System with diatonic staff and 6-6 note head pattern (DS66)

[Paul]

Hi all,

After having heard a number of times from people I've shown Clairnote
"...but music is based on diatonic scales..." I have been playing around
with a system for those who see things that way (although I don't share
this view). See attached, starting with the 'demo' file.

This system combines a diatonic staff with a 6-6
solid/hollow note head pattern. The note head pattern helps musicians
identify intervals and read music relatively (by interval). It also
reminds them when notes are sharp or flat due to the key
signature (or accidental signs). The staff's line pattern 'cycles'
every
two octaves. The line pattern is similar to
those of the traditional treble and bass clefs, so the staff can be used
for the bass and treble pitch ranges. (The lower part of the staff
aligns with the treble clef staff and the upper part aligns with the
bass clef staff.) This alignment also makes it easier to learn both
systems.
Traditional key signatures and accidentals are used. Traditional rhythm
symbols are used except half notes are indicated by double stems.

This system is similar to Classic Nydana (http://nydana.se/classic.html)
except it prioritizes consistency of interval appearance over
consistency in the appearance of individual notes. Thus it maintains a
consistent line-space alternation and cycles every two octaves rather
than every octave. (Classic Nydana has two adjacent space notes -- A
and B -- to have a diatonic staff that cycles every octave.)

Some advantages of the diatonic staff are vertical compactness / density
of information. Assuming you have already memorized the key signatures
(ahem...) the "visual field" of the staff represents only the notes in
the key, etc. The system also offers a lot of continuity with the
traditional system, (if that's your thing) while addressing some of its
shortcomings (reading by intervals, remembering key signatures, multiple
clefs for piano, etc.).

One interesting feature is that (assuming no accidental signs are in
effect) intervals are easy to distinguish both at the level of "thirds,
seconds, etc." and at the level of "major third, minor third, major
second, minor second, etc." Not sure how much that matters since the
former level is easily derived from the latter in chromatic staff systems.

I still prefer Clairnote for all the usual reasons but it's fun to try
and design systems under different constraints / with different goals.
And it seems like this approach / combination of features should be part
of the conversation. Eventually I'd like to add it to the MNP wiki.

Cheers,
-Paul

[gguitarwilly]

Hi Paul,

I too prefer Clairnote..

There's a few things that bother me about this new notation: just as in TN, notes of one colour in one position can be two different pitches, depending on accidental.

This is even worse if one is accustomed to Clairnote where this is not the case.

Then there's no octave consistency. And finally, the whole tone rows hurt my eyes! They consist of seconds and thirds visually...

I'm afraid Paul, your Magnum Opus has already been created. Let's focus on getting it out into the world!

Willem

Op zondag 12 maart 2017 23:10:00 UTC+1 schreef Paul Morris:

[Doug Keislar]

Hi Paul,

That's interesting. It's always good to experiment with different
principles, if only to show why some solutions don't work as well.

I don't see any point in abandoning the octave cycling. You're doing
that simply so lines and spaces can always alternate? For that minor
benefit (if it even is one), you've doubled the number of lines and
spaces a student whose note names a student has to learn to recognize.
Let me know if I'm missing something, but it seems like DS66 throws the
baby out with the bathwater.

For a diatonic staff, I prefer the Nydana staff. It seems much easier
to learn.

Doug

[John Keller]

Hi Paul,

My feeling is you should have just used a six line staff. Having the gap for a D line is more likely to cause mixup of C and D.

Adding a line above treble and below bass to make them equivalent was something i thought of when I was about 12!

Reading the music in 66DS seems easy enough, but writing it might be harder.

Cheers,
John

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[John Keller]

Also the staff looks like Klavar with 3 and 2 lines.

Jk

[Paul]

Hi all,

Thanks for your thoughts! For the most part I can't really disagree
with anything you said...

On 03/13/2017 04:19 PM, Doug Keislar wrote:
> I don't see any point in abandoning the octave cycling. You're doing
> that simply so lines and spaces can always alternate?

