Key signatures

[John]

I'm interested in discussing the importance of key signatures. Even
in systems with chromatic staves there is still a tendency to describe
a method for stating the entire scale that exists in the beginning of
a song and then not one for describing the changes throughout the rest
of the song. I've noticed, especially in songs with multiple
modulations away from not just the original tonic but outside of the
related modes to a different diatonic scale, that it is
inconsequential to know what the starting point of the song is scale-
wise when improvising, comping, or sight reading. Can anyone point
out advantages to this system?

The real importance in traditional notation for me lies in the chord
symbols that display the changes that may occur every two beats so I
was also curious if someone could point me towards any notations that
have devised a new system to display chord symbols and used them in
place of any sort of key signatures.

John

[Jim_Plamondon]

On Jul 24, 12:22 am, John <jlmori...@gmail.com> wrote:
>   I'm interested in discussing the importance of key signatures.

Well, you asked for it. ;-)

In the key-independent JIMS Isomorphic Music System (previously known
as the ThumMusic System), the key signature is not usually specified,
enabling the performer/conductor to choose a key that is convenient to
a given performance's particular collection of constraints (e.g.,
vocal ranges).

However, the notation must still provide a means of indicating key
changes in the course of a piece, as described in the "key change
indicators" section of http://www.thummer.com/thummusic.pdf, starting
on page 31.

This notation conveys the key-shift's vector -- up a major third, down
a perfect fifth, etc. -- without reference to specific pitches (Bb,
C#, etc.).

On the (now-defunct) Thummer, the user would execute a key change by
(1) pressing a thumb-operated "shift" button; (2) playing two notes in
sequence to specify the key-shift vector; and then (3) releasing the
"shift" button.

The effect of pressing the shift button was determined by the first
button pressed thereafter. For example, if you pressed shift and then
Ti, the next button pressed would select a MIDI instrument sound
(piano, accordion, organ, etc.). To specify a key shift, the first
button pressed had to be Re; the second button's interval from that Re
would determine the key-shift vector. Ideally, then, the key-change
vector notation in JIMS/ThumLine would also always start on Re, to be
as consistent with the user-interface gesture as possible. This is
somewhat different from the key-shift vector notation rules specified
in the above-referenced document, which was written before the Thummer
prototypes (including the shift button) were implemented.

The overloaded meaning of the "shift" button is more complex than I'd
like, but the alternative is to have a zillion single-meaning thumb-
operated buttons, and I like that a lot less. The Thummer already has
a zillion finger-operated buttons; overloading their meaning, when
using the shift key, seems like the simpler choice.

The bottom line is that
=> the notation of the key-change, and the performance gesture
for controlling a key-change, should be as isomorphic as possible. <=

As an ideal of isomorphism, consider the symbols for the consonants in
Korea's Hangul writing system (http://en.wikipedia.org/wiki/
Hangul#Consonant_jamo_design). The character for a given consonant
actually shows you how to make the sound to which it corresponds. The
density of information in such symbols is remarkable. That is the
standard of isomorphism -- that is, of consistency of mapping between
symbol and concept -- to which I apsire.

Compared to that standard, lead sheet chord symbols such as "CMaj" and
"Csus4" are utterly without merit (other than backward compatibility
with standard practice). They represent the sounds of the English
names of the chords. They couls just as meaningfully be Cfoo or Cbar;
you just have to memorize what "foo" and "bar" mean, and how those
meanings map to instrument-control gestures. Nashville numbering and
Roman numerals are no better by this standard.

In JIMS/ThumMusic, chord symbols represent the stack of intervals that
define a chord (see "ThumChord Symbols," p. 32 of the above-referenced
document). The document describes these as being strings of standard
ASCII characters, which is not entirely satisfactory (especially for
the seconds). It would be much better to use a dedicated font, with
each interval-stack being shown with its correct shape and context,
more like the ThumField column of Table 4 on page 33 of the above-
referenced document. Using the ThumField symbol as a printed chord
symbol, prefaced by its root-name (and its inversion numeral, if any)
would define such a chord completely.

A ThumFiled-like chord symbol shows the performer what pattern of
buttons to press, and its root indicator tells the performer the
button on which to start that pattern. The inversion indicator, which
I consider to be an advanced feature, tells the advanced performer
what inversion of that chord to play. It is my understanding that
standard lead-sheet chord symbols don't (can't?) indicate inversions,
although classical music's figured bass is used specifically for that
purpose.

Obviously, the pattern of button-intervals shown in a ThumField chord
symbol is unique to the Wicki note-layout. It tells you everything
about the pattern of buttons to press on that note-layout, and nothing
whatsoever about the user-interface gesture(s) needed to produce that
pattern of intervals on any other musical instrument. That's is
entirely consistent with my goal of maximizing ease-of-learning
through the development of a complementary notation and instrument.
Even with the Thummer dead (for now), the ease of implementing the
Wicki layout on the QWERTY keyboard, or on an iPhone, or on an AXiS 49
or whatever, makes its complementary notation potentially useful.

However, I recognize that it has little or no value to players of
traditional instruments, such as the piano.

My two cents. ;-)

-- Jim

[Michael Johnston]

> in systems with chromatic staves there is still a tendency to describe
> a method for stating the entire scale that exists in the beginning of
> a song and then not one for describing the changes throughout the rest
> of the song.

Yes, and some notation such as lead sheets will often show the key
signature at the beginning and then not again. The first time I saw
this, I was concerned, but the laid-back gentleman explained that
writing the sigs on every line was time consuming and did it really
help, really?

I'm restoring an organ piece from 1874 with multiple errors. The
engraver forgot accidentals and laid out some notes that don't match up
with others. In two places, the flats at the end of a measure were a key
that the note was to have been a natural earlier in that measure. The
key signature makes this easier to figure out and more reliable. If
similar mistakes were to be made on a modern piece with a chromatic
staff, would it be possible to figure out what the original intent was?
Don't think so.

> The real importance in traditional notation for me lies in the chord
> symbols that display the changes that may occur every two beats so

Any new systems that hopes to survive in the popular music world must
accommodate this. Some of my customers still use these in fake books.

http://michaelsmusicservice.com/music/Rio.MyPerkyBaby.html Scroll down
to Perky and you'll see the simple chord symbols for those who use them.
There's also a cryptic registration that means something to Hammond
players. <g>

Cheers!
Michael
--
MICHAEL'S MUSIC SERVICE 4146 Sheridan Dr, Charlotte, NC 28205
704-567-1066 ** Please call or email us for your organ needs **
http://michaelsmusicservice.com "Organ Music Is Our Specialty"

[Ken on Google Rushton]

Hi,
a comment. One thing I've noticed is that there is a large difference, when playing on a jammer, between major and minor songs. the placement of the note vectors is just totally different.
Like wise for the one modal song I've tired, Greensleeves; in this song it seems obvious that is really is in two modes. Knowing the "real Key" (major vs minor) is important on the Jammer in learning how to place the fingers.

So, I think a good notation should include information on the mode.

Ken.

