord.

 

It then follows that the lower auxiliary note (mordent) decorating this C# on beat 2.5 should be a B#. 

 

Whatever algorithms midi-to-score writers use to deal with non-diatonic notes, they are simple, and are unlikely to be foolproof in all situations composers may require.

 

The point of my example was to show that it IS possible, with correct notation, to have an Fb and B# simultaneously. And then, if the question is asked what interval is that?, the ONLY correct answer would be "a triply augmented 4th".

 

You (and Google) may say that this is ridiculous, but it IS the correct answer, in terms of traditional music theory!

 

Cheers, John K

 

 ----- Original Message -----

From: Nextstep Musical System

To: musicn...@googlegroups.com

[Nextstep Musical System]

On Sat, Apr 28, 2012 at 8:52 PM, John Keller <jko...@bigpond.net.au> wrote:

Hi Enrique,

 

 

 

 

You (and Google) may say that this is ridiculous, but it IS the correct answer, in terms of traditional music theory!

 

 

 

Hi John, I did not put any qualifier to the use of the nomenclature, just showed the only reference I found about it, I guess all Spanish speaking musicians will fault the question as I have not found an equivalent terminology and all tries failed to find anything.

 

However my point is that the evolution of the conventional system is about pruning and adding and it seems that such nomenclature has already been pruned or as a consensus not a common practice, consequentially should not be included into a common practice table, in any case in a separate note as a notation exception.

 

B.R.

Enrique.

[Paul Morris]

Nextstep Musical System wrote:

On Sat, Apr 28, 2012 at 11:49 AM, Paul Morris <pa...@paulwmorris.com> wrote:

(I have a draft of a tutorial that discusses this -- that there are two ways
of reading music, either by individual notes/pitches, or by interval
relationships.  Notation systems can support both of these types of reading
to one degree or another and both should be considered.)

Paul, you may have also a draft of a tutorial about when we apply fire
to a vase with water it turns hot.

:-) 

Hi Enrique,  Right, so this tutorial is not for those on this forum like yourself who have already thought through these things.  Its target audience is new people who have not considered that you can read music by intervals as well as by individual notes, and so clearly representing intervals might be just as important as clearly representing individual notes. 

As you know, alternative notation systems can make it possible to really and fully read by intervals in a direct and straightforward way, something that is not possible in TMN.  It's new and unexplored territory for music education (always being able to see and understand the interval patterns of scales, chords, etc.).

I started on this tutorial years ago and had to set it aside because of time constraints.

It results shocking (and somehow insulting to me) that after more than
two years trying to take the MNP out of its little world, basically
limited to notation and anachronic criteria you subtlety and slowly
are changing your talk as though you were getting to some novel
conclusions.

It is true, everything I have exposed here has not made a dent on the
MNP official website presentation, which I think remains wrongly
focused on the isolated notation of music, I feel it has caused
reflection, mostly perceived through silence and afterward comments.

The sun cannot be covered with a finger and eventually there will be
people with other values that put everything within context in a truly
professional way, you guys had the chance but I think missed it.

I intended to be patient but there is a limit and I think I am wasting my time.

I'm sorry you feel that way.  We are an all-volunteer organization and that limits how much we can do with our website and how quickly we can do it.  We do have a wiki that allows anyone to contribute and add to the content of our site.  You have sent some interesting PDFs to this forum about your Nextstep Musical System.  You could certainly feel free to start a new MNP Wiki page about your system and add that same information to it. 

Regards,
-Paul M

[Nextstep Musical System]

On Mon, Apr 30, 2012 at 8:24 PM, Paul Morris <pa...@paulwmorris.com> wrote:


>   You have sent some interesting PDFs to this forum about your
> Nextstep Musical System.  You could certainly feel free to start a new MNP
> Wiki page about your system and add that same information to it.
>
> Regards,
> -Paul M
>

Hi Paul, thanks for offering the wiki but the project is dynamic and I
can hardly keep up with one site, I hope soon will be able to organize
a bit everything and have a permanent presence of its own on the web.

I still have a lot to say, some of it are improved versions of what I
have already said and others I have never talked about; I remain
puzzled if the NMS is really ignored here or pretended to, whether it
was misunderstood or not paid attention, whether people are driven by
genuine search of solutions or simply affected by the NIH syndrome,
whether the MNP's attitude towards the NMS is the product of
conviction or of obscure interests.

I understand that the NMS is a sort of negation of the principles that
have ruled the MNP and similar thinkers, but when approaches or ways
of thinking have failed for so long, the least they can do is
reconsider to find out what is wrong and give a little bit of space in
their minds to newer approaches and ways of thinking.

B.R.
Enrique.

[Dan Lindgren]

Bob wrote:
> One puzzle is why the perfect intervals should be less elastic
> than the imperfect intervals.

Not sure if I have the "correct" answers to this puzzle, but the
perfect fifth is the generator of all other intervals ever since the
heyday of the ancient Greeks; and maybe we don't like to fiddle
with it for that reason. The more likely reason, though, is
perhaps the fact that the two notes of a perfect interval have
more partials in common than the notes of a third. So, when
we hear the two notes together in a perfect fourth or fifth, it
will sound really bad when they are not in tune (cf. the wolf
fifth). All coinciding partials will then interact with each other,
and it may create very fast and unpleasant beat rates.

It is interesting to note that people can generally accept a
fifth or fourth that is slightly sharper than pure, but not the
opposite.

Dan

[Doug Keislar]

Yes, I think the explanation (in your first paragraph below) about
coinciding partials is correct. Also, it's comparatively easy to hear
the third harmonic of a note (in most musical timbres), whereas hearing
the fifth harmonic is usually harder. The third harmonic is an octave
and a fifth above the fundamental; the fifth harmonic is two octaves and
a major third. So it's probably not only beating, but also pitch
perception that comes into play in making the fifth more sensitive to
mistuning than the third.

In European music in the Middle Ages, the fifth was considered a
consonance but thirds were not, so polyphony would focus on fifths and
fourths. That's the context in which the perfect and imperfect
nomenclature arose. Many other musical cultures feature the consonance
of the perfect fifth, even if (as in Arabic cultures) their scales also
use intervals strange to Western ears, such as a neutral third (halfway
between major and minor thirds) or the interval halfway between a major
second and a minor third. The drone in Indian music (as played on the
tambura) is typically a perfect fifth.

Doug

[Doug Keislar]

P.S. I just realized that my first paragraph might be confusing for
readers who aren't familiar with acoustics. The third harmonic
corresponds to the interval of a perfect fifth (plus an octave), whereas
the fifth harmonic corresponds to the interval of a major third (plus
two octaves). Confusingly opposite! So what I meant was that the
interval of a perfect fifth (not the fifth harmonic) is more sensitive
to mistuning than is the interval of a major third (not the third harmonic).

[Bob Stuckey]

Thanks for these thoughts on the inelasticity of the Perfect
intervals. Their extreme sensitivity to mistuning seems an important
factor in this puzzle. They are all highly contrasted with their
neighbours , particularly the unison and octave. The perfect fourth
and fifth both have a discordant interval as a neighbour, the
augmented fourth or diminished fifth (the tritone) . When we play a
melody in parallel fourths or fifths the tritone sticks out like a
sore thumb.

As the ratio involve higher numbers contrast with neighbours gets
blurred. When we move to the next ratios 4:5 (major 3rd) and 5:6
(minor third) the distinction is mild so the we can play a melody in
parallel 3rds (in effect a mixture major and minor thirds) without any
feeling of discontinuity and without telling the difference without
stopping to think about it.

The ratios 5:6 and 6:7 are so close that three semitones can pass for
either of them according to context. In the chord sequence D7b9 B7b9
the three semitones between f# and a performs the role first of 5:6
then of 6:7

5:6 , 6:7, (approximately 3 semitones) and 7:8, 8:9 and 9:10
(approximately 2 semitones) are all sufficiently similar that in a
black note pentatonic scale the steps don't sound terribly distinct
unless you stop to analyse it.

Likewise 5:7 and 7:10 are both approximated by 6 semitones which can
pass for either according to context as in the changing roles of b and
f in the sequence G7 Db7 (the tritone substitution). Also 4 semitones
between c and e can pass for 5:4 in the chord of C and for 7:9 in the
chord of D9.

And again 2 semitones is not so distinct from one semitone that we
can't string them together into a diatonic scale without any feeling
of discontinuity.

There is a parallel discussion going on in another email thread. Why
do we keep contorting a seven note scale when we have got the unit of
the semitone to describe intervals?