Well, I didn't want to completely recreate Classic Nydana. ;-)

Actually, the goal was consistency of interval appearance. For example,
in TN and DS66 thirds are always notes on adjacent lines or adjacent
spaces. In Classic Nydana the irregularity in the line pattern (A and B
both on spaces) disrupts this consistency. DS66 improves on TN since
you can tell the difference between (say) major and minor thirds from
the solid/hollow notehead pattern (as long as no accidentals are in play).

The gambit is that while you sacrifice some ease of learning at the
beginning, the consistency for intervals that you gain would be more
valuable in the long run. (?) (But then, for that, you'd be even better
off with a system like Clairnote...)

John, I considered a 6-line staff but all those lines hurt my eyes, and
I think it will be easier to learn the lines and spaces when there are
groups of two and three. But you're right C and D might get confused at
first until you learned the staff better.

Funny, it was in my early 20s, when I started to learn piano again, that
I realized adding a line to the treble and bass staves made them
equivalent. You were way ahead of me! Searching the internet to see if
anyone else had come up with that idea was how I discovered the MNMA
(now MNP).

One thought behind this approach is that often incremental changes have
more success in gaining adoption... so maybe an incremental step like
this system would have broader appeal? Probably not... but it's kind of
in the vein of throwing things at the wall to see what sticks...

At least, when someone says they don't like the chromatic staff
approach, I can point them at this system instead, although chances are
they probably won't like it either... since the hollow and solid notes
for pitch seem to also be a stumbling block for those used to TN...
(Maybe using colored notes would be the most incremental way to go?
Although I'm not keen on having the full system work in black and white...)

Anyway, rest assured this won't take my focus away from Clairnote...

Cheers,
-Paul

[Joseph Austin]

Paul,

I'm still waiting for someone to make the case for "diatonic" music.

Most arguments I've seen for "diatonic" notation stress the need for distinction between A-flat and G-sharp,
which is basically an appeal to just intonation theory.
I've explored a couple of interpretations of "diatonic" scales based on:
(a) spiral of fifths
(b) the tonnetz, which is basically interlaced spirals of fifths (2:3) offset by major/minor thirds (4:5:6).

The problems of just diatonic tuning are well-known.
And if it isn't "just", then is it really "diatonic", or is it only an archaic way of representing ET?

I cannot accept a notation as being "diatonic" that has enharmonics.
The traditional sharps and flats will be fine for just-fifth-spiral music [scales / pentatonic / jazz?],
but if you want to include just thirds [chords / classical harmony], you will need more accidentals than the customary sharps and flats.

To comprise a major key with it's dominant major and relative, tonic, and melodic minors in just thirds,
from my tonnetz calculation,
requires about 13 or 14 different pitches from 3 or 4 different fifth-spirals, including [for C major] both an A-flat and a G-sharp,
along with a couple different tunings of D and A.

If you were to propose a theory of "barbershop" or "just" or "jazz" harmony and corresponding notation,
I would be happy to study it.

But I'm questioning whether this proposed "diatonic" notation actually matches any actual "diatonic" musical theory.

Don't we need to know what problem we are trying to solve before proposing a solution?

For my purposes, solfedge shape-notes (or Curwen hand-signs) are all the 'diatonic" notation I need;
(they can adapted to any staff or no staff),
and if we need to do modulation among keys, then a "chromatic solfedge" notation is easy to construct;
I've offered my "chroma-tonnetz" chromatic shape-notes as an example.

Joe Austin

[Paul]

Hi Joe,

Yeah, the arguments for diatonic notation that I'm addressing (that I
don't really agree with) are more those that argue that diatonic scales
(however they are derived or defined in terms of precise pitch
intonation) are the default set of notes for western music, ergo the
notation system should have a diatonic staff, not a chromatic one. So
more an argument in terms of pragmatics than of underlying theory,
taking diatonic scales as a given and not attempting to derive or
justify them from first principles...

Cheers,
-Paul

[Joseph Austin]

Paul,

But as i've argued before, from my (admittedly limited) experience,
the practical value of the "diatonic scale" is knowing the individual (relative) pitches:
do re me fa sol la ti.