[Jim_Plamondon]

On Jul 26, 12:58 am, Ken on Google Rushton <bogrush...@gmail.com>
wrote:

> I think a good notation should include information on the mode.

Agreed. Hence, in JIMS/ThumLine, one of the "scale dots" that defines
the current scale is a "tonic indicator," indicating the tonic of that
mode, as described starting on page 23 of the document at
www.thummer.com/thummusic.pdf.

Many songs that "sound minor" are actually in a mode of a non-diatonic
scale, such as the double harmonic ("gypsy minor") or melodic.
Traditional notation has no means of describing a song's current scale
or mode. Providing this data, as JIMS/ThumLine does, is very helpful
in conveying the relationship between a song's scale and its chords,
which is arguably essential to good improvisation (http://
www.outsideshore.com/primer/primer/ms-primer-4.html).

I don't recall having seen this mentioned elsewhere in this forum (but
that could just be senility, which, for me, kicked in at birth...).

[John]

> This notation conveys the key-shift's vector -- up a major third, down
> a perfect fifth, etc. -- without reference to specific pitches (Bb,
> C#, etc.).
>
> On the (now-defunct) Thummer, the user would execute a key change by
> (1) pressing a thumb-operated "shift" button; (2) playing two notes in
> sequence to specify the key-shift vector; and then (3) releasing the
> "shift" button.

I didn't realize that this was part of the concept of the thummer, to
change the transposition of the instrument for every change of key
that occurs in a song, very interesting. Although I can see this
being extremely useful, I can also see it as being extremely difficult
as well it creating inconsistancy in the expression of musical ideas
in relation to the shape/order of buttons being pressed. I assume
that the conveniences were worth the difficulty and inconsistancy?

> In JIMS/ThumMusic, chord symbols represent the stack of intervals that
> define a chord (see "ThumChord Symbols," p. 32 of the above-referenced
> document).  The document describes these as being strings of standard
> ASCII characters, which is not entirely satisfactory (especially for
> the seconds).

I really like this method a lot, it displays the chord directly and
intuitively once the symbols are defined to the reader, but there is
probably room for improvement in the form of the symbols, like you
said. I even think that this method could be tweaked slightly to
incorporate every step in the scale in thirds up to the thirteenth
which would eliminate the need for any key signature in the staff
itself at all. Then all that is necessary is another method to
identify the tonic in the chord symbol, unless the original tonic
indicator would be preserved.

> The inversion indicator, which
> I consider to be an advanced feature, tells the advanced performer
> what inversion of that chord to play. It is my understanding that
> standard lead-sheet chord symbols don't (can't?) indicate inversions,
> although classical music's figured bass is used specifically for that
> purpose.

I think that once a specific inversion of the chord is specified that
it might as well be written out in notation. The point of chord
symbols is to give the instrumentalist who interprets them the option
to voice the chord however he wants to, and this includes not just
putting the third vs. the fifth on top with all of the other pitches
falling in directly below. The pitches that make up the chord can be
spread out on the instrument in any order to create different colors
depending on the interpretation of the player. On piano it is typical
to put the third and seventh in the left hand and then color tones in
the right hand in the higher registers such as the fifth, ninth, and/
or thirteenth, once again depending on the interpretation of the
instrumentalist. How would or should an inversion effect the
construction of these types of voicings?
Seems to me any information conveyed by a chord symbol outside of
simply the notes that the chord is comprised of would be extraneous/
inconsequential to anyone who wanted to create his own feel or
interpretation.
Of coarse the other point of chord symbols is to lead a non chordal
instrumentalist in soloing and once again any information outside of
the notes comprising the chord itself seems, to me at least,
unimportant.

> Obviously, the pattern of button-intervals shown in a ThumField chord
> symbol is unique to the Wicki note-layout. It tells you everything
> about the pattern of buttons to press on that note-layout, and nothing
> whatsoever about the user-interface gesture(s) needed to produce that
> pattern of intervals on any other musical instrument. That's is
> entirely consistent with my goal of maximizing ease-of-learning
> through the development of a complementary notation and instrument.
> Even with the Thummer dead (for now), the ease of implementing the
> Wicki layout on the QWERTY keyboard, or on an iPhone, or on an AXiS 49
> or whatever, makes its complementary notation potentially useful.
>
> However, I recognize that it has little or no value to players of
> traditional instruments, such as the piano.

What worries me most is not that this method doesn't relate to other
instruments but that it doesn't display (directly) how the chord is
constructed interval-wise and therefor doesn't give the player of the
wicki-hayden layout the opportunity to interpret the chord how he
wants when comping. Also it doesn't require an understanding of the
construction of the chord in the first place which would make the
method for interpreting the chord while improvising indirect. One of
the goals in notation should be the apparency of tonal relationships
and this chord notation doesn't make it so. This method seems like it
could function more like an instrument specific notation where the
composer gives a specific voicing or inversion of a chord using the
shape on the layout to create a feel that he specifically desires for
the piece. Still, this would be a lot of work for such a small
payoff, to have an instrument specific system of chord notation that
has the disadvantages previously mentioned.
Is the lack of tonal understanding worth the ease in reading/playing
this method?

[Jim_Plamondon]

On Jul 28, 1:53 am, John <jlmori...@gmail.com> wrote:
> I didn't realize that this was part of the concept of the thummer, to
> change the transposition of the instrument for every change of key
> that occurs in a song, very interesting.  Although I can see this
> being extremely useful, I can also see it as being extremely difficult
> as well it creating inconsistancy in the expression of musical ideas
> in relation to the shape/order of buttons being pressed.  I assume
> that the conveniences were worth the difficulty and inconsistancy?

What inconsistencies are you referring to, John?

Keep in mind that, on the hypothetical Thummer:
0) One can play using standard pitch names, in 12-tet, and get all of
the ease of use and expressive power of the Thummer, simply by
ignoring all of the other cool stuff it can do.
1) Although the accompanying hand can move freely over its keyboard,
the Thummer is strapped to the arm of the melodic hand, limiting its
range of motion. This forces the Thummer keyboards to be tiny, each
with only three octaves of 19 buttons per octave (57 buttons total).
2) The Thummer was designed to support Dynamic Tonality (http://
en.wikipedia.org/wiki/Dynamic_tonality) in addition to standard 12-
tone equal temperament. In Dynamic Tonality, the pitch of all notes
except the tonic changes when the tuning changes. Hence, when using
Dynamic Tonality, it is necessary to specify the tonic.
3) Although the Thummer has only 19 buttons per octave, these 19
buttons cover the tonal gamut of the syntonic temperament, no matter
how finely one sub-divides the octave. The major tonic triad, for
example, is DoMiSo whether the tuning has 5, 7, 12, 17, 9, 31, 53, or
an infinite number of notes per octave. This is not just true for
diatonic chords, but for chromatically altered chords, too, no matter
how "distant" the current key from the original key (since electronic
transposition keeps the current tonic centered on the keyboard). This
is perhaps the single most-misunderstood feature of the Thummer.
People simply cannot come to grips with the notion that a keyboard
with only 19 buttons per octave can support music written in (say) 31-
tone equal temperament. What they're overlooking is that only a small
subset of those 31 notes are used in any one key, no matter how
chromatic that music is. You only need, at most, 19 buttons per octave
to control that subset ("the tonal gamut") in any given key or tuning.
4) JIMS/ThumMusic notation, and Thummer keyboard fingering, is the
same in any syntonic tuning, no matter how many or few notes there are
per octave.