Joe suggested that the reason why scales tend to stop at seven is they
form good strings of (roughly) pure intervals (with no ratio part
larger than 6) . Rather going against this theory is the traditional
Thai scale in which there are seven roughly equal steps, approximating
the interval of the 7th root of 2. It functions perfectly well as a
scale. It has unfortunately been swamped by Western equal temperament
which has been adopted by Thai pop musicians and I could only find one
example of the traditional scale on youtube

http://www.youtube.com/watch?v=GOclGpDqscQ

Doug also mentioned the intervals of Arabic scales which do not fit
into the string of simple ratios model. So I would like to
suggest another reason for the 7 maximum. Societies need unisons and
octave to achieve conformity across genders and generations. They need
scale steps because its really hard to gets bunch of people sing a
pitch glide together but they don't need too many steps as the
intervals would become too subtle and the melodies hard to remember.
Seven notes fills the octave without becoming too dense. Our culture's
scale becomes so influential that we would prefer to perceive that
one of our precious seven has moved slightly than to admit more than
seven. In MIDI code the notes are numbered in simple semitone order
but when we hear a realisation of a MIDI file we we try to map the
notes on to our 5,6 or 7 note scales where ever possible, stretching
and shrinking where necessary. However this perception of sharpening
and flattening is subjective and there will never be unanimity over
which note has been sharpened or flattened, through music theory tries
to impose its conventions. I doubt the tuning of a note has much
influence on these perceptions of movement.

We seem to pick up the scales of our culture intuitively just as we
pick the vowels of our mother tongue. There is no real need for a
scale to follow a string of simple ratios to be socially useful
however if it does it's a kind of of bonus in that it allows all kinds
of key and root shifts and suggestions especially if extended through
equal temperament.

None of this offers any solutions for notation reform but might
suggest that there is more going on than just semitones, elegant as
they are.

Bob

[Paul Morris]

Nextstep Musical System wrote:
> Hi Paul, thanks for offering the wiki but the project is dynamic and I
> can hardly keep up with one site, I hope soon will be able to organize
> a bit everything and have a permanent presence of its own on the web.

Hi Enrique, I can certainly understand that, as it is hard to find time
for this stuff. It would be nice to have your system and approach
documented on its own site. That would make it easier to understand I
think.

> I still have a lot to say, some of it are improved versions of what I
> have already said and others I have never talked about; I remain
> puzzled if the NMS is really ignored here or pretended to, whether it
> was misunderstood or not paid attention, whether people are driven by
> genuine search of solutions or simply affected by the NIH syndrome,
> whether the MNP's attitude towards the NMS is the product of
> conviction or of obscure interests.

What do you mean by "NIH syndrome"? I haven't heard of that before.

> I understand that the NMS is a sort of negation of the principles that
> have ruled the MNP and similar thinkers, but when approaches or ways
> of thinking have failed for so long, the least they can do is
> reconsider to find out what is wrong and give a little bit of space in
> their minds to newer approaches and ways of thinking.

It does seem like you have a unique or at least different approach with
NMS, maybe with different basic assumptions, compared with a lot of the
other approaches or systems. A lot of the more active folks on this
discussion list have their own systems and approaches, and/or tend to be
partial to their own way of seeing things. It is not surprising that
those who are interested enough in this stuff to participate on the
list, also have pretty own well-formed views about it. But it is still
helpful to try and keep an open mind about these things, and look at
them from different angles.

Cheers,
-Paul

[Doug Keislar]

Paul, "NIH" is "not invented here." It's often used of people at tech
companies who disdain technologies not developed in-house. I believe
Enrique is using it to refer to notation inventors who are interested
only in their own systems.

Enrique, I hope you continue to participate in the MNP Forum. In my
opinion, your system is unique (especially the reference notehead
approach) and has many valuable features. I like its correlation across
notation and nomenclature. I do think that it would help a lot to have
a site on the Web where its features could easily be studied, whether
that's the MNP Wiki or your own site. I get the impression that not
everyone has understood it.

It would definitely be desirable for the MNP site to have more info
about nontraditional rhythm notation, including systems where note
durations are indicated by the length of a line (as in your NMS) or by
extension dots as in Klavar, and so on. The MNP's Web master (Paul)
volunteers his time, which is limited, and that's why he set up the Wiki
to let other people add material. I hope more people take advantage of it.

Doug

[Dan Lindgren]

Good points, Doug. It's very tempting to explain musical
intervals with the way harmonics are spaced. The intervals
used by professional musicians are usually close to the
intervals found between the harmonics, but only for the
perfect intervals; the thirds found among the harmonics are
not the ones that you would typically hear in actual music.

The overtones form intervals with the fundamental, but there
are also intervals that can be found between overtones. The
perfect fourth resides between the third and fourth harmonic,
and so on.

Maybe one should weigh in the order in which these intervals
appear in the harmonic series; and also, like you suggested,
the relative strength of the individual harmonics.

Dan

[Dan Lindgren]

Thanks for sharing these thoughts, Bob. Let me add another
example of scales that don't fit the conventional ones. In
traditional Swedish folk music, there are flutes with tunings
that differ from what we are used to:

http://www.sheerfolk.com.ar/tag/spilapipa/#.T64rEL8cgnV

Dan

[Keislar, Doug]

Hi Dan,

Thanks for the interesting URL about the Swedish folk flutes.

One detail I'm wondering about: The authors says:
"the 3rd tone sounds 25-30% lower, the 6t tone 25% lower, and the 7th tone 25-30% lower than what they would sound in a tempered major scale"
but this statement can't be understood without knowing what the units are that the percentages are applied to. Certainly not Hz, probably not cents from the tonic. I suppose the units are equal-tempered semitones.

Doug

________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Dan Lindgren [ny.d...@ownit.name]
Sent: Saturday, May 12, 2012 2:58 AM
To: The Music Notation Project | Forum
Subject: [MNP] Re: Interval Specificity Table

http://www.sheerfolk.com.ar/tag/spilapipa/#.T64rEL8cgnV

Dan

--

[Dan Lindgren]

Hi Doug,

I wondered about that, too. I searched and found this in a
Wikipedia article:

"The traditional Harjedalspipa is made from spruce and tuned
in the key of A# at the bottom (all six finger holes covered).
The scale includes some blue notes, in particular the third,
sixth and seventh which are flat by 20-25 cents compared to
the equal temperament scale. Today, instruments are made
also in other keys and temperaments."

Dan

[Joseph Austin]

On May 9, 2012, at 9:44 PM, Bob Stuckey wrote:

> None of this offers any solutions for notation reform but might
> suggest that there is more going on than just semitones, elegant as
> they are.
>
> Bob
>

I suspect there is more going on than semitones, or pitches or intervals, for that matter.
But isn't it possible that that "more" could be captured in notation?

If we give any credence to Pythagorean harmony theory, it's the ratios of the frequencies that determine the aesthetic "value" of the interval.

Agreed, traditional notations, or even reformed notations based on equal intervals, don't give any clue to the frequency ratios.
For example, in the 12-tone chromatic scale, the number of semitone intervals gives no clue to the "good" harmonic ratios.
How is it evident that 12 semitones is the "purest" interval (after the unison), which historically we call the octave (2:1)?
Of course you could write it as 12/12. But then 6/12 (six semitones) might look like the next best harmony,
whereas in fact this is the infamous tritone.
The "perfect" harmonies are the 7/12 (3:2 or "fifth) and the 5/12 (4:3 or "fourth").

Looking at a 12-position chromatic staff, nothing really jumps out at you to suggest the 12/12 (octave), 7/12 and 5/12 (fifth/fourth), 4/12 (8/12), and 3/12 (9/12) (major/minor thirds/sixth) are "consonant" and the others are "dissonant".

But the staff isn't the only notational device we have at our disposal.
I had earlier suggested a 3x4 notehead shape/color system, based on Euler's Tonnetz (and borrowing from Roy Pertchik, Enrique and others), that would expose at least the major/minor thirds.
Such a system wouldn't even need a staff, except to distinguish octaves.

The point being, that a notation can be created to emphasize whatever aspects are deemed to be most important, possibly obscuring others deemed less important.

It might indeed be possible to develop a numeric notation based on harmonic ratios instead of scale steps.
To some extent, that might involve switching from a "pitch-based" or absolute to an "interval-based" or relative notation.

I think that idea deserves it's own thread, so I'll start a new one.

Joe Austin
DrTechDaddy.com

[Nextstep Musical System]

On Thu, May 10, 2012 at 4:10 PM, Paul Morris <pa...@paulwmorris.com> wrote:

>
> It does seem like you have a unique or at least different approach with NMS.......


Hi, Paul I have insisted that qualifiers like unique, original,
interesting and the like have no value per se, they mean nothing, not
even "improvement" as anything could be an improvement; alternatives
to the conventional system have to be a "significant improvement as a
system not as notation".

The focus on just improving readability of staff notation is likely to
continue to fail; with very few exceptions (it comes to mind J.
Plamondon) chromatic staff variants have not taken the time to be
presented as systems, consequentially they are not alternatives to the
conventional system.

On the other hand most chromatic notations based on numbers could be
considered as systems, as numbers could have their own complete
support, but the importance of being a complete system has not being a
concern for the MNP or similar approaches, and this has been
mistakenly under estimated.

Nobody will pay attention or understand the NMS until they realize
that only a "significantly improved system" is an alternative to the
conventional system; meanwhile I would better advice tablatures,
klavar or piano roll falling notes instead of any of equally
complicated chromatic staff variants as they can be quickly learned
and don’t hurt.

B.R.
Enrique.

[Nextstep Musical System]

On Thu, May 10, 2012 at 4:34 PM, Doug Keislar <do...@musclefish.com> wrote:
> Paul, "NIH" is "not invented here."