Learned that way, the whole-step/half-step intervals are largely hidden, but never confused.
Given any two syllables, I can learn to sing the interval independently of counting "half-steps".
(And, if I sing in just intonation, independently of "knowing" the difference in size of the various "seconds" and "thirds" etc.)

But when the scale syllables are replaced by uniform note symbols,
the visual distinction among the seven pitches disappears.

I'd say whatever advantage your suggestion offers comes from the alternation of colors,
distinguishing odd and even "semitone" intervals. But doesn't that presuppose the transition from diatonic to ET?
There are no "semitones" is a pure diatonic scale, or rather, there are several different varieties of semitones.

Clairnote's two-color scheme is quite useful for ET on a Janko,
where the whole/half-step distinction has uniform physical significance.
But wouldn't a seven-shape shape-note scheme be even much more effective for "diatonic" music?

Shape notes were quite popular in earlier centuries, when people actually sang hymns in 4-part harmony.
I'd speculate they fell out of favor as singing in harmony fell out of favor,
and the pitch-positional notation useful for instrumentalists became dominant over the "moveable-do" notation favored by singers.
As you know, I have been proposing and using a moveable-do shape note system superimposed on a fixed-pitch-position staff,
to simultaneously satisfy the "diatonic" singers and the "ET" instrumentalists.
And, I would argue, thinking in solfedge would greatly facilitate playing "by ear", and perhaps even encourage composition.

Joe Austin

[gguitarwilly]

Hi Joe,

The initial goal of the Music Notation Project was to find a notation that serves a number of purposes, which might be described in short as 'a notation that can do everything TN does, but is better'. 

It all depends what you want out of a notation if it is better or even optimal for the use you make of it.

I find the 6-6 colour distinction of Clairnote useful, not only on Janko. When I play guitar, the alternating colours tell me if I should skip one, two, three or four frets in a split second. The colours also help with singing the right intervals.

The fact that intervals are always represented in a consequent way is only achieved by using twelve note positions. I think the distinction between diatonic and ET notation (I prefer to call it chromatic) is a bit artificial. Very often in tonal music 'inbetween-dominants' occur, and it ís useful to keep being able to see major thirds standing out in such cases too.

The problem with moveable do on a fixed grid is that depending on key, there are different note shapes in the same position, keeping one from firmly ingraining a combination of colour and shape with position to help remember note names.

But your system might actually be very useful specifically for singers, as it combines easy recognition of intervals with solfege.

Willem

Op vrijdag 17 maart 2017 15:35:09 UTC+1 schreef Joseph Austin:

[Joseph Austin]

Willem,

I'm just asking those who insist on notations that distinguish between G-sharp and A-flat 

to offer their theory of harmony that defines the difference.

I've suggested two theory options: Spiral of 2:3s (aka "fifths")  and Tonnetz, or "honeycomb of 4:5:6" (aka "thirds"),

both of which are based on just intonation.

I claim that the TN system of sharps and flats only accommodates the "spiral of fifths", 

it cannot accurately distinguish all the pitches of classical or "diatonic" harmony which is based on "thirds".

Since TN itself cannot "completely" distinguish all the pitches of the just Tonnetz,

it is disingenuous to criticize ET as an "incomplete" system.

Joe Austin

[gguitarwilly]

Hi Joe,

It seems there actually is a difference in pitch between G sharp and A flat, and that this difference is indeed based on just intonation.

A capella choirs and string ensembles, to name some examples, will be capable of actually producing these different pitches, and may rely on the note name/notation as a visual clue to what intonation to produce, although I suspect their ears will be a more important factor.

But there is a more prozaic reason for distinguishing between G# and Ab, as far as I know, and that has to do with convention in note naming. When naming the notes in the A major scale, the seventh note would be called G sharp simply because otherwise you'd have A flat followed by A, and it is a convention that note names occur only once in a given scale. 

Composers seem to have managed quite well using TN to express their ideas, so I would guess they were not thinking in terms of the spiral of fifths.

I can't see the idea that intonation should be dependent on how individual notes are written; my guess is that it is necessary to understand the harmonic function of notes in the overall structure. If one plays a piece in the key of C, there are no sharps and flats. So what clue would a musician have as to how to intonate the b note?