> I think that once a specific inversion of the chord is specified that
> it might as well be written out in notation.

The existence and continued use of figured bass (http://
en.wikipedia.org/wiki/Figured_bass) suggests that there are cases in
which the inversion must be notated. JIMS/ThumMusic meets this need,
simply by prefacing a chord symbol a single digit indicating the scale
degree that's in the bass. No leading digit = root position; 3 = first
inversion; 5 = second inversion; 7 = third inversion, and so on.

Hence, JIMS/ThumMusic provides a single system of chord symbols which
can indicate inversions (with a leading digit) or not (without the
leading digit). A novice, capable of reading chord JIMS/ThumMusic
chord symbols but encountering a leading digit for the first time,
could simply ignore the leading digit, and still play the right notes
(if not, perhaps, in the optimal right octaves). Compare this to a
novice, capable of readng chord symbols (Edim, Csus4, etc), who
encounters figured bass for the first time. Figured bass is not an
addition to traditional chord symbols; it is a completely separate
symbol-system, which one must learn independently.

> What worries me most is not that this method ...doesn't display (directly) how the chord is

> constructed interval-wise and therefor doesn't give the player of the
> wicki-hayden layout the opportunity to interpret the chord how he
> wants when comping.  Also it doesn't require an understanding of the
> construction of the chord in the first place which would make the
> method for interpreting the chord while improvising indirect.   One of
> the goals in notation should be the apparency of tonal relationships
> and this chord notation doesn't make it so.

> Is the lack of tonal understanding worth the ease in reading/playing
> this method?

I do not understand your point at all. The Thummer's keyboard is
isomorphic, so each line from button to button on a ThumFiled glyph
(see http://www.thummer.com/thummusic.pdf, page 33, Table 4,
"ThumField" column) corresponds to a specific tonal interval. For
example, in that Table's top-most row, the diminished 7 chord is shown
as a stack of three minor thirds, one on top of the other. The shape
of each minor third is identical, of course, because the keyboard is
isomorphic.

Likewise, the second row of the said table shows the half-diminished 7
chord as a stack of two minor thirds with a major third on top.

In short, a ThumField glyph shows you the pattern of buttons to press
to play it, which is *exactly the same thing* as telling you the stack
of intervals from which the chord is constructed. It is both a
tablature and a harmonic analysis.

The ThumField glyph would be preceded by the name of the root on which
it was to be played (Do, Re, Mi, etc.), and optionally by a digit
specifying the inversion, as discussed above.You can SEE in the glyph,
and feel under your fingers, the difference between (for example) a
fully-diminished and a half-diminished 7, and know that that
difference will be seen and felt consistently no matter what root it
is played on (when playing on a Wicki-Hayden note-layout, at least).

Hence, it seems to me that the ThumField chord glyph DOES exactly what
you says it does NOT do: it displays the stack of tonal intervals from
which it is constructed (in root position), thereby faciliating the
acquistion of tonal understanding.

Unless I'm missing something?

[John]

> What inconsistencies are you referring to, John?

Sorry for not making myself clear and making you go through all of
that explanation.
If one is supposed to transpose the instrument so "do" in the layout
is the current "do" in the chord changes at every change, then the
interval between the note one plays directly before the change and the
one directly after would not be reflected in the wicki/hayden layout
correct?
If I were to play the tonic (do) of the current chord, there were to
be a modulation up a fourth, one used the shift key to get there, and
then were to play the same button, it would now produce a fourth above
the previous pitch, even though it was the same button correct?
That is the inconsistancy. I recognize the brilliance of the Thummer's
use of the only nineteen tones per octave which reflects the only
tones in a tuning that one would ever musically use seeing as they are
they include the tonic and the nine stacks of the chosen size of the
fifth above and below the tonic, as well as the fact that modulation
must then occur in transposition of the instrument so that consonance
is preserved in every key change. But the fact that after using the
shift key one can not easily recognize how to play a certain interval
from the note previously played because the actual pitches represented
by the buttons has changed once again makes me a bit skeptical. When
improvising or playing by ear while simultaneously changing key using
the shift button, wouldn't keeping a melodic movement over key shifts
be very difficult? Or have I interpreted the use of the shift button
incorrectly?

> The existence and continued use of figured bass (http://
> en.wikipedia.org/wiki/Figured_bass) suggests that there are cases in
> which the inversion must be notated. JIMS/ThumMusic meets this need,
> simply by prefacing a chord symbol a single digit indicating the scale
> degree that's in the bass. No leading digit = root position; 3 = first
> inversion; 5 = second inversion; 7 = third inversion, and so on.

Although I have never needed the information it likely has no downside
for anyone who just ignores it, thanks for the example where it is
relevant.

> Hence, it seems to me that the ThumField chord glyph DOES exactly what
> you says it does NOT do: it displays the stack of tonal intervals from
> which it is constructed (in root position), thereby faciliating the
> acquistion of tonal understanding.

Again sorry, I should have used the word indirectly far more often,
and I should have thought through what I was saying a little more
thoroughly. It seems that in order to create an understanding of the
construction of the chord from the chord glyph one has to go backwards
from the glyph to the intervals then back again to create some other
interpretation of the chord if desired. But I guess this really is
the same as the use of the ASCII symbols because those to have to be
interpreted as intervals so...
Yes, your right, that was a pretty dumb thing to say :P I wasn't
making the connection that the shape of the glyph was also, because of
the isomorphic layout, a direct representation of the interval, the
exact same as the ASCII symbols, so clearly it is not just an easy way
out for wicki-hayden players My fault.

[Jim_Plamondon]

On Jul 29, 3:39 pm, John <jlmori...@gmail.com> wrote:
> > What inconsistencies are you referring to, John?
>

> If I were to play the tonic (do) of the current chord, there were to
> be a modulation up a fourth, one used the shift key to get there, and
> then were to play the same button, it would now produce a fourth above
> the previous pitch, even though it was the same button correct?
> That is the inconsistancy.

Correct!

You're asking a very reasonable performance-related question: "is it
easier to move your hands to a new key's pitches, than to move a new
key's pitches to your hands?" My answer is, it's six of one, half a
dozen of the other. Where you stand depends on where you sit. Comme
ci, comme ça. Are you a Mac, or a PC?

Think of it as follows: you've got a piece of paper marked with the
pitch-mapped Wicki-Hayden note-layout (C, D, E, etc), and above it, a
transparent sheet marked with the interval-mapped Wicki-Hayden note-
layout (Do, Re, Mi, etc.), each aligned with the other. When you're
in C, the diatonic notes Do, Re, Mi, Fa, So La, and Ti in the
transparent sheet align with the corresponding notes C, D, E, F, G, A,
and B on the paper sheet beneath. When you change keys to G Major,
one of two things has to happen:
- either you slide the transparent Do, Re, Mi sheet over the surface
of the fixed-in-position C, D, E sheet to align the Do, Re, Mi notes
with the pitches of G Major,
- or you slide the paper C, D, E sheet below the surface of the fixed-
in-position Do, Re, Mi sheet to align the pitches of G Major with the
Do, Re, Mi notes.