Hi Doug, your right about the NIH syndrome it applies from companies
that do not want to license patented inventions and instead prefer to
work around their own ideas, to software developers that do not want
to use other companies components without solid reasons, the syndrome
is real and not necessarily a completely negative thing, for me it is
an attitude, a mind-set of some people and when I see someone working
around the shape of note heads or the lines but the result do not
propose something significantly different and new, well I can't help
thinking of it.

B.R.
Enrique.

[Paul Morris]

Nextstep Musical System wrote:
> On Thu, May 10, 2012 at 4:10 PM, Paul Morris<pa...@paulwmorris.com> wrote:
>
>> It does seem like you have a unique or at least different approach with NMS.......
> Hi, Paul I have insisted that qualifiers like unique, original,
> interesting and the like have no value per se, they mean nothing, not
> even "improvement" as anything could be an improvement; alternatives
> to the conventional system have to be a "significant improvement as a
> system not as notation".
>
> The focus on just improving readability of staff notation is likely to
> continue to fail

Hi Enrique,

I don't know what more to say except that at this point I'd rather learn
more about your NMS, since I already know that you think your approach
is superior and that other approaches are destined to fail. It's more
interesting to me to consider concrete proposals than to rehash the same
debates in such abstract terms.

Anyone who cares to read about my flexible approach to nomenclature with
TwinNote can do so here:
http://twinnote.org/learn/key-signatures-and-accidental-signs/

I will say that the kinds of music notation software that make it (a lot
more) practical to use an alternative notation system have only been
available for a very short time. That makes it harder to make
predictions about the future based on the past.

Cheers,
-Paul

> ; with very few exceptions (it comes to mind J.
> Plamondon) chromatic staff variants have not taken the time to be
> presented as systems, consequentially they are not alternatives to the
> conventional system.
>
> On the other hand most chromatic notations based on numbers could be
> considered as systems, as numbers could have their own complete
> support, but the importance of being a complete system has not being a
> concern for the MNP or similar approaches, and this has been
> mistakenly under estimated.
>
> Nobody will pay attention or understand the NMS until they realize
> that only a "significantly improved system" is an alternative to the
> conventional system; meanwhile I would better advice tablatures,
> klavar or piano roll falling notes instead of any of equally
> complicated chromatic staff variants as they can be quickly learned

> and don�t hurt.
>
> B.R.
> Enrique.
>

[Nextstep Musical System]

On Mon, May 21, 2012 at 7:02 PM, Paul Morris <pa...@paulwmorris.com> wrote:
>
>
> Hi Enrique,
>
> I don't know what more to say except that at this point I'd rather learn
> more about your NMS, since I already know that you think your approach is
> superior and that other approaches are destined to fail.  It's more
> interesting to me to consider concrete proposals than to rehash the same
> debates in such abstract terms.
>

Hi Paul,

What I consider superior is the system as a solution to one of the
long-time existing approaches for an improved general purpose systems,
for approaches I mean: (1) the improvement of the diatonic system and
(2) a native and complete chromatic system; chromatic staff notation
without a complete theoretical support to music (at least as we
already have it) is not an alternative.

Having a wrong approach at solving problems is not the worst, the
worst is canonizing it and not having the attitude of correcting it
continually if necessary, and I consider it is necessary correcting
the obsession of giving more importance to the graphical proportional
distribution of notes in chromatic staff notation (sometimes
imaginary) THAN keeping a reasonable simple compatibility with the
diatonic system.

My comments are not only about the NMS and the reference head
notation but also about the weakness and flaws of the evolution of
staff notation into chromatic, which has not happened just for
subjective reasons but also for objective ones.

So far the only abstract for me remains your claimed compatibility
with the diatonic conventional system, especially after I finally gave
full (simple 100%) compatibility to the NMS with the conventional
diatonic system through supplementary (not alternative) resources;
your fight with key signatures and accidental signs is half the way,
it requires also diatonic counting (cycling), as chromatic counting
and conversion through a table is not feasible.

The intention of having a native chromatic solution 100% compatible
with the conventional one in a simple way was not in my original
purposes, however it has been the result of giving some space to other
people interests, somehow useful and probably so far a unique feature
of a native chromatic solution.

B.R.
Enrique.

[Paul Morris]

Nextstep Musical System wrote:
> chromatic staff notation without a complete theoretical support to music (at least as we
> already have it) is not an alternative.

Hi Enrique, You are making this assertion (and have made it before),
but an assertion is only as persuasive as the reasons for making it.
Can you be more specific about the reasons that have lead you to this
conclusion?

I think that using a chromatic staff notation system with the
traditional nomenclature and theory ("theoretical support"), with
alternative key signatures and accidental signs to clarify the identity
of enharmonically equivalent notes is a perfectly viable approach. Can
you say specifically why you disagree?

(This approach would be for those who want to retain the difference
between enharmonic equivalents and want to be able to easily communicate
with other musicians by using the same names for notes, intervals, etc.
Anyone can always use TwinNote with a new naming system and theory
instead if they want. Again see:
http://twinnote.org/learn/key-signatures-and-accidental-signs/ )

> Having a wrong approach at solving problems is not the worst, the
> worst is canonizing it and not having the attitude of correcting it
> continually if necessary, and I consider it is necessary correcting
> the obsession of giving more importance to the graphical proportional
> distribution of notes in chromatic staff notation (sometimes
> imaginary) THAN keeping a reasonable simple compatibility with the
> diatonic system.

Can you tell us in specific details how NMS maintains this compatibility?

> So far the only abstract for me remains your claimed compatibility
> with the diatonic conventional system, especially after I finally gave
> full (simple 100%) compatibility to the NMS with the conventional
> diatonic system through supplementary (not alternative) resources;

I don't know anything about NMS's supplementary (not alternative)
resources. Can you give any specific details about them?

> your fight with key signatures and accidental signs is half the way,
> it requires also diatonic counting (cycling), as chromatic counting
> and conversion through a table is not feasible.

I don't know what you mean by diatonic or chromatic counting (cycling).
Perhaps you can explain what you mean in more specific detail?
Perhaps a specific example of how it works in NMS would help?

Cheers,
-Paul M

[Nextstep Musical System]

Paul, believe me that your comments plus the indifference of most
knowledgeable people reading these posts have caused me reconsider
over and over, as I cannot find other explanation that I am so wrong
that do not even deserve being corrected.

On the other hand I don’t think my comments are so abstract, I think
of them as basic concepts which have been shaped as I understand
better the conventional system and its evolution; as anyone else I
still think it has some inconsistencies that should be improved,
however it has become 'very clear' to me that there is a huge
difference between improving it while keeping its diatonic integrity
AND evolving into a purely chromatic system.

I know the words 'diatonic and chromatic' are used in several ways but
'twelve tone system' also has been given a specific meaning, for which
I propose at least within the context of this discussion think of:
(1) the conventional system as a 'seven tone-name system' that can
handle much more than twelve different tones (and that is why I
previously called it a "diatonic" solution).
(2) a "chromatic" system as a 'twelve tone-name system' that can
handle only up to twelve tones.

Neither the words diatonic nor chromatic fully apply or are restricted
to these definitions but inventing words might be more confusing.

My point has been that the prevailing practice uses only twelve tones
and given its importance it deserves a native theoretical support,
given that by having only twelve tones it also has much less intervals
and chords, for which it could be assumed that it would be simpler.

However not every possible native support has to be simpler than the
diatonic solution, especially when applied to a mostly diatonic music
and practice, it should be simpler for dodecaphonic music.

The conventional nomenclature is based on diatonic counting (1-7)
which is well defined in a diatonic notation that cycles the series
(repeat) after 7; a chromatic notation that do not have a well defined
way of such way of counting would have to use an additional method to
convert from its chromatic counting (1-12, 0-11) into diatonic one,
the conventional method is already complicated to add additional
complications.

The 7 spaces of the 5-line background (supplementary) in a piano
keyboard layout provides to the NMS the diatonic counting, I will
explain later how to qualify the intervals, enharmonic equivalence
(compatibility) but want to know if I made it simpler to understand
now or disagreements.

B.R.
Enrique.

[Keislar, Doug]

Hi Enrique,

So do I understand correctly that you are currently envisioning a notation system with your system of reference noteheads (previously described in this forum), but now superimposed on a backdrop consisting of a piano staff like Klavar? That is news to me. Like Paul, I find it easier to discuss the advantages and disadvantages of different approaches when there are concrete examples to look at. Are you not ready to show illustrations of this system yet? I'm curious to see it.

Best,
Doug
________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Nextstep Musical System [mtall...@gmail.com]
Sent: Wednesday, May 23, 2012 9:16 PM
To: musicn...@googlegroups.com

Subject: Re: [MNP] Interval Specificity Table

[Nextstep Musical System]

Hi Doug,

Well, in all documents I have shown labeled as 'overview' I have
talked about the symbolic nature of the reference head technique to
notate pitch, which allows the use of supplementary backgrounds for
different purposes, and have shown several of them, even one for the
guitar which applies also for any string instrument.

The piano background was originally used to map notation and
instrument and a way for learning the conventionally assigned pitches
to the symbols; when I considered the possibility of having a way of
using the conventional nomenclature with the RH notation I saw that
the white keys of the piano could provide that diatonic counting that
is missing in a 12 position/symbol system and talked about it on those
documents.