He/she would simply have to know it is the leading tone, and know that the intonation would have to be according to that function.

If I remember correctly, you've mentioned '12 TET theory' in previous posts. But is there such a thing, apart from atonal music theory?

12TET is simply a practical solution to 'a glitch in creation'( meaning that just intonation, alas, cannot be attained on an instrument with twelve tones per octave), it is merely a tuning facilitating the playing in different keys on a single musical instrument.

But the underlying music theory of western music, played by strings, orchestra, choir or a piano tuned to 12TET, is most often based on classic harmony theory.

Maybe I don't understand enough about classic harmony theory? Does TN and the note naming it uses do a poor job of expressing the basic principles of classic harmony theory?

Willem

Op dinsdag 21 maart 2017 02:45:24 UTC+1 schreef Joseph Austin:

[Joseph Austin]

Willem,

On Mar 24, 2017, at 4:37 AM, gguitarwilly <zwa...@gmail.com> wrote:

Maybe I don't understand enough about classic harmony theory? Does TN and the note naming it uses do a poor job of expressing the basic principles of classic harmony theory?

Since I'm in basic agreement with the rest of your post, let me comment on just this one question.

TN note naming, so far as I understand it, it based on the spiral of 2:3 ratios, and the seven-letter note naming scheme.  So after cycling from F C G D A E B you encounter a note between the F and G (an octave or two higher). What to call it?

it you are going "up" you call it F-sharp.  Then next time around, the note between F-sharp and G-sharp, we call F-double-sharp. [Why not G, you may ask?  Because it needs an "F" letter name to preserve the 7-letter sequence.]

Going the other way, "down", after B E A D G C F we encounter a note between B and A. So we call it B-flat;

next time around, we encounter the note between B-flat and A-flat, so we call it B-double-flat. Etc.

Ok, so this whole scheme is based on 2:3 ratios and 7 letter names.  Counting the 2:3 interval on the diatonic scale spans 5 notes, so the interval is called a "fifth", which makes "perfect" sense in diatonic reckoning. In ET, this ratio is approximately 7 half-steps.  It is possible to build a scale from five consecutive pitches in 2:3 ratio, with their octaves.

We call this the pentatonic scale.  But the scales built on G# and Ab are not the same frequencies, if you "do the math".

Now lets  proceed to classical harmony.  I've heard it arose in England.  They discovered the intervals of 4:5:6,

the major triad.  By reversing the intervals (5:6, 4:5) we get 10:12:15, or the minor triad.

On the diatonic scale, these intervals are 3 (diatonic) notes apart. But 4:5 and 5:6 are not the same sound. (On a piano,

they are either 3 or 4 ET notes apart.) So we have "major" and "minor" thirds.

What's more, you cannot get "thirds" or 4:5:6 from the pentatonic scale, because 5 is relatively prime to 4 and 6, i.e. to 2 and 3). No multiples of 2's and 3's will ever give a multiple of 5, and vice versa.

So consider the Tonic triad on C.  The unison and fifth are the C and G of the pentatonic scale.

But what about the middle note?  It is "close" to the pentatonic "E", but not exactly.  For the minor triad, same story for the "C" in A C E.  So what should we call this note? For now, let's just call it Note-prime.

Now we can form a major scale from three major triads (and their 1:2 "octaves"): F A' C E' G B' D

(which is traditionally written starting on C.)  Or, we could use minor triads: D' F A' C E' G B'  and get a minor scale.

And let's try the dominant of C:  C E' G B' D F#' A

So put it all together: D' F A' C E' G B' D F#'  we end up with notes from two different interlaces spirals of fifths, with two flavors of "D" (re)  [Sometimes you will see a circle-of-fifths written with major chords on the outside and minor chords on the inside, which is an accurate picture as far as it goes, if you recognize the F# is not Gb but two distinct ends of a spiral that wind around forever in both directions.  (There are many examples on the internet of the "spiral" of fifths, but a quick search didn't turn up any examples of two interlaced (major and minor) spirals.  Guess I'll have to create my own.)