It's like looking out of a train's window, to see an adjacent train
moving...or, is your train moving, and the other one stationary? All
you know is that they are moving *relative to each other.*

If the buttons are labeled with DoReMi, the pitches move on a key
change. If the buttons are labeled with C, D, E, then the current
diatonic scale must move on a key change. Either way, something's
staying the same, and someting else is moving. The question is, which
thing deserves emphasis? The pitch or the interval? Whichever thing
deserves emphasis, should stay fixed; the other thing should move.
Traditionally, pitches are fixed, and intervals move. When you change
key from C Major to G Major on the piano, you shift your hands seven
keys (seven semitones) rightward, thus moving the roles of DoReMi to a
new set of pitches. JIMS/ThumMusic (www.igetitmusic.com/papers/
JIMS.pdf) emphasizes intervals, so in it, intervals are fixed, and
pitches move.

As to which one's easier, well, I don't know, although I have my as-
yet unconfirmed suspicions. As to which one's more FAMILIAR, it's no
contest: having the buttons labelled with pitch names is more familiar
to today's musicians. So no musician who is already familiar with C,
D, E-labelled buttons is going to prefer the DoReMi-labelled approach,
all else being equal.

The advantage of DoReMi-labelled is its consistency between octaves,
keys, and tunings. Its primary disadvantage is its unfamiliarity. The
perfomance issues are, in Thumtronics' very limited experience, a
wash, so consistency wins.

--- Jim

[Evan Lenz]

Jim_Plamondon wrote:
> As to which one's easier, well, I don't know, although I have my
> as-yet unconfirmed suspicions.

I would think it has a lot to do with the type of music you're playing.
If the music is very tonal and unambiguously so (e.g., pop music or 18th
century Classical), then the shift button makes a lot of sense. But the
further you venture toward tonal ambiguity or atonality, the shift
button becomes something I wouldn't know what to do with.

Based purely on conjecture (and ignoring your other criteria such as
mobility), I think I might like the Janko approach better for playing a
wider range of music on the tonal/atonal spectrum. There's no hard
distinction where you have to decide when to hit the shift button. (This
is one of the reasons I hate traditional notation for atonal music:
composers using arbitrary key signatures just because that's what the
notation expects.) Instead, on the Janko layout, for strictly tonal
music, you just shift your hands the appropriate interval, and for
everything less than strictly tonal all the way to full-on atonality,
the user interface transitions smoothly with no hiccups.

You're right, it's six of one, half a dozen of the other. My point is
that which one is likely to be more natural has everything to do with
what kind of music you're playing.

Evan

[Keislar, Doug]

I sympathize with Evan's point about the type of music.

But let's be clear that whether a device has an automatic transposition button, as proposed for the Thummer, has nothing essentially to do with whether it has one isomorphic key layout (such as Wicki-Hayden) vs. another (such as Janko).

Doug

[Evan Lenz]

You're right. Thanks for the clarification. I was too much associating
Wicki-Hayden with the Thummer in my mind. Any isomorphic key layout has
the advantage I described, which is...umm...isomorphism.

Evan

[John]

Theoretically considering ones mindset I see how really there is no
difference between moving ones hands vs. moving ones mind, your six of
one/half of a dozen, but in practice if one is leading to the key
change with a melodic line or is repeating a riff over a different key
change for contrast, I can only see confusion in figuring out where to
go once the shift key would be hit, because in this case perhaps the
fingers would not move pitch-wise and would now have to move to play
the "same" thing. Maybe this is a good thing, because then it would
require the performer to know the interval relationships in all the
modulations in a tune, and maybe it might not be because it might lead
to less playing by ear what sounds good and more so "playing the
changes".

I guess this is the type of thing that can only be clarified through
experiences and trials, which unfortunately will not be happening
anytime soon.
Unless you think, Ken, that you would be able to implement a similar
technology in your remapping software to the Thummer's shift key?
Instead of choosing two keys for half step transpositions, perhaps one
key could be devoted to shift and you could employ the use of the
intervals on the instrument's button field for transposition, as on
the Thummer?

I don't know how difficult this would be seeing as I have no
programming experience, maybe what I've proposed is unreasonable,
especially seeing as you've got so much on your plate as it is when it
comes to revamping your software. I appreciate what you've done so
much already but hopefully this would be an easy modification?

[Paul W Morris]

I'll just add that I agree with John's and Evan's thoughts on this. I
think the advantages of using such a shift key would largely be
limited to genres of music that mostly stayed in one key per musical
work. (See Shape Note notation and the Sacred Harp vocal repertoire
for a good example of this.) My hunch is that with any modulation or
ambiguity in the tonality of a work, you would quickly lose more than
you would gain by using such a transposition key and pitch-relative
approach. The interval relationships between the notes on either side
of the transposition, or between musical works, would become less
clear and explicit, for example.

It seems to me that with an isomorphic instrument and notation the
interval relationships are already clear, and the relationship of any
note to a tonal center (or centers, to the extent that there is one)
is a function of the interval relationships between that note and
other notes. Although I understand the thinking, I'm not sure that it
would be that much more helpful, especially in the long run, to try to
always keep the tonal center (assuming there is one, only one, and you
can tell what it is), or the diatonic pattern of intervals, at the
same position on the staff or instrument.

That's just my take on it.

Cheers,
Paul M

[John]

I think what it comes down to is alternate tunings; if you want them
AND a compact key surface (with fingering invariance across tunings),
you need a wicki/hayden layout with a shift key so that the important
pitches of the current key (the nineteen tones from the nine
implementations of the stack-and-reduce method in each direction
around the tonic) can all appear on the instrument at the same time.
If you don't mind playing, not to mention paying for, an instrument
with an enormous key surface that can contain every note in say a 53
tone equal temperament on it's large surface at all times, one can
instead move one's hands to modulate but then one loses consistent
fingering in each different micro tuning of the instrument, not to
mention have to move one's hands all over the place, likely a more
troublesome affair than getting used to the shift key.

Is this correct?

I'm not saying I'm not still a little skeptical about how easy it
would be to get used to using a shift key, but the more I think about
the alternatives that still include alternate tunings, the more it
sounds like it is *probably* the best option.

John

[Paul W Morris]

That's a good point John -- if you take as a given a smaller number of
keys that will be compact enough to fit under one hand-span (as on a
Thummer) then a transpose key makes a lot of sense as it opens up a
wider range / additional keys to play in, especially if you want to
use alternate tunings where more keys are needed. Also, on a Thummer
there's the goal of keeping the hands in one place to keep the thumbs
on the pitch-bend joysticks for greater expressivity. So these two
characteristics of the Thummer contribute to the use of (need for) a
transpose/shift key, as well as the motivation to highlight common
interval patterns (the intervallic consistency of keys, diatonic
scales, etc.) Although, for me those interval patterns are already
clear from the isomorphism of an instrument or notation system, and
you can also keep a consistent, invariant representation of pitches as
well as intervals.