However I don’t like a permanent piano background that makes the
notation look cluttered; at this point I am so used to the symbols
that don’t need the background lines, then started to use another
method, which is the one I have not shown here yet.

Consider and think of the NMS as a modern system, which completely
rest on technology and its future depend on it, the NMS is the
implementation of novel notation methods that allow expanding the
traditional concept of a fixed general-purpose system into a modern
concept of a multi-purpose system (feasible only in our times).

After embracing the multi-purpose concept I started to completely
remove the focus on notation and emphasizing more on 'complete system'
and 'music education', saying that notation is just a visual component
of our whole theoretical support to music and struggling with
terminology that could make basic concepts look abstract.

I will present some examples of what I am talking about, maybe I will
reduce the overview as much as possible, as so many things together
does not seem to work, I lost the hosting I had, now moving to new
one.

B.R.
Enrique.

[Nextstep Musical System]

Ok, I have found something we can use as a reference, fig 1 & 2 are
what I mean the full compatibility, however fig 3 & 4 is what I
actually use and have implemented; having a distinction between the
white and black keys of the piano is useful anyway regardless of
additional music theory; here do not appear double accidental but
consider it would be like coloring one of the white keys (now in
black) accordingly.

My intention has rather been using the NMS nomenclature on the
conventional system than the other way around, I find it much more
useful and practical with a lot of advantages, however it requires
mastering both systems; so if anyone finds a flaw on the method I
appreciate letting me know as I actually don’t use it that much.

I think the best use of color on music notation could be what is shown
on this excerpt, if there is anything simple and practical that can be
done to the publication of music scores, THIS IS IT. The NMS will have
at least f.3 & 4 from the beginning, if in the future it becomes
common practice in TN, we will converge there.

B.R.
Enrique.

[Nextstep Musical System]

Let me add something, the k-signature that appears in f. 1 & 2 is
similar to the conventional one but with more information, it shows
the tonic with the longest trace, dominant with second largest and the
rest of the notes that belong to the key with equal length, this
signature is not actually necessary to qualify the intervals like in
the conventional system, given that each note has the indication
whether natural, sharp , flat or double accidental, and the diatonic
counting of the spaces makes clear when same interval size has more or
less semitones (which is not seen that easily on the conventional
staff).

The p-signature that appears in f. 3 & 4 indicates the notes that are
actually used and their length reflect the proportion in which they
have been used, I also use i-signature (intervals) and d-signature for
degrees or all intervals in reference to the same note.

Enrique.

[Nextstep Musical System]

On Wed, May 23, 2012 at 12:52 PM, Paul Morris <pa...@paulwmorris.com> wrote:
>
> I don't know what you mean by diatonic or chromatic counting (cycling).
> Perhaps you can explain what you mean in more specific detail?  Perhaps a
> specific example of how it works in NMS would help?
>

Hi Paul,

I searched for ''diatonic counting'' and the term is not in common
use, the conventional terminology seems to be 'diatonic numbering' and
'diatonic number'; the problem for most alternative notations and
compatibility is that neither the diatonic number nor the quality of
an interval can be determined by counting semitones alone.

My point is that breaking with the possibility of naming intervals and
chords in the same way that is done in the conventional system would
require also the proposal of other alternative methods, the methods
could lead to the same names or different names.

The evolution of staff notation could then be defined as those that
allow keeping the nomenclature and those who don’t; there are very
simple reform that can be done to staff notation while keeping
everything else the same.

However I imagine the evolution of staff notation as a process of
accretion and later pruning but what happens is that accretion really
means complication, as we would have to cope with old and new and
nobody wants that, unless the new comes with significant new benefits
or do not represent big changes as the coloring of the flatten or
sharpen note heads I showed; the NMS has absolutely nothing to do with
the evolution of staff notation and I think it could make the
difference.

B.R.
Enrique.

[Paul Morris]

Hi Enrique,
Thanks for the pdf with example illustrations.� They help a lot!� I haven't had much time to look at them closely yet, but I'll try to respond to your message below about diatonic and chromatic counting.


Nextstep Musical System wrote:

On Wed, May 23, 2012 at 12:52 PM, Paul Morris <pa...@paulwmorris.com> wrote:

I don't know what you mean by diatonic or chromatic counting (cycling).
Perhaps you can explain what you mean in more specific detail? �Perhaps a
specific example of how it works in NMS would help?

Hi Paul, I searched for ''diatonic counting'' and the term is not in common
use, the conventional terminology seems to be 'diatonic numbering' and
'diatonic number'; the problem for most alternative notations and
compatibility is that neither the diatonic number nor the quality of
an interval can be determined by counting semitones alone.

Right, this is what my "Interval Specificity Table" is about, and what alternative key signatures and accidental signs are for.� The key signature tells you whether "non-natural" notes in the key are sharp or flat.� So if there are no accidental signs then the semitones (and key signature) are enough to tell you both the diatonic number and quality of an interval.

(Except for the rare exception of whether an interval is an augmented 4th or a diminished 5th.� One out of every 7� fourths and one out of every 7 fifths in a given key is not perfect but either augmented or diminished.)�

If there are accidental signs, then there are more possibilities.� In that case you just use the accidental signs to determine the name of the notes, and then based on the names of the notes you can tell the diatonic number and quality of an interval.�

I have to run, so that's all I can say for now.�� I will be away from email all weekend...

Cheers,
-Paul

My point is that breaking with the possibility of naming intervals and
chords in the same way that is done in the conventional system would
require also the proposal of other alternative methods, the methods
could lead to the same names or different names.

The evolution of staff notation could then  be defined as those that
allow keeping the nomenclature and those who don�t; there are very
simple reform that can be done to staff notation while keeping
everything else the same.

However I imagine the evolution of staff notation as a process of
accretion and later pruning but what happens is that accretion really
means complication, as we would have to cope with old and new and
nobody wants that, unless the new comes with significant new benefits
or do not represent big changes as the coloring of the flatten or
sharpen note heads I showed; the NMS has absolutely nothing to do with
the evolution of staff notation and I think it could make the
difference.

B.R.
Enrique.

[Nextstep Musical System]

Ok Paul, but I would still have to disagree until you show exactly
with examples your workaround, I hope with mine is understood what I
mean.

Diatonic numbering has absolutely nothing to do with key signatures,
accidental or number of semitones, those only intervene in the process
of qualifying the intervals.

Diatonic numbers (DN) come out of the very simple method of counting
every single line and space (including their own) between two notes in
a conventional staff notation score, it is a number very proprietary
to music theory in the conventional system, it has nothing to do with
anything else, and anyone trying to find a mathematical or logical
explanation out of those numbers, only will get confused.

As these numbers are native and exclusive of the conventional system,
any other music notation system would have to come up with a
workaround to have its equivalent, which obviously should be more
complicated.

I have to admit the NMS workaround method to find the DN is a bit more
complicated as it is not native to the reference head notation, the
same happens when trying to apply the native relational method of the
NMS to the conventional notation.

The additional complications of the NMS workaround are that it
requires counting only (and repeat) only the spaces between a 5-line
piano staff background; when the interval is between two notes that
are in spaces (black) that is it, but when a note is in a line
position, the space that is counted depends on the color of the note,
a fatten note (blue) will always count the space above and a sharpen
note (red) will always count the space below, a double accidental is
represented by coloring the notes in spaces accordingly and same rules
applies.

However, while the DN is harder to find in the NMS, the qualification
is made much easier given that it do not require (use) of a key
signature and depend much less on memory, overall I would say is about
the same.

Enrique.

[Nextstep Musical System]

I have reviewed this compatibility workaround and noticed that what I
said was the indication of double accidentals it is not, that is
required to be consistent with the indication of accidentals for all
natural notes, because of key signatures with more than five
accidentals, I use another simple resource for double accidentals.

My point is that with an alternative system I am interested in having
a simpler alternative for both the visual and not visual components of
music theory, if a system do not provide alternative support for
getting rid of enharmonic equivalents and the so complicated methods
of naming intervals and chords I would prefer for staff notation
sticking with the CS or maybe simpler reforms just to make the
diatonic system more consistent.

The NMS is that extremely simplified system with native support for
the prevailing 12-T practice, successions and patterns of intervals
(gestalts) that make feasible a world of possibilities in our times.


B.R.
Enrique.

[Nextstep Musical System]

On Sat, May 26, 2012 at 6:23 PM, Nextstep Musical System
<mtall...@gmail.com> wrote:

> As these numbers are native and  exclusive of the conventional system,
> any other music notation system would have to come up with a
> workaround to have its equivalent, which obviously should be more
> complicated.
>

I would better say DN are native of diatonic notation, as in staff
variants as the diatonic 2-line e.g. the one Dan uses in Nydana there
is almost no difference, the workaround is rather for chromatic
notations.

Enrique.

[Joseph Austin]

Toward Absolute Timing Notation

I'd like to report on my latest effort on rhythm notation reform.

Earlier I had suggested that TN timing/rhythm notation is in as much need of reform as the pitch notation,
although the time dimension has received relatively little attention.

I had suggested that we change timing from a relative to an absolute notation.
Specifically, instead of denoting the duration of notes, which requires the reader to calculate the starting (and ending) time/beat/count of each note by summing the durations of notes in a beat or measure, I suggested denoting instead the starting beat/count of each note. To facilitate this, I suggested that additional sub-bar lines could be added to the staff, e.g. at each count or major sub-count, and notes positioned with strict proportional spacing within a sub-bar.