Now, if we include the tritone in the dominant 7th chords for G in the major, D in the dominant, and E in the minor,

we get some extra notes F" C#" G#" from different spirals, depending on how you define the tritone. (Some define it as a minor third 5:6 from the fifth--which can be read from an extended Tonnetz; some as 4:5:6:7, etc.)

Now notice that, except for the pitches D and F", all the scale notes are distinct, so we can tune an instrument to play songs in just triadic harmony as long as we stick to a single diatonic key.  But if we want to combine say a D-minor and G7 chord in the same piece, we have a problem.  (Notice that the first prelude in Bach's Well-Tempered Clavichord begins with a Dm7-G7 progression.)  Today, of course, in ET, the ii7-V7 progression is pervasive.

But even more seriously, TN naming does not really distinguish between minor and major thirds.

It's true that minor and major chords have different note names:  C E G is major and C Eb G is minor--

but what about C# E G or C E G# or C E# G  etc.  What about  D F A  vs E G B vs F A C ?

The problem is the A B C D E F G sequence "reads" like equally spaced intervals, but it's not.

We know that there is no note between EF or BC.  There is indeed an E# and an Fb, a B# and a Cb, but they are not "between" but "on" the neighboring note.

Just looking at the letters of a given chord, you can't readily tell which intervals are major and which are minor.

The spacing of letters may be the same but the intervals are different;  the number of accidentals is not a reliable clue.  You just have to know where the "half-steps" occur in the letter sequence, and do a calculation.

It just amuses me when people get so indignant that ET notation obscures the distinction between G# and Ab

(which seldom occur in the same piece, although they theoretically could) but are unconcerned that TN obscures the distinction between major and minor thirds.  Furthermore, if "just intonation" is their concern, why no concern about the difference between what I've called D and D' or F and F", which occur routinely--though perhaps not in music written with just intonation in mind. 

It's like debating the virtues of butter vs margarine for your toast while ignoring the difference between wheat and rye,

or bagels vs muffins.

So i'll let you answer your own question. In that TN note-naming obscures "thirds" harmony--

"equalizes" the difference between major and minor thirds, and does not distinguish the "major" and "minor" spirals--

and given that "stacked thirds" is the basis of classical harmony, does TN naming do a good job?

The distinction between major and minor thirds provided by ET (12-step) notations, in my humble opinion,

is vastly more useful, in terms of harmony, than the distinction between G# and Ab.  The only thing we would lose my moving to a 12-name or "dozenal" naming scheme and staff from traditional is familiarity.  And, with use, the twelve-step scheme would become familiar quite quickly.

Joe Austin

[gguitarwilly]

Hi Joe,

I enjoyed reading your post, though certain passages are beyond my comprehension.

I'll try to summarize it: depending on manner of calculation, a note that is arrived at, starting at a given note and applying the calculation, will not always have exactly the same frequency. The way it is calculated allocates it to this or that spiral of fifths.

Although I'm not familiar with the details of pitch calculation, I know the difference between just intonation and ET. As a guitarist, one is reminded of this difference daily when tuning a guitar.

Now for note naming; I thought the difference between writing Ab or G# could have two reasons: intonation (a G# is intonated higher than Ab. Sharps are used in ascending chromatic passages, and flats in descending ones. I assume that that means the intonation of the ascending 'sharped' notes is higher than that of the descending ones) and the rule that every note name shall be present in a given scale only once. 

Looking up note naming in a music theory book, I found another reason which collides with the described use of accidentals in chromatic lines: to make the chord that results from various converging lines have a common note combination, note naming may be adapted to arrive at this familiar combination. For instance: although a in descending line an Eb occurs, this Eb is notated as a D# to produce the chord B7 (b, d#, f#, a), the V7 of the piece (prelude no4, chopin, measure 6).

To this may be added that if an Eb would be written there, and interval of a second would seem to be part of the chord visually, which confuses the reader/player.

Such switching of note names suggests that intonation is not important here, the instrument being a piano.

So, what should note names define? Pitch, according to which spiral of fifths notes are part of? intonation clues? Or function within chords or tonality? a clue to relative pitches?

I think I'm too biased with TN too answer that. For me, an E chord is e, g#, b, never e, ab, b. It would be necessary to start with a clear slate to be able to come up with alternatives. 