As you say, on an instrument with a larger key surface:

> one can instead move one's hands to modulate

but I don't think that that entails the following:

> but then one loses consistent
> fingering in each different micro tuning of the instrument,

If I understand Jim correctly then an advantage of the Wiki-Hayden
layout is that it remains isomorphic, retaining the same consistent
fingerings, across a wide range of tuning systems. So no matter where
you are on the isomorphic button field the fingering remains the same
in any given tuning, and even across tunings. So the shift/transpose
key doesn't figure in here. Unless I've missed something?

> not to mention have to move one's hands all over the place

Maybe it comes from having played guitar and piano, but I like the
idea of being able to directly and consistently see, feel, and know
where I am, and how that relates to where I was, and where I may be
going next. So I like keeping the pitches in the same place and
moving my hands instead. (Vocals are a bit of a different story...)

(There are some more in-depth discussions about this topic somewhere
in the Forum archives.)

Cheers,
Paul M

On Mon, Aug 3, 2009 at 4:44 AM, John<jlmo...@gmail.com> wrote:
>
> I think what it comes down to is alternate tunings; if you want them
> AND a compact key surface (with fingering invariance across tunings),
> you need a wicki/hayden layout with a shift key so that the important
> pitches of the current key (the nineteen tones from the nine
> implementations of the stack-and-reduce method in each direction
> around the tonic) can all appear on the instrument at the same time.
> If you don't mind playing, not to mention paying for, an instrument
> with an enormous key surface that can contain every note in say a 53
> tone equal temperament on it's large surface at all times,
>

[Jim_Plamondon]

On Aug 3, 3:44 am, John <jlmori...@gmail.com> wrote:
> I think what it comes down to is alternate tunings; if you want them
> AND a compact key surface (with fingering invariance across tunings),
> you need a wicki/hayden layout with a shift key so that the important
> pitches of the current key (the nineteen tones from the nine
> implementations of the stack-and-reduce method in each direction
> around the tonic) can all appear on the instrument at the same time.
> If you don't mind playing, not to mention paying for, an instrument
> with an enormous key surface that can contain every note in say a 53
> tone equal temperament on it's large surface at all times, one can
> instead move one's hands to modulate but then one loses consistent
> fingering in each different micro tuning of the instrument, not to
> mention have to move one's hands all over the place, likely a more
> troublesome affair than getting used to the shift key.
>
> Is this correct?

Yes, it's correct -- although I would emphasize the need to "keep the
keyboard tiny" over the need to "support alternative tunings." One's
melodic hand is strapped to the Thummer, which -- as on a concertina
-- severely restricts its range of motion over the keyboard. Reaching
the outermost-buttons of the 19-button-per-octave keyboard is quite a
stretch, and potentially ergonomically risky (can you say "class
action lawsuit"?). By keeping the tonic in the center, the ergonomic
risk is dramatically reduced.

I never wanted to mention the "ergonomic risk" point while Thumtronics
was alive, but now that Thumtronics is bankrupt, what the hell.
Musicans have the second-highest rate of repetitive stress injury
(RSI) after typists. The manufacturers of traditional instruments
can't do anything about the ergonomic risks inherent in the design of
their instruments, because those instruments' designs have been
standardized for centuries, and the ergonomic risks of playing the
violin, guitar, etc. are well-known. Playing the violin damages your
neck; playing the guitar damages your wrist; etc. I know a small woman
who herniated herself playing concert piano, because she had to bang
on the keys so hard (relative to her small size).

I wanted to make a safer instrument, for two reasons: first, it was
the right thing to do, and second, I wanted to avoid being sued to
death in a consumer class-action lawsuit.

Makers of traditional instruments are protected from such lawsuits by
history, but if the Thummer had been as successful as I had hoped, it
was almost certain that some California lawyer would eventually gin up
a class action suit against Thumtronics (see http://llr.lls.edu/docs/41-3shafton.pdf).
Therefore, I had to design every aspect of the Thummer with the
"reduction of ergonomic risk" in mind.

By keeping the tonic in the center of the keyboard, the average wrist
flexion is reduced to almost nothing, so the risk of RSI injury is
similarly reduced. Any Thummer player who did NOT use the Thummer this
way would be using the Thummer "improperly," and hence lose the right
to sue Thumtronics for any injury resulting from such improper use.

Arguably, designing an instrument to minimize RSI is just proper user-
centered design: "think of the customer first, last, and always."
However, these days, one has to think of the customers' laywers, too.

This is not to say that tonic-centering is a red herring; it is a very
useful feature, when using a teeny tiny keyboard -- especially when
using alternative (or dynamic) tunings, and it fits very well with
isomorphic notation such as JIMS/ThumMusic (www.igetitmusic.com/papers/
JIMS.pdf).

Arguably, addressing long-term considerations such as these burned up
Thumtronics' cash before it could get the Thummer to market. C'est le
mort.

[John]

>but I don't think that that entails the following:

>> but then one loses consistent
>> fingering in each different micro tuning of the instrument,

>If I understand Jim correctly then an advantage of the Wiki-Hayden
>layout is that it remains isomorphic, retaining the same consistent
>fingerings, across a wide range of tuning systems. So no matter where
>you are on the isomorphic button field the fingering remains the same
>in any given tuning, and even across tunings. So the shift/transpose
>key doesn't figure in here. Unless I've missed something?

I'm not positive to tell the truth but I think my reasoning is
correct.

If playing in anything but 12-edo, an attempt to play in a key not
associated with "do" on the thummer will lead to the incorrect tuning.
This is because (I think) when changing the tuning of the thummer one
is changing the parameters creating the intervals starting at do and
advancing outward on the instrument. So the farther away from do you
get spacially (and therefore farther from the relatedness of the note
from a tuning perspective) on the thummer, the more of an "impact" on
the change in pitch of this note the changing of the parameter will
have. This leads me to believe that the farther you get away from the
assigned do on the instrument, the farther away the tuning would be
from being "correct" if you were to choose this as your new new tonic.
Playing the IV or V as one's tonic might sound ok, the II and flatted
VII keys might sound iffy too, but if one were to attempt modulate to
a tonic even less related to the set tonic of the thummer, I'm pretty
sure that it would not be the correct tuning and would sound pretty
icky.

Could be wrong,
John

[John]

Just to clarify, my reasoning should apply to any wicki/hayden layout,
not just the thummer's. Though i constantly said "on the thummer", I
should have said "on the wicki/hayden layout.

[Paul W Morris]

On Sat, Aug 8, 2009 at 2:55 AM, John<jlmo...@gmail.com> wrote:

> This leads me to believe that the farther you get away from the
> assigned do on the instrument, the farther away the tuning would be
> from being "correct" if you were to choose this as your new new tonic.