Adding extra bar line styles to the notation would require a modification to notation software.
As an alternative, I have been experimenting with variations of conventional notation that can be scored with
TN software such as Finale. It turns out that a combination of beams and ties can go a long way to visually positioning the notes to the beats.

As an example, I've scored highly syncopated melody [Elton John's "Bennie and the Jets", 1974] which I notated in 4/2 time
with the primary minimal note value as an eighth note (my original score uses 1/16, which I doubled for clarity of presentation.)



I've scored the melody with only two note values: each count is either a half-note symbol or a beamed set of four eighth note symbols, which visually divide the count into equal time intervals. The duration of each tone is then indicated by ties. Thus, two tied eight notes replace a quarter note, three tied eights replace a dotted quarter, etc. For more complex music, it would be possible to vary the divisions from count to count, as long as each count is divided into equal sub-parts. In summary, the counts are indicated by beams, and the durations by ties.

The advantage of this representation is that one can visually determine, without calculation, at which count or subcount an individual tone begins. Also, there is no notation difference for a given duration whether the note starts on a beat, off a beat, or is held across a count or a measure.

In a sense, this approach is just a notational substitute for the " 1 e & a 2 e & a " that students write above the score when learning a complex passage, combined with a crude approximation to Enrique's "note trace" notation for indicating duration. The key element, in my view, is that the timing of the music is indicated by specifying the temporal "position" of the note starts (and stops) with respect to the fixed beat and rhythm pattern (e.g., the drum track) of the music, rather than specifying only the "duration" of notes and requiring the reader to calcualte position as they play along.

Now I'd be the first to admit that this is not a satisfactory "permanent" solution to rhythm-notation difficulties,
but only a stop-gap to enable one with conventional score-writing resources to experiment with a "positional" rhythm notation.

But from my personal experience, it seems that it's "easier" to play syncopated tunes by "seeing" whether the note occurs on a "strong" beat or a "weak" or "between" beat. I'm finding that with practice I can play/sing the off-beat notes at the proper time while "tapping" a steady beat.

Finally, in the example I've included a couple other of my notational preferences. I've split lines at the ends of phrases rather than strictly at bar lines. And I've used the shape-note feature of Finale to notate the scale-degrees of pitches. I'm finding that "singing" (aloud or silently) the solfedge names of the scale degrees as I play is helping me recognize harmonic interval patterns and melodic sequences, and also helps with ear training.

[If the attachment does not appear, check on my website, DrTechDaddy.com]

Joe Austin
DrTechDaddy.com

[Doug Keislar]

Hi Enrique,

Thank you very much for the PDF; that makes it much clearer what you are
envisioning. So, to summarize your proposals:

Coloring:
-- The white keys of the piano are indicated by black noteheads (in TN)
or black trace lines (in NMS).
-- Flats are indicated by blue noteheads (in TN)or blue trace lines (in
the NMS variants of Fig. 1 and 2), and sharps by red. (However, this
seems to apply only to the black keys of the piano, not to pitches like Cb.)
-- In NMS variants of Figs. 3 and 4, all black keys of the piano are
shown by red lines; no distinction between sharps and flats.
-- There is no explicit indication of accidentals, and therefore nothing
corresponding to a "natural" symbol (as in the B naturals in measure
1). One has to refer to the key signature to tell whether a note is an
accidental.

"Staff" lines:
-- One variant (Fig. 1) has all five lines (as in Klavar) extending
across the page.
Another (Fig. 2 and 3) has only the C#/Db line extending across the
page, with the other lines shown as short lines crossing each bar line.
-- Fig. 4 instead has gray background bars as in earlier versions of
NoteTrace.

Signatures:
a "k" signature is a key signature that shows the seven notes of the
diatonic scale, with coloring as indicated above. The dominant note is
given a slightly longer trace (horizontal line) and the tonic note an
even longer one.
a "p" signature is the same as a key signature, except that the length
of the trace instead indicates the occurrence frequency of the diatonic
note. (No such information is given for chromatic notes.)

> The additional complications of the NMS workaround are that it
> requires counting only (and repeat) only the spaces between a 5-line
> piano staff background; when the interval is between two notes that
> are in spaces (black) that is it, but when a note is in a line
> position, the space that is counted depends on the color of the note,
> a fatten note (blue) will always count the space above and a sharpen
> note (red) will always count the space below, a double accidental is
> represented by coloring the notes in spaces accordingly and same rules
> applies.

I believe this is not quite correct. What about, for example, the
interval from A to B#, which is part of the C# harmonic minor scale? In
a keyboard-tablature kind of staff, such as Klavar or the background you
propose, these are both white notes (in Klavar) or both black notes (in
your system), but the interval is an augmented second, NOT a kind of
third. I think you might therefore have exaggerated the benefits of
what you are calling diatonic counting with a keyboard-tablature kind of
approach, and you might have correspondingly exaggerated the
disadvantages of a chromatic staff.


> Let me add something, the k-signature that appears in f. 1& 2 is

> similar to the conventional one but with more information, it shows
> the tonic with the longest trace, dominant with second largest and the
> rest of the notes that belong to the key with equal length, this
> signature is not actually necessary to qualify the intervals like in
> the conventional system, given that each note has the indication
> whether natural, sharp , flat or double accidental, and the diatonic
> counting of the spaces makes clear when same interval size has more or
> less semitones (which is not seen that easily on the conventional
> staff).

This is a clever idea. (Note that in the PDF file, the music is
actually in C minor, not in Eb major, but your longer traces are
indicating the tonic and dominant of Eb major. Easily corrected.)

Best,
Doug

[Nextstep Musical System]

Hi Dough, thanks for your comments, in previous posts I had already
corrected myself some of your indications, as I said, for me this is a
workaround for a native chromatic notation to be compatible with the
conventional nomenclature, It is something I had been working a while
ago and showed it in a rush but I think some key points can be made
out of this excerpt.

So let me summarize the workaround method:
Spaces of the piano staff have a correlation with the natural notes
but the equivalent notation of natural notes is ONLY with black notes
on any of those seven spaces.

Black notes ONLY will be in any of the seven spaces, never on a line.

Red notes are an equivalent indication of sharpen notes; a red note ON
A LINE represents the natural of the space below sharpened.

A red note on a space above a staff line, represents the natural of
the space below double sharpened.

A red note on a space above an adjacent space (e.g. on F,C) represents
the natural of the space below sharpened ( E#, B#); if necessary the
indication of double sharps for those notes (E,B) an additional
resource is used.

The same applies for blue notes as an equivalent indication of flatten
notes accordingly.

There are only seven note names, as colored notes (no black) have the
name of the natural they represent.

There is no need of additional accidental sings, and key signatures
may have other informative uses e.g. like the one in the example.

The method is consistent and flawless, given that this is only an
equivalent notation resource to represent naturals and accidentals;
the same DN and qualification of intervals can be determined without
charts, key signatures or accidental signs.

I should had shown only figs. 1 & 2 without k-signatures, which are
the one compatible, now let's forget about figs. 3 & 4, signatures and
everything else, which causes confusion and distraction (sorry), let's
better go point by point,

which now is diatonic numbers and chromatic notations, what do you or
anybody else think?


B.R.
Enrique.

[Keislar, Doug]

Hi Enrique,

Thanks for the explanation that red and blue notes can also occur on spaces.

So, going back to my question about the interval A to B#, in your system the A is a black note on the space for A (the space between the lines for G# and A#), and the B# is a red note in the space for C. Correct? Then, in terms of "diatonic counting," it still looks like a third (A to C) rather than a second, and you have to do a mental calculation looking at the red note to realize it's an augmented second. In traditional notation, you see immediately that it's some kind of second, but you have to do a mental calculation to realize it's an augmented second. In a chromatic notation, you see immediately that it's three semitones (or one-and-a-half whole tones), and you have to look at some supplementary accidental symbol (or coloring), if supplied by the notation system, to see that it's an augmented second rather than a minor third, etc.

It still seems to me that "diatonic counting" -- in other words, seeing that it's some form of second -- is most immediate with traditional notation, or with some similar alternative notation that has 7 degrees per octave. I don't think it's as immediate with either a piano-tablature notation (which has 12 degrees per octave) or with any other kind of chromatic notation. Note that in traditional notation the diatonic counting is immediate, no matter what the key signature is.

However, in practice, it's probably more useful to immediately see the size of the interval (e.g., in semitones) and only later concern yourself with whether it's a minor third or an augmented second. This is certainly true for many instruments, maybe not for vocalists.

I think we need to be careful to distinguish between "true" (i.e., 7-degree) diatonic notations and piano-tablature notations. Although the latter clearly show one diatonic scale (i.e., C major), they aren't really diatonic notations per se, in terms of the staff, because there are 12 degrees in terms of vertical position. You could say they're diatonic in terms of the coloring, but again, this is true only for C major. I would say that the piano-tablature notations are in fact chromatic notations of a certain sort. They emphasize the C major scale, but they make it more difficult to calculate intervals than in chromatic systems where the lines are regularly spaced (and/or where the notehead coloring has a regularly alternating pattern). Their main advantage is the correlation with the traditional piano keyboard and (to a lesser extent) some correlation with traditional pitch nomenclature. For someone who wants to learn to play piano music, reading from sheet music and never improvising or transposing or composing, they make a lot of sense.