For now, I'm happy using Clairnote, which makes is possible to distinguish between G# and Ab, which I find handy if I'm not sure how to name notes in a chord belonging to a certain key. But I often leave the accidentals out, focusing on the intervals within the music rather than on the note names.

To conclude: I'll keep a navel chord to classic note naming, imperfect as it seems, to keep in touch with musicians who are not into AN systems.

Willem

 

Op vrijdag 24 maart 2017 17:01:18 UTC+1 schreef Joseph Austin:

[Joseph Austin]

Willem,

I'd say you are beginning to discover why using a 7-letter naming scheme extended to encompass  a spiral of fifths condensed into a twelve-position "circle"  of fifths for describing "thirds" harmony played on ET instruments can be confusing.

Which is why many of us would just as soon abandon the whole thing and move to ET notation.

Joe Austin

[Keislar, Doug]

Willem,

You make some very good points.

Re: "a G# is intonated higher than Ab"

Intonation is more complicated than that. That statement is true in Pythagorean tuning, but not in just intonation (5-limit or higher). In just intonation, G# is typically lower than Ab (and similarly for other pairs of enharmonic equivalents).

You can take most assertions about how musicians really tune intervals with a grain of salt.  Many such assertions are written by people who are intrigued with the mathematics but haven't done scientific measurements of actual musical practice.  Back when I was looking into this question (some decades ago), I found conflicting evidence in the scientific literature on studies of musical intonation in practice.

It's reasonable to assume there are conflicting criteria in musical practice.  For example, a G# as part of a sustained E-major chord by expert barbershop quartet singers, or string players, might tend toward just intonation, whereas a G# in a more melodic context by the same musicians might tend toward Pythagorean tuning.  As a kid learning violin, I was taught to make G# higher than Ab (for example) -- as in Pythagorean tuning, though my teacher didn't use that explanation, just a melodically motivated one.

In my own studies of musicians' judgments of perceived intonation, I found that they tended to hear equal-tempered harmonic intervals (major thirds and perfect fifths) as in tune (as compared to, say, those intervals in just intonation or Pythagorean tuning -- the distinction being the most relevant in the case of the major thirds, which have greater variation across tuning systems).

So I'm pretty skeptical of any claims that a single theoretical tuning system defines musical practice.  Tuning is a ball of wax, and the more dogmatic or simplistic someone's statements about it are, the more skeptical I tend to be about what they have to say.

Regarding the reasons for choosing between enharmonic equivalents, the other reasons you mention (having 7 unique letters in the pitch names of a diatonic scale, and harmonic considerations) seem generally more valid to me than tuning. 

Doug

---

From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Joseph Austin [drtec...@gmail.com]
Sent: Monday, March 27, 2017 5:09 PM
To: musicn...@googlegroups.com
Subject: Re: [MNP] System with diatonic staff and 6-6 note head pattern (DS66)

[Keislar, Doug]

Thanks, Michael.  Paul has a very good discussion of intonation with respect to enharmonic equivalents here:
http://musicnotation.org/tutorials/enharmonic-equivalents/
but we could expand it slightly to incorporate some of the points I made in that Forum post (especially the contradiction between different tuning systems).

Doug

---

From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Keislar, Doug [do...@musclefish.com]
Sent: Monday, March 27, 2017 9:32 PM
To: musicn...@googlegroups.com
Subject: RE: [MNP] System with diatonic staff and 6-6 note head pattern (DS66)

[Keislar, Doug]

Oops, I was replying publicly to a private message from Michael Johnston.  On closer inspection, I now see that a footnote in that tutorial already mentions the contradictions between tuning systems.

Doug

---

From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Keislar, Doug [do...@musclefish.com]

Sent: Tuesday, March 28, 2017 7:36 AM

[Paul]

On 03/28/2017 10:36 AM, Keislar, Doug wrote:

Paul has a very good discussion of intonation with respect to enharmonic equivalents here:
http://musicnotation.org/tutorials/enharmonic-equivalents/

Thanks Doug, although, credit where credit is due, Doug's editing and suggestions on this tutorial, e.g. coming up with the musical example/comparison, really made it much better than it would have been working on my own.