Good point, and on second thought I think I was mistaken and you're
absolutely right on this (as Jim's post also confirms). It seems
obvious now, as it's the same problem that historically lead to the
development and use of 12-Tone Equal Temperament, 12-TET. Other
tuning systems are more or less optimized for one key, and so
different keys are not enharmonically equivalent, so playing the same
thing in different keys will sound different. As you point out,
modulations will make notes sound somewhat more or less out of tune as
the key moves away from the one that's been optimized in that tuning
system (usually Cmaj / Amin). So each key has its own particular
'color', as the intervals of the key/scale are slightly different in
each one. I think this still holds even if your instrument has 19 or
more notes per octave in order to have "enharmonically equivalent"
notes (like C# and Db) tuned differently.

So it seems that in non-12-TET tuning systems, when modulating or
playing the same thing in different positions on the wiki-hayden
layout, fingering would stay the same for the same intervals, but the
precise tuning of these intervals would vary. Just like on a piano
not tuned to 12-TET.

This also means that Jim's dynamic tuning would require the use of a
shift/transpose key when modulating, unless one didn't mind the
different 'colors' of the different keys.

Paul M

[Jim_Plamondon]

There are two issues in "key color:"
(1) dimensionality mis-match, and
(2) the exposure thereof.

DIMENSIONALITY
All meantone tunings are inherently TWO-dimensional, being based on an
octave reduced stack of tempered perfect fifths -- hence the perfect
fifth dimension and the octave dimension. A piano keyboard is ONE-
dimensional, so the piano-mapping of meantone is to "true meantone"
what a (2D) shadow is to a 3D object. When you cast a shadow of a 3D
object on the ground, the resulting shadow is 2D -- its "depth"
dimension is lost. To map a 2D meantone tuning to the 1D piano
keyboard, you have to choose whether to include A# or Gb, for example.

Hence, the piano's "shadow" of meantone is irregular -- that is, not
all of its tempered perfect fifths are the same width -- only because
the piano keyboard's one-dimensional nature forces you to tune a
single black key to either A# or Gb (and the same for all other
"enharmonic" pairs). If you choose A#, then chords that include Gb are
going to sound wrong, because you have to play them with A#. This
inevitably leads to "wolf intervals" -- intervals that are tuned so
far from their proper ratios that they sound like wolves howling.

These wolf intervals are NOT inherent to meantone tunings. Rather,
they are the result of mapping a 2D temperament to a 1D keyboard. All
isomorphic note-layouts are 2D; on them, there are no wolf intervals
in any meantone tuning. Meantone's reputation for "limiting the
ability to modulte freely, due to its 'wolf tones' " is entirely
undeserved...when using an isomorphic keyboard. The same is true for
most other temperaments (e.g., irregular well-temperaments). To fit a
2D tuning onto the piano, its arms and legs must be broken, which
inevitably cripples it -- whereas it is undamaged on an isomorphic
keyboard (all of which are 2D).

The history of tuning & temperament has been polluted by the West's
single-minded focus on the piano keyboard. FOR THE PIANO KEYBOARD, 12-
tone equal temperament almost certainly is the best compromise,
despite its limitations. But isomorphic keyboards, being inherently
two-dimensional, enable a much wider range of tunings and temperaments
to be explored WITHOUT COMPROMISE.

The same is true for well-temperaments, such as Bach's, which are
neither equal not regular. In a well-temperament, some intervals of a
given interval-class are wider or narrower than others -- but they are
still of their given interval-class. On an isomorphic keyboard, a
given interval-class has a given shape wherever it occurs, whatever
its width. However, the NEED for well-temperaments is much lower on
an isomorphic keyboard, because it's 2D, and hence doesn't cripple 2D
tunings the way a piano keyboard does. Well-temperaments are a piano-
driven kludge.

So, using an isomorphic keyboard removes a restriction on tuning that
was historicaly imposed by the piano keyboard. However, to exploit
this, one has a choice: one either provides an enormous number of
buttons per octave (288 per octave, in the case of H-Pi's rather
ridiculous microtonal keyboards), or one uses relatively few buttons
(no more than 21) per octave and uses electronic transposition to keep
the current tonic centered on the keyboard. This latter approach not
only leads to a much smaller instrument, but also enables Dynamic
Tonality.

ORIGIN-TONIC INTERVAL
Consider a fixed-pitch instrument such as the piano, tuned to a
(crippled 1D version of) 1/4-comma meantone. It is tuned to maximize
the consonance of a given key, usually C major (and hence also the
other modes thereof, e.g. a minor). As one modulates away from this
key, on an acoustic piano, one can't adjust the tuning on the fly; one
is stuck with the tuning one started with. Each progressive modulation
to keys more distant from C Major -- that is, each widening of the
interval between the origin note and the current tonic -- exposes more
of the compromises made in the crippling mapping of a 2D tuning to a
1D keyboard.

These flaws are the source of "key color."

On an isomorphic keyboard, none of these crippling compromises must be
made in the first place, so no such flaws are exposed by progressive
modulations. Hence, there is no "key color" on an isomorphic keyboard,
unless one uses an irregular temperament, such as Bach's well-
temperament. However, well-temperaments are kludges, designed to
minimize the crippling effects of the dimensionality mis-match between
2D temperaments and a 1D keyboard, so there isn't much point in using
them on a 2D keyboard such as an isomorphc keyboard.

Bottom line: "key color" is an artifact of the piano keyboard. It's
not a feature; it's a bug.

[Jim_Plamondon]

On Aug 8, 1:55 am, John <jlmori...@gmail.com> wrote:
> I'm not positive to tell the truth but I think my reasoning is
> correct.
>
> If playing in anything but 12-edo, an attempt to play in a key not
> associated with "do" on the thummer will lead to the incorrect tuning.
> This is because (I think) when changing the tuning of the thummer one
> is changing the parameters creating the intervals starting at do and
> advancing outward on the instrument. So the farther away from do you
> get spacially (and therefore farther from the relatedness of the note
> from a tuning perspective) on the thummer, the more of an "impact" on
> the change in pitch of this note the changing of the parameter will
> have. This leads me to believe that the farther you get away from the
> assigned do on the instrument, the farther away the tuning would be
> from being "correct" if you were to choose this as your new new tonic.

You have correctly identified a sticky issue, but one with a known
solution.

The problem is the relationship between the tuning's origing note[0,
0] and the tonic's note[a, b] (where 'a' is the number of octaves, and
'b' the number of tempered perfect fifths, in the interval-vector from
the origin to the tonic).

Let's say that you start a piece in C Major. The origin note[0,0] and
the tonic[a, b] are on the same note, that is, b = 0 (b defines
"interval class," e.g. all Do's have the same b). Let's say that b =
0 = Do; therefore, Do is on [x, 0] (x being "some octave;" we don't
care which one).

Now, you modulate to G Major. The tonic has changed from [x, 0] to
[x, 1]. Why "1"? Because we've "moved up one perfect fifth," that is,
increased b by one.

Do we change the origin to G? No. The *origin note[0, 0]* starts,
and stays, on an overall piece's tonic -- that is, the tonic that a
piece starts on and, generally speaking, ends on. That way, no matter
how many modulations one executes -- whether of mode, key, tuning, or
even of temperament -- the final tonic's pitch will always be the same
as the starting tonic's pitch. You'll always come "home."

When we modulate from the initial C Major to G Major, the position of
the *current tonic* changes from [x, 0] to [x, 1]. That is, we moved
the tonic by the interval [0, 1]. If we then modulate to, say, D
minor, then we move the tonic by [0, 1] again (the origin stays fixed
at [0, 0]).

And so on. As we modulate from key to key, we're just adding intervals
to the current tonic's vector-from-the-origin.

As I just added in a different reply below, "key color" is an artifact
of the loss of dimensionality -- "shadowing" -- caused by the attempt
to squeeze a 2D temperament on to a 1D (piano) keyboard. No such
shadowing takes place when mapping a 2D temperament onto a 2D
keyboard, so there's no "key color" on a (2D) isomorphic keyboard
(although one could always kludge one up, if one really wanted to do
so). Key color is a *bug,* not a feature.

So, there is no interaction between using the "shift" key to change
tuning and "key color," because on an isomorphic keyboard, there's no
"key color" bug.

[John]

> Do we change the origin to G?  No.  The *origin note[0, 0]* starts,
> and stays, on an overall piece's tonic -- that is, the tonic that a
> piece starts on and, generally speaking, ends on. That way, no matter
> how many modulations one executes -- whether of mode, key, tuning, or
> even of temperament -- the final tonic's pitch will always be the same
> as the starting tonic's pitch. You'll always come "home."
>
> When we modulate from the initial C Major to G Major, the position of
> the *current tonic* changes from [x, 0] to [x, 1]. That is, we moved
> the tonic by the interval [0, 1]. If we then modulate to, say, D
> minor, then we move the tonic by [0, 1] again (the origin stays fixed
> at [0, 0]).

> So, there is no interaction between using the "shift" key to change
> tuning and "key color," because on an isomorphic keyboard, there's no
> "key color" bug.

I'm a little confused now. It sounds like here you are saying that
when one modulates using an isomorphic keyboard with a shift key, one
is neither changing the tuning nor transposing the entire instrument
to the new key, whereas I thought this was the case and this solved
the problem of how one would no longer be playing in the *correct*
tuning if one were to attempt to modulate with one's fingers on the
originally tuned layout.

Are you saying that all the tonics of the keys to which you modulate
will always be the pitches that were derived from the original tonic
and its tuning, but the tuning of the instrument will still be changed
for each modulation? And is the intent to have the current do on the
"do" button at all times, or is it to keep the original tonic in its
position for the entirety of a piece or section in which it is the
over all tonic?

[Jim_Plamondon]

On Aug 9, 3:17 pm, John <jlmori...@gmail.com> wrote:
> Are you saying that all the tonics of the keys to which you modulate
> will always be the pitches that were derived from the original tonic

> and its tuning, [...]

Yes.

> [...] but the tuning of the instrument will still be changed
> for each modulation?

No. Key-change modulations do not affect the tuning; only changes to
the widths of alpha (syntonic P8) or beta (syntonic P5), which
*define* the tuning, can change the tuning.

> And is the intent to have the current do on the

> "do" button at all times [...]

Yes...keeping in mind that "the current Do" and "the current tonic"
are not the same thing. For example, the tonic of minor (diatonic
Aeolian mode) is La, not Do.

> [...] or is it to keep the original tonic in its
> position for the entirety of a piece [...]

Yes.

I appreciate your interest and attention to detail. I apologize for
not having elucidated these concepts more clearly.

:-)

[John]

> Yes...keeping in mind that "the current Do" and "the current tonic"
> are not the same thing. For example, the tonic of minor (diatonic
> Aeolian mode) is La, not Do.

Oh! I think I see. As long as the modulation is within the modes of
the original diatonic scale, there is no need to transpose the entire
instrument because the "tonic" and "do" can be two different things.
And also the building of a tuning off of do mode is applicable to all
other modes of that diatonic scale, so the shift key is not used at
all when modulating within a given diatonic scale.

But what of modulations that take you outside of the current diatonic
scale, such as a progression from Cmaj7 (do=C) --> Abmaj7 (do=Ab) -->
F7 (do=Bb) --> G7 (do=C) --> Cmaj7 (do=C)...? Is this when the shift
key is used, to get to a new do?

> No. Key-change modulations do not affect the tuning; only changes to
> the widths of alpha (syntonic P8) or beta (syntonic P5), which
> *define* the tuning, can change the tuning.

I think I'm using "tuning" incorrectly. When I say change the tuning
for the instrument, I don't mean change the width of the beta, I am
just referring to the building of the same tuning off of a different
note. You've already explained this is unnecessary for modulations
within the current diatonic, but does one have to do that (change the
note around which the tuning is built) in an example like the one
above where the modulation takes you outside of the current diatonic
scale? And is this a case where it is done automatically by the shift
button?

> I appreciate your interest and attention to detail. I apologize for
> not having elucidated these concepts more clearly.

Thank you for your willingness to elaborate, I appreciate it a lot for
two reasons. 1. It's just nice to know what the intent for the
function of the thummer was because it reflects more study (I should
think) than anyone else has put into this sort of field, and 2. If we
are going to be building jammers I would like to be putting the best
concepts into practice.

[John Keller]

Hi John,

If i can butt in here, jim p explained to me a while back re the same
concerns about the "modulations" you are referring to. A chord progression
such as

Cmaj7 (do=C) --> Abmaj7 (do=Ab) -->
F7 (do=Bb) --> G7 (do=C) --> Cmaj7 (do=C)...?

is not really a modulation and he would not use the shift key.

Only "shift" when the key signature in TN actually changes!

Cheers, john K

----- Original Message -----
From: "John" <jlmo...@gmail.com>
To: "The Music Notation Project | Forum" <musicn...@googlegroups.com>
Sent: Tuesday, August 11, 2009 9:35 AM
Subject: [MNP] Re: Key signatures


>

[John]

Ok, cool. That actually makes the shift button make a lot more sense
ergonomically to me, seeing as one is not using it possibly every two
beats!
Thanks for all of the explanation :-]

John M

[Doug Keislar]

The other thing to keep in mind is that although the Thummer uses an isomorphic layout that is theoretically infinite, the actual instrument (prototypes only, alas) has only 19 notes per octave.  So when you play in keys that have lots of flats or sharps, you'll run off the side of the keyboard (button-field) when you try to play some familiar patterns that you've learned in, say, C major.  Unless you use the shift button.  In the case of 12-TET, where sharps on the right side of the instrument recur as flats on the left side, you can instead change the pattern to a different shape to use enharmonic equivalents -- but this approach diminishes the advantage of an isomorphic keyboard.  (The same problem of having to change the physical shape of a pattern -- and therefore having to learn more than one shape for a given set of pitches -- occurs constantly on a two-level 6-6 keyboard, where there are two shapes for each pattern, and not as often on a six-level Janko, where there are ironically many more possible shapes. Paul Vandervoort settled on five rows as the best practical compromise for a 6-6 layout.)

I'm not convinced that 19 keys per octave is enough for an isomorphic layout, unless one limits oneself to music that is not harmonically adventuresome.  But then the Thummer is strapped to your hand (in its primary use, although it can also be laid flat like a keyboard), so there are built-in ergonomic limits anyway.  I suppose it's fine for 99% of commercial popular music, and after all it was designed with commercial success as its goal.

Doug

[Ken on Google Rushton]

I'm wondering if two reprogrammed Axis-49's (set for W/H mode) placed side by side would do to make it 14 keys wide. Of course there would be a 6 cm gap. . . 

 

Ken.

[Jim_Plamondon]

Here's a document that describes a short chord progression in JIMS
notation:
www.igetitmusic.com/papers/JIMS_Sample.pdf

It's a scan of a hand-written document, so it's not as clear as
perhaps it should be.


---------------------
Chord: C - F - G - E - a - d - E - A
Key: C a A
---------------------

The initial stack of "scale dots," to the left of the crescent-scaped
JIMS clef, indicate the diatonic scale (Do, Re, Mi, Fa, So, La, Ti,
Do). Each note is indicated by a circular dot, except for Do. The
diamond-shaped scale dot on Do indicates that it is the tonic. Hence,
the song starts in "diatonic Do-mode" (Ionian/major).

The scale dots provide a guide to *harmonization.* In any scale (as I
understand it), one builds a chord on a given root by stacking scale-
based thirds on it. The scale dots indicate the stack of notes from
which such scale-based thirds are to be drawn. Melodic lines can, and
often do, depart from the harmonizing scale, albeit usually in
systematic ways (which are beyond the scope of this posting).

The above progression's first three chords, built by stacking thirds
from the current (diatonic) scale, are:
DoMiSo (C-E-G)
FaLaDo (F-A-C)
SoTiRe (G-B-D)

...commonly known as the "I-IV-V" chord progression or cadence.

Then there's:
(1) A mode change, from Do-mode to La-mode. No UI gesture is required
on the Thummer's keyboard to effect this change, because the same
pitches are associated with the same biuttons before and after a mode
change. It is just information provided to make the piece's harmonic
context clear.

(2) A scale change, from diatonic to harmonic minor. No UI gesture is
required. The new stack of scale dots does not include So, but does
include Si. The scale dots indicate that Si should be used instead of
So when stacking thirds for harmonization. Having this information is
very useful when improvising.

Note-head shape: natural notes use the traditional oval note-head
shape. Chromatic alterations use a triangular note-head shape, with
the direction in which the note-head points (up or down) indicating
the direction of alteration. Sharpened intervals (those on the right-
hand side of the Thummer's Wicki/Hayden note-layout) are indicated
using upward-pointing triangles ("sharp on top"); while flattened
intervals (those on the left-hand side) are downward-pointing
triangles ("flat on top"). For example, Si, being the sharpened
version of So, is indicated with an upward-pointing triangle, whereas
Le, being the flattened version of La, is indicated with a downward-
pointing triangle, both on the same vertical staff location (i.e.,
both appearing on the line between the So-space and the La-space).

The progression's next three chords, built by stacking thirds from the
current (harmonic minor) scale, are:
MiSiTi (E-G#-B)
LaDoMi (A-C-E)
ReFaLa (D-F-A)


Then there's:
(3) A mode change, from La-mode to Do-mode. No UI gesture is required.

(4) A scale change, back to diatonic. No UI gesture is required.

(5) A key change, notated as being "down a minor third" from Re down
to Ti.

For key changes, a UI gesture is required.
- Press and hold the shift button (to indicate that something's about
to change),
- tap Re (which indicates the start of a key-change gesture),
- tap Ti (indicating the "interval of modulation," relative to Re),
then
- release the shift button (to execute the change).

This gesture transposes the note-button mapping by the specified
interval, from Re to whatever (in this case, down a minor third to
Ti).

This same key change could have been notated as being "up a major
sixth" instead, with an arrow pointing from Re up to Ti (rather that
down to Ti, as shown). The latter results in notes that are an octave
higher than the former. In either case, the notation unambiguously
describes the key change interval -- and thereby the button-presses
needed to effect the key change.

The chords would usually be played with the left (accompanying) hand,
whereas the key change gesture would be played with the right
(melodic) hand. (Left-handers would probably reverse these roles.)
The need to play a key-change UI gesture is a "cost," relative to the
traditional mapping of buttons to fixed pitches, but one gets an
enormous amount of flexibility -- and a tiny keyboard, with all of the
expressive capabilities thereof -- in return. Think of it as changing
crooks on a pre-valve brass instrument, or moving the capo on a
guitar...but much faster. Because of this need to transpose pitches
on key changes, JIMS notation is only useful on trivially-transposed
instruments such as the Thummer & human voice.

The progression's final chords, after the key change, are
SoTiRe (E-G#-B) [or, preferably, SoTiReFa (E-G#-B-D)]
DoMiSo (A-C#-E)

g# is Si before the key change, and Ti afterwards. Same pitch,
different buttons. Why different buttons? Because that pitch fills a
different tonal role in C Major (and a minor) than it does in A Major,
and JIMS notates tonal roles, not pitches.

I've notated all of the chords in root position, for clarity. In
practice, the progression would probably use a mix of inversions to
provide better voice leading, but that's beyond the scope of this
discussion. I've also described the chords in "XxYyZz" form, rather
than using ThumChord or ThumField symbols, again for clarity.

The resulting JIMS notation provides:
a) a complete harmonic analysis of the notated music.
b) a 1:1 mapping between "notes on the staff" and "buttons to hit,"
just as traditional notation does. This is a pre-requisite for its
use in performance.

By providing such detailed harmonic analysis/context, JIMS is arguably
more "complicated" than traditional notation. But if that information
is NOT provided, then deriving it oneself -- as one must do when using
pitch-based notation -- is even MORE complicated, requiring the use of
parallel notations such as Roman numeral notation, figured bass,
Nashville Numbering, etc.

Likewise, transposing a piece written in JIMS notation to another key
is trivial. Indeed, you'll note that in the attached example, no key
is notated. The notation is the same in all keys. If a key must be
specified, then a single pitch (e.g., C4) can be associated with the
initial tonic diamond. To transpose the notation, erase the C4 and
write in some other pitch, and voila! -- it's transposed.

Similarly, the notaton -- and the buttons pressed on the keyboard --
is the same for all tunings of the syntonic temperament. Whether the
tuning has 5, 7, 12, 17, 19, 22, 24, 31, or an infinite number of
notes per octave; whether it's equal or unequal; whether it's regular
or irregular; even if it is a Just Intonation tuning -- in all of
these cases, the notation *and fingering* of a given piece is exactly
the same. This consistency of notation and fingering is essential for
dynamic tonality (www.igetitmusic.com/papers/DynamicTonality.pdf).

I appreciate this group's continued interest in this approach.

Thanks! :-)

--- Jim