On the other hand, for someone who wants to grasp the intervallic structure of music (necessary for composing, improvising, and transposing), the chromatic systems with a regularly alternating pattern (usually of lines and/or notehead coloring) may be better. (Express Stave has this feature in terms of notehead shape rather than color.)

Doug

________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Nextstep Musical System [mtall...@gmail.com]

Sent: Tuesday, May 29, 2012 9:55 PM

To: musicn...@googlegroups.com
Subject: Re: [MNP] Interval Specificity Table

Hi Dough, thanks for your comments, in previous posts I had already

B.R.
Enrique.

--

[Nextstep Musical System]

On Wed, May 30, 2012 at 1:48 AM, Keislar, Doug <do...@musclefish.com> wrote:
> Hi Enrique,
>
> Thanks for the explanation that red and blue notes can also occur on spaces.
>

> So, going back to my question about the interval A to B#, in your system....


Doug, I think we have to go a step back to the name of the notes, I
maintain that for a chromatic notation to use the nomenclature of the
conventional system requires some workaround at least to:
(1) use only seven note names
(2) determine the diatonic numbers
(3) qualify the intervals

Then when it comes to conventional nomenclature we have to use the
conventional concepts of natural notes and accidentals; the spaces
correlate with the naturals (notes/names), however:
Only black notes are naturals.
Colored notes are always sharpened or flatten notes.

Black notes are always on spaces and have the space name.
Colored notes may be on lines or spaces but use the name of the
corresponding natural, which is what I explained in the previous post.

Then when we see a note colored in red occupying the C space we name
it B# not C, however we play the same note as if it were in black.

Coloring the notes is just an alternative way of representing flats or
sharps, then we have the same flexibility of the CS of naming the same
note in different ways.

Diatonic numbering never counts the lines, or space of the note that
we are determining the DN if the note is colored, but only count the
space of its corresponding natural, which in the case of A-B# are only
two spaces (A and B), maintain the workaround is consistent and
flawless.



Enrique.

[Joseph Austin]

Doug, Enrique,

If you want a notation that exposes both pitches and intervals, I'd like to put in another plug for my StaffTonnetz notation,
especially when used as a shape-note notation (identify the twelve symbols with scale degrees rather than absolute pitches).

StaffTonnetz uses a 3x4 color/shape combination of noteheads, but as factors, not as a hierarchy as Enrique's Reference Heads.
Thus in ST, minor thirds have the same color and major thirds have the same shape.

Doug argues that TN relates the notes to the diatonic scale.

Strictly speaking, this is only true for the key of C.
In other keys, TN also uses the accidentals to transpose the notes of that diatonic scale to the notes of the C-scale; in fact, this usage takes precedence over the interval-modification role. So, for example, in the key of Eb, a fa-sharp becomes A natural (explicit), as there's no other way to notate A-flat sharp! The confusion is especially evident when shape-note noteheads are used--fa sharp would be notated as the shape for "fa" on the line/space for "Ab" (implied flat by the key signature), but with an explicit natural sign (to "sharpen" the implied flat), which then looks like it should read "fa natural" but in fact it is only "A natural" (as a keyboard note) but "fa sharp" as a scale degree.

In that context, I'm not sure I understand the oolors in Enrique's Fig 3 & 4.
At first I thought the difference between 1+2 and 3+4 was that 1+2 colors relate to the piano keys but 3+4 colors relate to the diatonic scale.
If in fact we were to use colors indicate "sharp" and "flat" diatonic notes, then Bb Eb and Ab traces would be black, (but with the heads positioned on lines if a staff is used). IF the scale tones are raised ("natural" to "sharp" or "flat" to "natural"), then and only then the traces would be red. E.g., the A natural in the first chord at the beginning of measure 3, but NOT the Eb, which would be black. So in Enrique's figs 3,4, I would color the E(b) F# An C: black, red, red, black.

StaffTonnetz, of course, does not make the sharp/flat/natural explicit, but it does highlight the intervalic relationship,
so Eb F# An C (do re# fa# la) would have color/orientation: gray-up, gray-left, gray-down, gray-right; four noteheads of the same color but different shapes, indicating three minor third intervals (or inversions thereof), that is, a diminished seventh chord.
(That's not even so clear from the TN, since the Eb-F# are on adjacent line-space, not space-space as you would expect for a third, which it is, along with the other two. Or, you could write the chord as E(b), Gb, Bbb, Dbb to explicitly notate the minor thirds and diminished fifths! )

So which is more important, the scale degrees or the intervals? Do the scales generate the intervals or do the intevals generate the scales? I've been operating from the premise that the intervals (specifically, major and minor thirds) genterate the scales (and chords), so it's more useful to identify the major and minor thirds than to distinguish a diminished fifth from an augmented fourth.

On the other hand, if we were to add appropriately colored note traces to StaffTonnetz noteheads used as shape-notes, we could have both! And overlay that on a 7-5 staff, and you've got "everything".

Joe Austin
DrTechDaddy.com

[Nextstep Musical System]

On Wed, May 30, 2012 at 5:05 PM, Joseph Austin <drtec...@gmail.com> wrote:
> Doug, Enrique,

>
> In that context, I'm not sure I understand the oolors in Enrique's Fig 3 & 4.

Joe, let's forget about fig.3 & 4 for now, it was my mistake mixing
them with 1 & 2, I could explain latter why I am using them now
instead of 1 & 2 but I would like to keep the focus on the
compatibility of chromatic staff with TN, which I think has been a
weak point of chromatic staff notation for a long time and it has not
been paid due attention.

I think it deserves a more generic analysis, before pushing individual
preferences or arguing:
whether the NMS workaround for compatibility is flawless or not
which is better, if tablatures, diatonic or chromatic notations
which is better, if cipher (symbolic), staff (positional), graphic,
StaffTonnetz or reference head notation as techniques for notating
music.

First things first

Regardless of preferences there should be a consensus (understanding)
that an alternative to the conventional notation is not necessarily an
alternative to the conventional system, the conventional notation is a
component of the CS, which is a complete system, and a minimum
requirement for an alternative is being an equivalent to a complete
system not just to notation, otherwise we would be going backwards.

Can we all agree on that?

Enrique.

[Doug Keislar]

Hi Enrique,

Yes, I agree with your point. Maybe not quite as strongly. But I agree
that an alternative system should consider not only notation, but also
nomenclature and instrument design. It's much better to get the
advantages of correlation between all three of these aspects than to
consider just one alone. Your NoteTrace and I assume NMS are great
examples (well, of correlation between notation and nomenclature at
least -- I'm not sure about instrument design).

I would also say (as others have said recently) that timing information
should be thoroughly considered. Many of the systems on the MNP site
just adopt traditional rhythmic notation, because they focus on pitch.

Doug

On 5/31/2012 6:19 AM, Nextstep Musical System wrote:
> On Wed, May 30, 2012 at 5:05 PM, Joseph Austin<drtec...@gmail.com> wrote:
>> Doug, Enrique,
>>

>> In that context, I'm not sure I understand the oolors in Enrique's Fig 3& 4.
>
> Joe, let's forget about fig.3& 4 for now, it was my mistake mixing
> them with 1& 2, I could explain latter why I am using them now
> instead of 1& 2 but I would like to keep the focus on the

[Joseph Austin]

Enrique,

I guess my issue is that I'm struggling to understand exactly what "the system" is.
Traditional notation and "theory" keeps getting in the way!

If it's really all about scales and chords made from 4:5:6 frequency ratios ("just" major/minor "thirds"),
or if it's really about scales and chords made from powers of the twelfth root of two,
then shouldn't the harmony theory and notation reflect that?

My approach would not be to try to preserve "compatibility" with all the idiosyncrasies of TN in an effort to preserve the "system",
but rather to try to identify the essential features of the system in the state to which it has presently evolved,
and come up with a new "clean" and consistent explanation and notation to replace the hodge-podge accretion of features it has accumulated during it's evolution.

I assume everyone is proceeding in good faith to expose what they consider essential and eliminate what they consider counter-productive to understanding and performing music. I use "my" notations for my own learning and they work for me; I assume others are having success with their performance and their students.
Actually, "my" notation has evolved from other notations I've seen on this forum and elsewhere, and I'm happy to advocate for what I consider may be original insights,
such as the adaptation of Euler's Tonnetz to a 12-shape notehead system, which also owes a lot to Roy Pertchik and yourself, and to John Keller and Peter Jackson, among others.

The intent of my earlier post was to help us separate the "system" from accidentals.
I think too much effort preserving accidentals, especially the ones in the key signature, is misplaced,
when chromatic systems such as your twelve-symbol noteheads avoid the need for accidentals for the key signature,
and when there may be more complete and consistent ways to distinguish major/minor/augmented/diminished intervals.

Joe Austin
DrTechDaddy.com

[Nextstep Musical System]

On Thu, May 31, 2012 at 1:48 PM, Doug Keislar <do...@musclefish.com> wrote:
> Hi Enrique,

>  Your NoteTrace and I assume NMS are great examples (well, of
> correlation between notation and nomenclature at least -- I'm not sure about
> instrument design).
>

If what you mean is some visual correlation of notation and
instruments as a sort of orientation, yes it does with both the
mapping backgrounds and the advantage that reference heads have over
staffs that they can be printed on instruments with keys or strings.

Enrique.

[Nextstep Musical System]

On Thu, May 31, 2012 at 2:05 PM, Joseph Austin <drtec...@gmail.com> wrote:
> Enrique,
>
> I guess my issue is that I'm struggling to understand exactly what "the system" is.
> Traditional notation and "theory" keeps getting in the way!
>

Maybe as much as I struggle with terminology, let's say "there is
music and there is a theoretical support to it", like "there is a
language and there is the theoretical support we create around it".
Previously I used the term 'interface with music' but music theory or
music education may cover the idea as more in common use terms.

I think what I mean by "the system" is what makes a difference between
a passive listener and an active one, is like everything else but the
music itself, music is the language.

I have taken this paragraph from the latest overview doc I have been
writing, intended as the presentation as a system.

"Even though some elements of music education such as notation,
nomenclature, terminology, musical mental processes or operations,
methods of analysis, and orientation with musical instruments note's
layout are interconnected, an attempt will be made for organizing this
paper into Notation, Control and Analysis of music."

Maybe, The system == Notation + Control + Analysis (of music)

Enrique.

[Nextstep Musical System]

P.S.

Then what we need ( and what the NMS is) is a system for notating,
controlling and analyzing music, I hope soon could present the whole
doc.

Enrique.

[Joseph Austin]

Enrique,

It may be an arbitrary choice, but I think we need to pin "system" down a little more.

Seems to me, concerning pitch, we have two systems:

1. the equal-tempered 12-tone chromatic scale, to which most instruments are tuned,
which is the system we use to "control",
2. the seven-pitch diatonic scale and corresponding chords, generated from a sequence of the intervals we call major and minor thirds, theoretically consisting of pitches (frequencies) in a 4:5 or 5:6 ratio, respectively,
and in practice consisting of intervals of 4 or 3 semitones of the chromatic equal-tempered scale,
which is the system we use to "analyze".

The notational system, then, needs to accomodate both of the above.
So, we have the traditional notation system of the 7-positon staff, corresponding to the seven positon diatonic scale,
and the system of sharps and flats designed to add the additional tones of the chromatic scale to the staff.

There are two uses for the accidentals:
1. to indicate that certain staff positions should be interpreted as "black" notes instead of "white" notes,
in order to use the staff for keys other than C major.
2. to indicate non-scalar notes in any key, e.g. for minor keys, modulating into a foreign key, or just for chromatic passing tones, and also, for changing one chord interval to another interval (major, minor, augmented, or diminished).

The use of the same sharp and flat symbols for both 1 and 2 leads to conflicts, such raising the seventh in C minor
((B flat) sharp) or diminishing the fifth in E-flat major ((B flat) flat), so we add natural, double-flat, and double-sharp.

Considering analysis, I think the primary tasks are identifying the notes of a scale (or which ones are NOT in the scale) and identifying the intervals of chords. Since the staff does not distinguish between "major" and "minor" intervals, one must simply memorize which intervals of the scale or of a chord are major and which are minor. And for keys other than C major/A relative minor, one must memorize which sharps or flats are part of the key signature and which represent chromatic alterations from the scale,

Now if we switch from a 7-position staff to a 12-position staff, or corresponding system of 12 noteheads, is there still any need for sharps and flats?
For use (1), identifying which "black" notes to use, the 12-position staff (or 12 symbol notehead system) solves this problem without recourse to accidentals--each distinct note had a distinct staff position or notehead symbol.

For use (2), for analysis purposes we might still want to know if a given non-scale tone represents raising a lower scale tone or lowering a higher scale tone. But why would it matter? Perhaps the compooser is modulating into a different key, or is alterning a chord, and we would like to "recognize" the new key or chord. That recognition might by complicated by replacing the note in the "new" scale or chord with an enharmonic, thus confusing it with a different scale or chord.

But I aargue that, using just 12 notehead symbols based on the Tonnetz, it is possible to both identify the scale degrees (as well as TN does) and to idenitfy the chord intervals--major and minor thirds--that make up most chords in conventional music.

But what about "non-conventional" music (whose scales and chords might not be derived from major and minor thirds?
It's not clear to me, without a more detailed exposition of the "system" of such music, that the traditional sharps and flats are any more relevant to understanding or analysis than the 12-semitone scale.

So I consider the Tonnetz-based notehead system relevant to a discussion of the "Interval Specificity Table" in that it relates directly to the intervals that are the basis of the most common chords and the generators of the most common scales.
Furthermore, if we understand "fifths" as a combination of two "thirds", we can eliminate the need for "perfect", "augmented" and "diminished" fifths as a separate category of intervals. Why maintain terminiology for five kinds of intervals when all the necessary relationships can be explained in terms of combinations of two kinds? [minor+minor= diminished; major+major=augmented; and both major+minor and minor+major (thirds) give "perfect" fifths. Typically, understanding is improved when the number of independent concepts is reduced.

So if I grant you that the total system must include analysis as well as notation,
I argue you must concede that the system which offers the better "analysis" is to be preferred,
notational values otherwise being similiar.

You see, in my view, the choice between a notehead system such as your reference heads with hierarchic cycles of 3 within 4 (A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3) and a system such as StaffTonnetz with independent 4 x 3 cycles (A1 B2 C3 D1 A2 B3 C1 D2 A3 B1 C2 D3) is not merely one of preference (e.g., I use triangles while you use rectangles and circles),
but is solidly rooted in the mathematical theory of the system. The Tonnetz cycles relate directly to major and minor thirds, which in turn relate directly to harmonic theory of chords. Of course, your bottom, middle, top trace positions also relate to minor thirds. But what, on the other hand, is the theoretical relevance of your grouping of tones into white/dark and square/circle? Furthermore, it is not even isomorphic with respect to key change. One key will start with 2 white rectangles, another with a combination of rectangle and circle; one with two notes the same color, another with different colors, etc.

Similarly, any method used to relate a chromatic system to the diatonic system should eliminate the ambiguity of the traditional accidentals system which does not differentiate between (1) relating scale tones to instrument tones and (2) relating non-scale tones to an alternative scale or chord pattern. It's not just an issue of "I like red but you like blue"; it's whether we even include the key-signature flats at all, considering they are not only unnecessary but also confuse the meaning of the accidentals that really represent the non-scale tones!

I don't think I'm just pushing a preference; I arguing for a "system".

Joe Austin
DrTechDaddy.com

[Nextstep Musical System]

On Mon, Jun 4, 2012 at 5:38 PM, Joseph Austin <drtec...@gmail.com> wrote:
> Enrique,
>
> It may be an arbitrary choice, but I think we need to pin "system" down a little more.
>

It is not so important what everyone considers a complete system, for
this discussion we may consider anything that is possible in the
conventional system other than a transcription; my perception is that
chromatic staff alternatives to the conventional notation improve
readability and simplify notation, but has not been concerned with
demonstrating an overall improvement or an overall simpler system.

>
> I don't think I'm just pushing a preference; I arguing for a "system".
>

I understand comparisons are inevitable and necessary but If anyone is
going to compare it should be apples to apples.


B.R.
Enrique.

[Joseph Austin]

On Jun 7, 2012, at 3:40 PM, Nextstep Musical System wrote:

> ... my perception is that

> chromatic staff alternatives to the conventional notation improve
> readability and simplify notation, but has not been concerned with
> demonstrating an overall improvement or an overall simpler system.

Enrique,

What do you mean by "overall improvement" or "overall simpler"?
Do you mean, "does the notation expose the harmonic or theoretical structure or purpose of the music?"
Or, "Does the notation express the "musical idea" in a more direct way?"

I was thinking of a analogy.

Music is an aural "language"; it's notation is a written language.

Similarly, we have natural oral languages with written counterparts.
Some languages, like English, have a written structure (spelling and grammar) that is notoriously irregular and difficult to master,
while some have a nearly phonetic spelling or very regular grammar,
while still others use ideographic symbols that may give scant clue to pronunciation.

Traditional music notation is like English spelling--derived from a hodge-podge of sources and evolutions that has not quite kept pace with the evolution of the performance medium itself.
Chromatic notation is like a "phonetic alphabet and spelling"--greatly simplifies the transition between the oral and written forms, but in itself does nothing to simplify the grammar or assist in the transfer of meaning.

So are you suggesting we need an "ideographic" notation that gets to the heart of the "meaning" itself, independent of just identifying the sounds?
So how might you notate notions like harmonic or rhythmic "tension and resolution" or whatever the components of "musical ideas" happen to be?
What features of NMS do you believe illustrate the "overall improvement and simplification" you speak of?
For example, how do you see your chromatic noteheads as being essentially different from a chromatic staff?

Personally, I think notations like the moveable-do shape-note system, which exposes the pitches in relation to the scale,
and the Staff-Tonnetz notehead system, which exposes the major and minor third intervals of chords and melodies,
do in fact concern themselves with improving the "overall system" in it's ability to express more of the underlying structure of the music itself beyond just notating the pitch sequence.

Of course, more could be done. We might try to encode the intervals of just intonation, or the functional harmonies of Riemann or Hoffman-Engl, etc. in an attempt to capture the "essence" of the tension/resolution that perhaps constitutes the "meaning" of the music itself. I have searched for some alternative for expressing rhythm, which is a component especially of jazz and Latin music that I think is virtually absent from TN and which doesn't seem to be seriously addressed by most other proposals on this forum. And I've also advocated for something as simple as printing music in "verses and stanzas" like poetry, in order to expose the form of the composition, instead of compressed to get the maximum number of notes on a line and page. (I think this is important especially for students, who should understand that music has a structure, and is not just a string of notes.)

As for "simplification", I and others have experimented with notations that could be created with a word processor or spreadsheet instead of requiring laborious hand-drawing or complex and expensive notation software. (After struggling with Finale, I developed sympathy for the ancient authors who had to chisel their compositions in stone!).

Joe Austin
DrTechDaddy.com
"Music is poetry; why print it like prose?"

[Ivaylo Naydenov]

What is right should be the most simple solution. And accurate of course. If music is some kind of a sound language then its grammar and alphabet should strictly emphasize the tones, intervals (scales, melody) and chords (harmony).

Todays way of western and european music language is: 12 tones with some usable 20 intervals. Contrary to that it has French phonetics, English grammar and German writing structure?! Joking here... but you got the idea. The solution is very simple once you realize that piano keyboard design is old, awful and some kind of a special case. Learn to fix that and the rest is obvious.

:D

[Joseph Austin]

Naydenov:

Yes, but several people have offered "Janko" instruments but people didn't buy them!

There are over 25,000 pieces published in Klavarskribo 7-5 staff notation, but only 800 people belong to the organization (according to Wikipedia).

There are several excellent proposals on this forum, but none of them seem to have much of a following.

So the AVAILABILITY of the "fix"  isn't the full answer.

Is that because we haven't really found the "fix"?

People, especially young people, seem to love to play music, 

and some are willing to master the most difficult and unintuitive instruments to do so.

But many get discouraged and quit.

I keep thinking that it's not enough to have an instrument, or a notation; 

we need a pedagogy!  We need a system that can be used to teach children, and that older students can use on their own,

that will give them a sense of success and progress so they stay with it.

I think maybe the problem is we teach "reading" and "writing" before we teach "listening" and "speaking."

What good does it do to have a "language" if you  can't comprehend what other people are saying, and don't have anything to say  yourself?

Of all the notational systems I've seen described, only the Circle of Fifths and the Tonnetz have much to say about creating and resolving harmonic tension.

And I haven't found anything yet that discusses rhythmic tension/release at all.

Any ideas?

Joe Austin

[Ivaylo Naydenov]

Hi Austin,
I couldn't agree more to the need of pedagogy system. In fact the suggested "fixes" are not one nor two. There are many (just see the Forum).
My point is that the Conventional Notation System is somehow derived from the poor design of the Conventional Piano Keyboard. Mentioning that it is difficult to learn (not impossible though) and there are better solutions primarily in the layout (the shape of the keys are still not yet good enough; see Daskin, Chromatone, Axis-64, Bilinear). Yes, the layout is Janko's idea and it is very simple and proven to work.

The problem is that there are only a few of such keyboards around the world and even less children that want to learn to play it. But they still want to play now, in band, in school thus taking the conventional choice.

Me personally, I do have two keyboard designs using Janko's layout. Both are usable. I do have a Notation System too (Plain Notation System; see the MNP Wiki page). At the moment I apply for a grant and a patent prior to the grant to make one (it's the better design I think) of my keyboards as a MIDI controller. Time will tell...

P.S. I still remember the day when I was 10-11 with great expectations about learning to play music. I saw the piano. I saw it has a poor keyboard design. I choose the drums, later - the guitar. Still do not play the synth although I have one here right next to me. :)

[Nextstep Musical System]

On Fri, Jun 8, 2012 at 2:58 PM, Joseph Austin <drtec...@gmail.com> wrote:
>
>
> Enrique,
>
> What do you mean by "overall improvement" or "overall simpler"?

Joe, notice I said 'chromatic staff alternatives' and not 'chromatic
notations', trying to keep Paul thread and because chromatic staff
variants have a very long history of proposals.

By overall I mean the different 'activities' not just playing
instruments or naming the 12 notes, Have you read about comparing also
the process of transcribing without the help of musical instruments?
or sight reading, or how to name intervals and chords, or comparing
musical mental process (advantages) of a 12 vs. 7 note-name systems or
analysis of music.

I have resisted the term 'music theory' usually saying 'theoretical
support to music' because for me theories have a more specific meaning
and the core of the NMS as a complete functional system does not
include theories, I would better say 'academic support to music' which
includes that core and also theories.

Now back to our point instead of 'complete system' we could say, Have
chromatic staff proposals been presented as a better 'academic support
to music' or a better alternative to music education?

B.R.
Enrique.

[Peter Jackson]

Thank you Joseph for mentioning Klavarskribo. This notation is however much more firmly established than you say. It is true that the Dutch organization  (see www.klavarvereniging.nl) publishes a 25page glossy bimonthly magazine for its 900 members but there are many other players besides those in the Netherlands. For example our branch of the Klavar Music Foundation of GB, www.klavar.com.cn  told me this morning that they have 170 taking   regular lessons in Beijing   and since it was set-up in August 2011 has introduced klavar to 1,600 people.   The UK branch has since its inception  in  around 1945  taught  over 6,000 students world-wide. Our branch in Kunming has 70 current students; I have taught around 200 in Hong Kong while over 20,000 have visited the website (and hundreds downloaded the free lessons ) of the KMF of GB as you can see from www.klavarmusic.org  The site run by Bridget Jupp  also has taught numerous students see www.klavarmusic.com  I imagine. There are several other sites www.klavar.co.uk for example, which offer lessons besides the lessons in French and German and Dutch offered  by the  parent body www.klavarskribo.nl 

--
All the Best
Peter
(852)2982-1177
Mob 6771-2743

[Ivaylo Naydenov]

It may look odd but when I was 17 and studying Music on my own (guitar, drums, alternative piano keyboards also) I came up with the idea of Klavarskribo. I left it because it is connected to the Conventional Piano Keyboard that I consider poor in its design and functionality. In fact the Notation (I called it Piano Tabulature) was in my first edition of the Treatise On Pentatonics.

It is very strange how so many people come up with the same idea at different locations of the Earth. That is promising!

[Joseph Austin]

Peter,

As you may recall, I have experimented with a font that could allow Klavarskribo-style music to be created in a text processor or word processor such as Notepad or MS Word,

and even be incorporated as "text" into webpages. 

I also have a "12-shape-note" version of the font that I call StaffTonnetz, which has the additional feature of highlighting major and minor third intervals.

For details, see my website DrTechDaddy.com.

My feeling is that, if we could make it easy and inexpensive for teachers and students to create their own scores, and convert to/from a more generic representation such as MusicXML,

more teachers and students might be willing to use it.

Joe Austin

DrTechDaddy.com

[Joseph Austin]

Enrique,

I guess I agree, then, just switching from a 7-position (diatonic) staff with accidentals to a 12-position (chromatic) staff without accidentals doesn't help much with the analysis of diatonic music! It may, however, greatly assist in performance, sight-reading, etc. for instruments that in fact have a chromatic "keyboard" (or whatever system of frets or values it uses).

I personally have found it extremely helpful to learn to think in terms of scale degrees--do re mi ("musical" position) instead of key names--C D E ("instrument" position).
So in the absence of "shape-note" noteheads, I use the diatonic staff and signature and mentally "translate" the staff position to the scale degree of the key. So instead of thinking "C D E ..." as I play or sing, I think "do re mi..." and for chords, "I vi ii V7..." Having memorized the Circle of Fifths and the scale degrees that make up the principal intervals and chords, I can now recognize what I'm singing/playing as melodic and harmonic progressions, not just note sequences. But that's a lot of mental translation going on; it would save my brain if it could be "pre-translated" into suitable notation! Which is why I like moveable-do shape notes, especially shape that exhibit a similarity corresponding to major and minor thirds!

For actual performance, I find it's also useful for the notation to include fingering, and other notations. Student music often has this preprinted; later. we add it ourselves!
I think we could learn a lot by studying the notation that we actually USE to learn or play or study from, vs. the notation that comes directly from the publisher.
"Real" notation has a lot added to it, that our notation proposals are trying to regularize and integrate.
My scores will typically have added one or more of:

* Roman chord symbols to replace the letter-named chords;
* d r m f s l t (diatonic scale degrees) to supplement the voice line
* additional "bar" lines to mark phrase breaks, when phrase breaks don't match line breaks (which is almost always)
* count numbers 1 e & a 2 e & a, etc. to translate the notated durations into a performable beat and rhythm.
* finger numbers, especially changing the finger for a note or note for a finger, or cues for "thumb under" or repositioning.
* advisory accidentals

If I (and other students) find these sorts of things essential to understand and perform the music,
why are they not included in the "standard" notation?

Joe Austin
DrTechDady.com