I think Willem makes some good points about the conventions of naming notes based on the key or the chord and the relationships between them, etc.  This falls under the heading of "harmonic and melodic function".  We might add to the tutorial the example of the notes in a key always being (one and only one of) ABCDEFG (with sharps or flats applied via key signature).

I know less about tuning and find myself getting lost in the math when reading Joe's posts.  My take-away is that distinguishing between enharmonic equivalents for tuning/intonation purposes is complicated and not straightforward and the arguments for that are not water-tight.  My interests are more with notation which is somewhat orthogonal to questions of tuning/intonation (since you can play the same notated piece using different tuning systems). 

An interesting case for comparing diatonic and chromatic staves:

You have a melody and you want to play a harmony line (or melodic variation) in say, parallel thirds above or below the melody.  This is arguably easier on a diatonic staff than on a chromatic staff, since it represents only the diatonic notes in the current key (assuming we have already memorized the diatonic scale and key signature for the current key).

On a diatonic staff it is easier to see which notes are a "third" higher in the current key, and in general to work at the level of (generic, unspecified) seconds, thirds, sixths, sevenths, etc.   You don't have to worry about whether they are major or minor since this is determined by the key/key signature. 

On a chromatic staff playing a harmony line in parallel thirds is not as straightforward, since the staff itself doesn't help you decide whether you need to play a major or minor third for a given note.  In Clairnote you have the key signature which you can refer back to, to see which notes are in the current key, and that can help...

So chromatic staves make the _notated_ notes more explicit and straightforward, but if you want to play harmony notes that are _not_ notated, but need to be in the current key, then you have to rely more on your memory of the current diatonic scale and 'play by ear' skills.  For this a chromatic staff won't help you in the way a diatonic one can.  (Always trade offs...) 

Maybe when you get to the level of playing un-notated harmonic lines you're already good enough to do it without help from the staff?  But maybe it would be harder to get to that level...  Or perhaps because you've repeatedly seen diatonic scales and their interval patterns on a chromatic staff you will have internalized them better?  Is explicit better for learning than implicit?

My assumption has been that it's easier to learn and internalize what is more explicitly represented, but it could be that you just come to rely on that explicit representation and would internalize the patterns better if you _had_ to remember them because they weren't explicitly shown?  I'm full of questions that I don't know the answer to...

Cheers,
-Paul

[gguitarwilly]

Hi Doug,

"In my own studies of musicians' judgments of perceived intonation, I found that they tended to hear equal-tempered harmonic intervals (major thirds and perfect fifths) as in tune (as compared to, say, those intervals in just intonation or Pythagorean tuning -- the distinction being the most relevant in the case of the major thirds, which have greater variation across tuning systems)."

That's interesting. I sometimes play guitar in DADGAD tuning, and what really bugs me is the major third on the high E-string; it is way too high, which is all the more annoying since this particular open tuning is full of resonating overtones. I even created a temporaty fret out of a tin can and put it below the fourth fret, with satisfying result (apart from the rickety construction of a rolled up piece of metal and some tape).

Tuning down the string is no option, since then it is really out of tune with the two other D strings.

Another occasion where ET tuning was and is a problem, is when I'm playing the 'Gymnopédie no3'. Somehow, the ET tuning seems to create many problem spots in that piece.

I even had my piano tuner return in an effort to 'fix the problem', which of course he couldn't.

If you like, you could try it, and mark ill-sounding notes, so we could compare if it's the same spots we notice. (or anyone else; I'm really curious why I have this problem with this piece).

I've wondered; if one would know the math behind the notes in this piece (just intonation vs ET) it would probably be possible to predict which notes would sound worst.

It is interesting that ET seems to cause no problems in some piano pieces, but huge problems in others.

To include this tuning problem into the discussion about notation: it might be worthwile to think about how the notes in this particular piece could be best written, supposing the piece was played by some microtonal keyboard or a string ensemble.

Willem

Op dinsdag 28 maart 2017 06:32:12 UTC+2 schreef Doug Keislar: