Ideas for a simplified microtonal notation

There's just such a learning curve to micro-tonal theory...sometimes it makes me think "no wonder people are scared away from it so easily."
I intend this thread to be about any possible ideas to simplify "standard" micro-tonal notation.

Jacques told me ages ago to use the 12:13:15:17....format IE summarizing each scales as harmonic partials. I would simply call the above scale a "12th harmonic" scale because the ratios in it can all be summarized as being x over the 12th harmonic.
And, as such, diatonic JI would be an x/24 scale since it can be summarized (in most reduced form as)
24:27:30:32:36:40:45:48.
Note that the "x-th harmonic" format gives a fairly good sense of how much periodicity and JI-compliance a scale has...but leaves roughness out of the equation. An obvious example being the following scales
A) 21:24:28:35
B) 21:25:26:35

Note how scale B has it's smallest dyad at 25/26, which is much rougher than anything in scale B.
So I propose this "rating" of the scale
A) "21st harmonic, 24/21 minimum"
B) "21st harmonic, 26/25 minimum"

Now you might ask, what happens if something is de-tuned from or tempered off a harmonic series segment for whatever reason.

I did a test and found about the smallest ratio the human ear can hear as having a different tonal color is about 41/40.....so if something can't fit within the "40th harmonic" I propose the following notation...
"merges near 35st harmonic, approximate 38/37 minimum, exact notes of (list of notes as exact fractions)"
---------------------------------------------------------------------------------
If Just Intonation does one thing fairly well it gives us a quick way to look at fractions in a scale and take an educated guess at the levels of consonance we can obtain from it. I am just trying to think of a way the express micro-tonal music in such a way that
A) The average Joe can understand it and will feel less scared about using it
B) People can gain a quick sense of both the roughness and periodicity of the scale just at a quick glance (without sitting down and calculating anything)
C) People can easily compare JI scales with non-JI ones (with no cents vs. fraction and simple fraction IE 16/15 vs. complex fraction IE 161/147).
------------------------------------------------------

That's my idea for making micro-tonality easier to notate or approach...what are yours (for different ones and/or improvements to the one stated)?

When devising a notation for music, one must take into account his priorities concerning the music you want notated. If you want to notate just ratio's then something along the lines which you have described may be appropriate.

When dealing with rank 2 temperaments, however, there is a much much simpler approach. Rank 2 temperaments are, by definition, two dimensional, so as long as one has a two dimensional notation, you're all set. That is, one needs a notation that can define each possible note representation as a location in two dimensional space, where each location (or coordinate like (4,-2)) is that notes location in the stack of generators and periods. This works whether or not graphically the notation is actually two dimensional.

For example, this is possible on a one dimensional staff, using symbols (like accidentals) or alternate noteheads to represent the second dimension. Depending on which 2D temperament, the placement of each location in 2D space on the staff positions should be consistent with their possible relationships to adjacent staff spaces in pitch or frequency. Though Traditional notation does this and could theoretically notate a piece written anywhere on the syntonic temperament (or extended meantone temperament http://en.wikipedia.org/wiki/Syntonic_temperament), a far more ergonomic solution is JIMS. Instead of 7 lines/spaces per octave, it uses 12, and places each enharmonicaly equivalent pair (in 12-edo) on their own line/space. This allows the notation to function as a microtonal notation (it can represent any piece across the syntonic temperament) while actually being easier to read than traditional notation.

Note how rank 2 temperaments define the same location in the stack of generators and periods as having the same function, regardless of the size of the generators, and so a piece played in two tunings of the same temperament is predicted to function similarly. With a notation as described here, it will also look the same in notation.

An in depth look at JIMS notation system is here:
http://thummer.com/ThumMusic.pdf

A complete description of JIMS is here:
http://www.igetitmusic.com/papers/JIMS.pdf

And a (revised!) presentation discussing the topic is here:
http://www.slideshare.net/JlMoriart/fundamentals-of-music-3177075

John Moriarty

P.S. If you want, you can post your idea on the Music Notation Project forum, though I don't know how much of a response you'd get. They're more into the aesthetics of a chromatic notation, talking about colors and shapes, than they are about the actual theory behind the music which, in my opinion, should actually dictate the notation of music.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> There's just such a learning curve to micro-tonal theory...sometimes it makes me think "no wonder people are scared away from it so easily."
> I intend this thread to be about any possible ideas to simplify "standard" micro-tonal notation.
>
> Jacques told me ages ago to use the 12:13:15:17....format IE summarizing each scales as harmonic partials. I would simply call the above scale a "12th harmonic" scale because the ratios in it can all be summarized as being x over the 12th harmonic.
> And, as such, diatonic JI would be an x/24 scale since it can be summarized (in most reduced form as)
> 24:27:30:32:36:40:45:48.
> Note that the "x-th harmonic" format gives a fairly good sense of how much periodicity and JI-compliance a scale has...but leaves roughness out of the equation. An obvious example being the following scales
> A) 21:24:28:35
> B) 21:25:26:35
>
> Note how scale B has it's smallest dyad at 25/26, which is much rougher than anything in scale B.
> So I propose this "rating" of the scale
> A) "21st harmonic, 24/21 minimum"
> B) "21st harmonic, 26/25 minimum"
>
> Now you might ask, what happens if something is de-tuned from or tempered off a harmonic series segment for whatever reason.
>
> I did a test and found about the smallest ratio the human ear can hear as having a different tonal color is about 41/40.....so if something can't fit within the "40th harmonic" I propose the following notation...
> "merges near 35st harmonic, approximate 38/37 minimum, exact notes of (list of notes as exact fractions)"
> ---------------------------------------------------------------------------------
> If Just Intonation does one thing fairly well it gives us a quick way to look at fractions in a scale and take an educated guess at the levels of consonance we can obtain from it. I am just trying to think of a way the express micro-tonal music in such a way that
> A) The average Joe can understand it and will feel less scared about using it
> B) People can gain a quick sense of both the roughness and periodicity of the scale just at a quick glance (without sitting down and calculating anything)
> C) People can easily compare JI scales with non-JI ones (with no cents vs. fraction and simple fraction IE 16/15 vs. complex fraction IE 161/147).
> ------------------------------------------------------
>
> That's my idea for making micro-tonality easier to notate or approach...what are yours (for different ones and/or improvements to the one stated)?
>

Michael wrote:
> There's just such a learning curve to micro-tonal theory...sometimes
> it makes me think "no wonder people are scared away from it so
> easily." I intend this thread to be about any possible ideas to
> simplify "standard" micro-tonal notation.

Well, one problem is there's no such thing as a "standard" notation, even for such things as quarter tones. The reversed-flat symbol commonly used for a quarter tone flat represents a comma flat in Turkish notation. Another issue is that composers and performers have different needs as far as notation goes.

> Jacques told me ages ago to use the 12:13:15:17....format IE
> summarizing each scales as harmonic partials. I would simply call
> the above scale a "12th harmonic" scale because the ratios in it can
> all be summarized as being x over the 12th harmonic. And, as such,
> diatonic JI would be an x/24 scale since it can be summarized (in
> most reduced form as) 24:27:30:32:36:40:45:48. Note that the "x-th
> harmonic" format gives a fairly good sense of how much periodicity
> and JI-compliance a scale has...but leaves roughness out of the
> equation. An obvious example being the following scales A)
> 21:24:28:35 B) 21:25:26:35

So what would you do with the 7-limit tonality diamond, multiply all the ratios by 420? And that's a relatively small scale.

> Note how scale B has it's smallest dyad at 25/26, which is much
> rougher than anything in scale B. So I propose this "rating" of the
> scale A) "21st harmonic, 24/21 minimum" B) "21st harmonic, 26/25
> minimum"
> > Now you might ask, what happens if something is de-tuned from or
> tempered off a harmonic series segment for whatever reason.

Or what if the ratios of the intervals between notes in the scale are significant, as in Erv Wilson's golden horograms?

> I did a test and found about the smallest ratio the human ear can
> hear as having a different tonal color is about 41/40.....so if
> something can't fit within the "40th harmonic" I propose the
> following notation... "merges near 35st harmonic, approximate 38/37
> minimum, exact notes of (list of notes as exact fractions)" > ---------------------------------------------------------------------------------
> If Just Intonation does one thing fairly well it gives us a quick
> way to look at fractions in a scale and take an educated guess at the
> levels of consonance we can obtain from it. I am just trying to
> think of a way the express micro-tonal music in such a way that A)
> The average Joe can understand it and will feel less scared about
> using it B) People can gain a quick sense of both the roughness and
> periodicity of the scale just at a quick glance (without sitting down
> and calculating anything) C) People can easily compare JI scales with
> non-JI ones (with no cents vs. fraction and simple fraction IE 16/15
> vs. complex fraction IE 161/147). But this doesn't get rid of the need for calculation. Take for instance 8:9:10 vs. 36:40:45. What's the difference between these? It isn't immediately obvious that the interval between 8 and 10 is the same as between 36 and 45, and only the middle note is different, or that these are simply the same two step sizes in a different order.

> ------------------------------------------------------
> > That's my idea for making micro-tonality easier to notate or
> approach...what are yours (for different ones and/or improvements to
> the one stated)?

As a simplified notation, the 72-ET subset of Sagittal notation has some nice properties. For one, it's closely related to the standard notation for 12-ET, especially if you use the mixed-symbol version, and on the other hand, the symbols can be used to represent many common JI intervals. Then once you're familiar with 72-ET notation, it's not many steps from there to the Spartan subset of Sagittal, which works for many ET's and quite a few JI intervals.

But if you're already ignoring intervals smaller than 41/40 (42.7 cents), the 16.7 cent steps of 72-ET should be more than enough for a simplified notation.

On 21 February 2010 18:32, jlmoriart <JlMoriart@...> wrote:

> For example, this is possible on a one dimensional staff,
> using symbols (like accidentals) or alternate noteheads to
> represent the second dimension. Depending on which 2D
> temperament, the placement of each location in 2D space
> on the staff positions should be consistent with their possible
> relationships to adjacent staff spaces in pitch or frequency.
> Though Traditional notation does this and could theoretically
> notate a piece written anywhere on the syntonic temperament
> (or extended meantone temperament
> http://en.wikipedia.org/wiki/Syntonic_temperament),
> a far more ergonomic solution is JIMS. Instead of 7
> lines/spaces per octave, it uses 12, and places each
> enharmonicaly equivalent pair (in 12-edo) on their own
> line/space. This allows the notation to function as a
> microtonal notation (it can represent any piece across the
> syntonic temperament) while actually being easier to read
> than traditional notation.

Well, I read the introduction to JIMS, and I don't see what it has to
offer over conventional staff notation for meantone notation. That's
asserted but not demonstrated. If you know the reason then you can
enlighten me. Whether it's easier than traditional notation is a
matter of opinion. Chromatic notations aren't new and they never took
off for chromatic music, so why push them for microtonality?

Alternate noteheads for an extra dimension are a good idea. I thought
about them for tripod notation but didn't get them working with
LilyPond.

> Note how rank 2 temperaments define the same location in
> the stack of generators and periods as having the same
> function, regardless of the size of the generators, and so
> a piece played in two tunings of the same temperament is
> predicted to function similarly. With a notation as described
> here, it will also look the same in notation.

Same as with regular staff notation for meantone.

> An in depth look at JIMS notation system is here:
> http://thummer.com/ThumMusic.pdf

I don't get the microtonal implications of the notation. The keyboard
is all well and good. But it looks plain wrong when it comes to rank
2 temperaments in general. He says rank 2 temperament will work with
the ThumField. In fact, it assumes 5 tones and 2 semitones to an
octave, for suitable definitions of each interval. That's a
Pythagorean bias. You can only map temperaments with a one to one
mapping with Pythagorean intonation. That is, temperaments where an
octave and a fifth work together as the generators. That is,
meantone, schismatic, and mavila. Chromatic notation throws out
mavila.

Anyway, much as I support the general project (they pretty much agree
with me, after all) I'm unimpressed by this notation.

He doesn't mention jianpu, which I'm a bit miffed about. It's a
movable-doh system, one of the world's main notation systems (up there
with staff notation and guitar tablature), and western in origin (in
so far as that matters). It's also about the simplest system out
there (hence the name). If you're proposing something supposedly
simple for musical education it's jianpu that's your competition.

There's an assertion that Andrew Milne "was the first to recognize
the relationship between the structure of isomorphic note layouts
(such as the ThumField) and rank-2 regular temperaments – a
significant insight for which I suggest he deserves widespread
recognition." Is there any evidence for this? He's been sitting on
the idea for a long time if it's true. He doesn't mention it on his
website whereas Erv Wilson published it in the 70s, along with a
chromatic notation for meantone tied to a generalized keyboard. If
these were Mr Milne's ideas all along, it's time we set the record
straight.

> And a (revised!) presentation discussing the topic is here:
> http://www.slideshare.net/JlMoriart/fundamentals-of-music-3177075

"Flash Player 9 (or above) is needed to view presentations."

> P.S. If you want, you can post your idea on the Music Notation
> Project forum, though I don't know how much of a response
> you'd get. They're more into the aesthetics of a chromatic
> notation, talking about colors and shapes, than they are about
> the actual theory behind the music which, in my opinion,
> should actually dictate the notation of music.

This is this place, is it?

http://musicnotation.org/mnma/

Interesting, didn't know about it before. Looks like you have to pay
for the directory of proposals, acknowledged in Mr Plamondon's
article. And it's on paper, which I don't like, because I'm tired of
carrying books round the world and throwing them away. Dare I ask if
decimal notation's in there? It's too early for tripod.

Graham

Regarding this paper:
<http://thummer.com/ThumMusic.pdf>

p.14 in figures 15 and 16 Plamondon shows diminished
fourths in notation, and calls them 'major thirds', because
they 'span four semitones'.

He makes the same mistake that beginning music theory
students make, counting keys on a piano to name intervals.
If I ever saw a student draw a piano keyboard on his music
theory homework or test, it was an automatic F. Placing
diminished fourths alongside major thirds and calling them
by the same name is embarrassingly amateurish.

Here's an even more egregious basic error from his blog:
<http://www.igetitmusic.com/blog/2010/02/lesson-0040.html>

Under the heading: "Music & Pedagogy" he writes:

"Lesson 4 is the first lesson to introduce JIMS keyboard.
The keyboard is introduced by deriving the pentatonic scale
from an octave-reduced stack of (tempered) (major) fifths.
Notice that the lesson never qualifies the term 'fifth' --
that is, it doesn't call it a 'perfect' fifth or a
'major' fifth. I don't want to, or need to, open that
can of worms quite yet. All in good time."

Oh my goodness. There is no such thing as a 'major fifth'
anywhere in traditional music theory; fifths are Perfect,
Augmented, or Diminished. Another F on his homework.

I found these two errors in a few minutes, skimming the
paper and the blog. What other errors can you find? ...
on second thought, don't waste your time.

The JIMS notation is similar to the hundred or so notations
proposed in Gardner Read's compendium of proposed
Notation Reforms, in that its inventor does not know enough
about music to bring anything useful to the table.
(N.B. an exception in that book is a notation by Erv Wilson,
who certainly gets my respect.)

I don't mean this as an attack on Plamondon at all. The
Thummer is fine. I just can't believe these writings of
his are being taken seriously by anybody. At the very least,
he needs to take a basic music theory course himself before
trying to teach what he obviously does not understand.

Best wishes,
AAH
=====

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> When devising a notation for music, one must take into account his priorities concerning the music you want notated. If you want to notate just ratio's then something along the lines which you have described may be appropriate.
>
> When dealing with rank 2 temperaments, however, there is a much much simpler approach. Rank 2 temperaments are, by definition, two dimensional, so as long as one has a two dimensional notation, you're all set. That is, one needs a notation that can define each possible note representation as a location in two dimensional space, where each location (or coordinate like (4,-2)) is that notes location in the stack of generators and periods. This works whether or not graphically the notation is actually two dimensional.
>
> For example, this is possible on a one dimensional staff, using symbols (like accidentals) or alternate noteheads to represent the second dimension. Depending on which 2D temperament, the placement of each location in 2D space on the staff positions should be consistent with their possible relationships to adjacent staff spaces in pitch or frequency. Though Traditional notation does this and could theoretically notate a piece written anywhere on the syntonic temperament (or extended meantone temperament http://en.wikipedia.org/wiki/Syntonic_temperament), a far more ergonomic solution is JIMS. Instead of 7 lines/spaces per octave, it uses 12, and places each enharmonicaly equivalent pair (in 12-edo) on their own line/space. This allows the notation to function as a microtonal notation (it can represent any piece across the syntonic temperament) while actually being easier to read than traditional notation.
>
> Note how rank 2 temperaments define the same location in the stack of generators and periods as having the same function, regardless of the size of the generators, and so a piece played in two tunings of the same temperament is predicted to function similarly. With a notation as described here, it will also look the same in notation.
>
> An in depth look at JIMS notation system is here:
> http://thummer.com/ThumMusic.pdf
>
> A complete description of JIMS is here:
> http://www.igetitmusic.com/papers/JIMS.pdf
>
> And a (revised!) presentation discussing the topic is here:
> http://www.slideshare.net/JlMoriart/fundamentals-of-music-3177075
>
> John Moriarty
>
> P.S. If you want, you can post your idea on the Music Notation Project forum, though I don't know how much of a response you'd get. They're more into the aesthetics of a chromatic notation, talking about colors and shapes, than they are about the actual theory behind the music which, in my opinion, should actually dictate the notation of music.
>
> --- In tuning@...m, Michael <djtrancendance@> wrote:
> >
> > There's just such a learning curve to micro-tonal theory...sometimes it makes me think "no wonder people are scared away from it so easily."
> > I intend this thread to be about any possible ideas to simplify "standard" micro-tonal notation.
> >
> > Jacques told me ages ago to use the 12:13:15:17....format IE summarizing each scales as harmonic partials. I would simply call the above scale a "12th harmonic" scale because the ratios in it can all be summarized as being x over the 12th harmonic.
> > And, as such, diatonic JI would be an x/24 scale since it can be summarized (in most reduced form as)
> > 24:27:30:32:36:40:45:48.
> > Note that the "x-th harmonic" format gives a fairly good sense of how much periodicity and JI-compliance a scale has...but leaves roughness out of the equation. An obvious example being the following scales
> > A) 21:24:28:35
> > B) 21:25:26:35
> >
> > Note how scale B has it's smallest dyad at 25/26, which is much rougher than anything in scale B.
> > So I propose this "rating" of the scale
> > A) "21st harmonic, 24/21 minimum"
> > B) "21st harmonic, 26/25 minimum"
> >
> > Now you might ask, what happens if something is de-tuned from or tempered off a harmonic series segment for whatever reason.
> >
> > I did a test and found about the smallest ratio the human ear can hear as having a different tonal color is about 41/40.....so if something can't fit within the "40th harmonic" I propose the following notation...
> > "merges near 35st harmonic, approximate 38/37 minimum, exact notes of (list of notes as exact fractions)"
> > ---------------------------------------------------------------------------------
> > If Just Intonation does one thing fairly well it gives us a quick way to look at fractions in a scale and take an educated guess at the levels of consonance we can obtain from it. I am just trying to think of a way the express micro-tonal music in such a way that
> > A) The average Joe can understand it and will feel less scared about using it
> > B) People can gain a quick sense of both the roughness and periodicity of the scale just at a quick glance (without sitting down and calculating anything)
> > C) People can easily compare JI scales with non-JI ones (with no cents vs. fraction and simple fraction IE 16/15 vs. complex fraction IE 161/147).
> > ------------------------------------------------------
> >
> > That's my idea for making micro-tonality easier to notate or approach...what are yours (for different ones and/or improvements to the one stated)?
> >
>

> p.14 in figures 15 and 16 Plamondon shows diminished
> fourths in notation, and calls them 'major thirds', because
> they 'span four semitones'.

That pdf was for the benefit of those who visited the thummer website, already knew basic western theory, and wanted to see its connection to the Thummusic system. I've asked him about it and he is fully aware the the "mistake", though it was on purpose.

> There is no such thing as a 'major fifth'
> anywhere in traditional music theory; fifths are Perfect,
> Augmented, or Diminished. Another F on his homework.

There isn't in traditional theory, but there is in JIMS. Let's take a look at why interval names are so called in the first place:

They are derived from functions in the diatonic scale. Each general interval (except the unison and octaves) like second, third, etc, exists twice in the diatonic scale. The larger one gets the name major and the smaller one is called minor.

For example, in the C diatonic scale, there is a second that spans two semitones (excuse the use of semitones, they're so much easier to use than locations in a stack of fifths) from C-D, D-E, F-G, G-A, and A-B. There is also one than spans only one semitone, from E-F and B-C.
So, the larger is called the major second and the smaller is called the minor.

The same applies to the third. There are two sizes in the diatonic scale that can function as thirds, the smaller size is labeled the minor and the larger is called the major.

This, in traditional theory, applies also to the sixth and seventh. *If* this interval naming pattern were to be continued *consistently*, it would apply to the fourth and fifth as well.

Notice how in the C major diatonic scale, there is still a small and large version of both the fourth and fifth. The large fourth occurs between F and B, the rest of the fourths in the diatonic scale are small, so our traditional "perfect fourth" *should* be the "minor fourth", and our traditional "augmented fourth" *should* be the "major fourth". In other words, the lydian mode makes use of the *major fourth*, and every other mode uses the minor one.

The small fifth occurs between B and F, and the rest of the fifths in the diatonic scale are the larger instance of the fifth, so our traditional "perfect fifth" *should* be called the "major fifth", and our traditional "diminished fifth" *should* be called the "minor fifth". In other words, the locrian mode makes use of the *minor fifth*, and every other mode uses the major one.

He is referring to the major fifth as defined by his improved system of interval naming, not because he is making elementary mistakes.

Does this make sense?

John Moriarty

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> > p.14 in figures 15 and 16 Plamondon shows diminished
> > fourths in notation, and calls them 'major thirds', because
> > they 'span four semitones'.
[...]
>
> He is referring to the major fifth as defined by his improved system of interval naming, not because he is making elementary mistakes.
>
> Does this make sense?

I can understand that, but I think it is not justifiable.

In the diatonic scale, the tritone and the diminished fifth are like "anomalies" -- the quality of these intervals is rather different from the quality of perfect 4ths and perfect 5ths, and there is only one aug/dim against 6 perfect intervals. Major/minor 3rds and 6ths are more evenly distributed in a diatonic scale, and were not historically considered that opposed in quality. I don't support proposals that redefine quite traditional concepts in ways which are inconsistent with the traditional practice, erasing the history.

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:

> The small fifth occurs between B and F, and the rest of the fifths
> in the diatonic scale are the larger instance of the fifth, so our
> traditional "perfect fifth" *should* be called the "major fifth",
> and our traditional "diminished fifth" *should* be called the
> "minor fifth". In other words, the locrian mode makes use of the
> *minor fifth*, and every other mode uses the major one.
>
> He is referring to the major fifth as defined by his improved
> system of interval naming, not because he is making elementary
> mistakes.
>
> Does this make sense?

For what it's worth, in traditional theory, the difference
between major and minor intervals is 25/24, whereas the
difference between perfect and diminished/augmented is 256/243.
Ignoring this difference it implies srutal temperament,
which 12 supports but 19 does not...

-Carl

Hi John.

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> > p.14 in figures 15 and 16 Plamondon shows diminished
> > fourths in notation, and calls them 'major thirds', because
> > they 'span four semitones'.
>
> That pdf was for the benefit of those who visited the thummer
> website, already knew basic western theory, and wanted to see
> its connection to the Thummusic system. I've asked him about
> it and he is fully aware the the "mistake", though it was on purpose.

It reads as if the author is ignorant.

> > There is no such thing as a 'major fifth'
> > anywhere in traditional music theory; fifths are Perfect,
> > Augmented, or Diminished. Another F on his homework.
>
> There isn't in traditional theory, but there is in JIMS.
> Let's take a look at why interval names are so called in the
> first place:

Yes, let's do that. Read this:
<http://www.h-pi.com/theory/foreword.html>

Yours,
AAH
=====

> the quality of these intervals
> is rather different from the quality of
> perfect 4ths and perfect 5ths

I highly disagree. I find that the "major fourth" (traditionally the augmented fourth) has a very "fourthy" quality to it, and I would suggest that the only reason people don't connotate it with diatonic fourthness is because they are dissuaded from doing so by traditional theory and practice. The same would go for the fifths, the minor (traditionally diminished) version still sounding very much so like a fifth both melodically and harmonically.

> I don't support proposals that redefine
> quite traditional concepts in ways which
> are inconsistent with the traditional practice,
> erasing the history.

Is tradition so important as to impose a greater load on a learner of music theory? I wouldn't have thought so at least.

John Moriarty

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
>
> > the quality of these intervals
> > is rather different from the quality of
> > perfect 4ths and perfect 5ths
>
> I highly disagree. I find that the "major fourth" (traditionally the augmented fourth) has a very "fourthy" quality to it, and I would suggest that the only reason people don't connotate it with diatonic fourthness is because they are dissuaded from doing so by traditional theory and practice. The same would go for the fifths, the minor (traditionally diminished) version still sounding very much so like a fifth both melodically and harmonically.

You can find that, but these intervals have a history. Today, nobody would fear the "diabolous in musica", but this concept is relevant to understand old music. The different naming itself lead us to revise the history, to learn about old practices, their transformations, and therefore lead us to put our present impressions in a critical perspective.

>
> > I don't support proposals that redefine
> > quite traditional concepts in ways which
> > are inconsistent with the traditional practice,
> > erasing the history.
>
> Is tradition so important as to impose a greater load on a learner of music theory? I wouldn't have thought so at least.

Someone learning that way might become somewhat ignorant of history and musical culture. I see no sense in renaming old basic concepts (actually: deleting old concepts), or to be so indulgent as to avoid a so quite elementar and easy "load". That is a kind of comfort that brings no contribution (wealthy) to the musical culture.

Please excuse me the somewhat exaggerated comparison, but I think it is like denying the "Holocaust" or justifying terrorist wars on false claims of "terrorism": an interpretation of the facts that is more favorable for some group is presented as an universal truth in a way which is inconsistent with the actual historical facts.

Of course, one can argue (as you did above) that the traditional classification can cause a similar --conservative-- effect; that is an issue I think should be addressed from a comprehensive perspective, comparing old and current pratices, and maybe speculating for new practices, but not just deleting names or concepts.

To avoid misunderstaning: I consider valid to question and to redefine musical concepts from a creative perspective, as an esthetical approach (namely, treating "perfect" and "aug/dim." intervals as similar, not opposing them as consonance versus dissonance); but I don't agree that personal poetics should affect elementary instruction on conventional concepts (names!) in a radical way.

In some moment, your pupils must learn the traditional interval classification, if they are going to be professional musicians. Then you might have imposed a greater load on the learners, since they should learn intervals twice...

Hudson

>
> John Moriarty
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> For what it's worth, in traditional theory, ... the
> difference between perfect and diminished/augmented is 256/243.

Did you mean that? (It's a Pythagorean interval and I was expecting you to say 16/15 or 27/25. Even then I am not sure I fully understand which, or why this is so.)

Steve.

Well, let me add to the confusion (or give some clarity).
Classic augmented or dimished intervals are usually by 25/24 relevant to the
pythagorean interval.
A classic augmented fifth is 3/2 + 25/24 = 25/16
A classic augmented second is 9/8 + 25/24 = 75/64
A classic diminished fourth is 4/3 - 25/24 = 32/25

However intervals diminished by 135/128 or 16/15 are also called diminished,
sometimes wide diminished.
As for 27/25, I don't think that's ever used as a diminishing interval.

Marcel

--- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, "Carl Lumma"
> <carl@...> wrote:
> > For what it's worth, in traditional theory, ... the
> > difference between perfect and diminished/augmented is 256/243.
>
> Did you mean that? (It's a Pythagorean interval and I was expecting you to
> say 16/15 or 27/25. Even then I am not sure I fully understand which, or why
> this is so.)
>
> Steve.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > For what it's worth, in traditional theory, ... the
> > difference between perfect and diminished/augmented is 256/243.
>
> Did you mean that? (It's a Pythagorean interval and I was
> expecting you to say 16/15 or 27/25. Even then I am not sure
> I fully understand which, or why this is so.)
>
> Steve.

Yes, it's five 3:2s, the Pythagorean limma. In other words,
the terminology distinction is probably justified.

-Carl

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Well, let me add to the confusion (or give some clarity).
> Classic augmented or dimished intervals are usually by 25/24
> relevant to the pythagorean interval.
> A classic augmented fifth is 3/2 + 25/24 = 25/16
> A classic augmented second is 9/8 + 25/24 = 75/64
> A classic diminished fourth is 4/3 - 25/24 = 32/25
>
> However intervals diminished by 135/128 or 16/15 are also called
> diminished, sometimes wide diminished.
> As for 27/25, I don't think that's ever used as a diminishing
> interval.
>
> Marcel

The difference between a major 3rd and minor 3rd is 25/24.
The difference between a perfect 5th and diminished 5th is
usually understood in Pythagorean terms. This limma is the
same size as 25/24 in 12-ET, since 12-ET is a srutal
temperament. So JIMS seems to be assuming srutal temperament
by erasing the distinction.

2nds are also called major/minor, not aug/dim. If we
continue to assume that the maj/min terminology indicates
the 5-limit, then major 2nds are 9/8 and 10/9 and minor
2nds are 16/15, and the difference between them is again
25/24 or its 81/80 alternate, 135/128.

So the standard terminology makes sense.

-Carl

Carl wrote:

> The difference between a perfect 5th and diminished 5th is
> usually understood in Pythagorean terms.

Do you mean that a dim. 5th should be 1024/729 and that the aug. 4th should be 729/512? Not sure why that should be the case in the context of 5-limit triadic harmony.

In an ordinary 5-limit diatonic scale, a diminished fifth comes out as 64/45 and an augmented fourth is 45/32, which means they are higher or lower than their "unaltered counterparts" by 135/128.

If I take the three one-step intervals (9/8, 10/9, 16/15) and change the scale of "lmslmls" to "lmlsmls", the fourth will raise by 135/128.

If I stack two minor thirds, I get 36/25, which leaves a chroma of 25/24 to add up to 3/2.

Anyway, the Pyth. apotome doesn't seem to occur there.

Petr

>> There is no such thing as a 'major fifth'
>> anywhere in traditional music theory; fifths are Perfect,
>> Augmented, or Diminished. Another F on his homework.

> There isn't in traditional theory, but there is in JIMS. Let's take a look at why interval names are so called in the first place:

What are you doing then with the augmented/diminished seconds, thirds, sixths and sevenths?

Redefining terminology that has been established for centuries needs very good reasons (which I did not see so far), otherwise it only results in confusion. What are the reasons that conventional terminology is incompatible with your theory?

Best,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Just to be a bit more specific: if you are using other temperaments besides 12-TET (as you certainly do), or if you simply want to read classical music, then you need some terminology for, e.g., the interval C-A# (the augmented sixth).

Best
Torsten

---------------------

>> There is no such thing as a 'major fifth'
>> anywhere in traditional music theory; fifths are Perfect,
>> Augmented, or Diminished. Another F on his homework.

> There isn't in traditional theory, but there is in JIMS. Let's take a look at why interval names are so called in the first place:

What are you doing then with the augmented/diminished seconds, thirds, sixths and sevenths?

Redefining terminology that has been established for centuries needs very good reasons (which I did not see so far), otherwise it only results in confusion. What are the reasons that conventional terminology is incompatible with your theory?

Best,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
http://strasheela.sourceforge.net
http://www.torsten-anders.de

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> > The difference between a perfect 5th and diminished 5th is
> > usually understood in Pythagorean terms.
>
> Do you mean that a dim. 5th should be 1024/729 and that the aug.
> 4th should be 729/512? Not sure why that should be the case in
> the context of 5-limit triadic harmony.
> In an ordinary 5-limit diatonic scale, a diminished fifth comes
> out as 64/45 and an augmented fourth is 45/32, which means they
> are higher or lower than their "unaltered counterparts" by
> 135/128.
> If I stack two minor thirds, I get 36/25, which leaves a chroma
> of 25/24 to add up to 3/2.

The 5-limit chromatic unison vector is 25/24, and the commatic
vector is 81/80. That means all the 5-limit chromatic shifts
in the diatonic scale are 25/24 or its equivalents. But the
scale also has a valid 3-limit interpretation. In tunings where
these interpretations differ, having different terminology may
be useful.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> The difference between a major 3rd and minor 3rd is 25/24.
> The difference between a perfect 5th and diminished 5th is
> usually understood in Pythagorean terms. ...
> 2nds are also called major/minor, not aug/dim. If we
> continue to assume that the maj/min terminology indicates
> the 5-limit, then major 2nds are 9/8 and 10/9 and minor
> 2nds are 16/15, and the difference between them is again
> 25/24 or its 81/80 alternate, 135/128.

I see the point - but I have not heard this before. I was expecting that if one was Pythagorean, the other would be too; and if one contained a factor 5, the other would too.

And, wait - minor 2nd = 256/243 and augmented unison = 25/24 - that implies major 2nd = 800/729 ... ?

Steve.

Hi Steve,

I see the point - but I have not heard this before. I was expecting that if
> one was Pythagorean, the other would be too; and if one contained a factor
> 5, the other would too.
>
> And, wait - minor 2nd = 256/243 and augmented unison = 25/24 - that implies
> major 2nd = 800/729 ... ?
>
> Steve.
>

12tet notation does not translate to correct 5-limit JI.
You cannot say an augmented something is allways x/x.

As far as I'm personally concerned. All 5-limit intervals used in common
practice music are these:

Interval class (*: not unique), Number of incidences, Size:
1: 3 25/24 70.672 cents classic chromatic semitone, minor
chroma
1: 4 16/15 111.731 cents minor diatonic semitone
1: 1 27/25 133.238 cents large limma, BP small semitone
2: 4 10/9 182.404 cents minor whole tone
*: 4 9/8 203.910 cents major whole tone
3: 1 75/64 274.582 cents classic augmented second
3: 1 32/27 294.135 cents Pythagorean minor third
*: 6 6/5 315.641 cents minor third
*: 6 5/4 386.314 cents major third
3: 2 32/25 427.373 cents classic diminished fourth
*: 7 4/3 498.045 cents perfect fourth
4: 2 27/20 519.551 cents acute fourth
5: 2 25/18 568.717 cents classic augmented fourth
5: 2 45/32 590.224 cents diatonic tritone
5: 2 64/45 609.776 cents 2nd tritone
5: 2 36/25 631.283 cents classic diminished fifth
6: 2 40/27 680.449 cents grave fifth
*: 7 3/2 701.955 cents perfect fifth
7: 2 25/16 772.627 cents classic augmented fifth
*: 6 8/5 813.686 cents minor sixth
*: 6 5/3 884.359 cents major sixth, BP sixth
7: 1 27/16 905.865 cents Pythagorean major sixth
7: 1 128/75 925.418 cents diminished seventh
*: 4 16/9 996.090 cents Pythagorean minor seventh
8: 4 9/5 1017.596 cents just minor seventh, BP seventh
9: 1 50/27 1066.762 cents grave major seventh
9: 4 15/8 1088.269 cents classic major seventh
9: 3 48/25 1129.328 cents classic diminished octave

You will find all these intervals in the following interval matrix:

1 2 3 4 5 6 7 8 9 10
1/1 : 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
9/8 : 16/15 10/9 32/27 4/3 64/45 40/27 8/5 5/3 16/9 2/1
6/5 : 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1
5/4 : 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1
4/3 : 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1
3/2 : 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1
8/5 : 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1
5/3 : 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1
9/5 : 25/24 10/9 5/4 4/3 25/18 40/27 5/3 16/9 50/27 2/1
15/8: 16/15 6/5 32/25 4/3 64/45 8/5 128/75 16/9 48/25 2/1
2/1

This is my 6-limit harmonic model.
After these come 7-limit intervals in my opinion.

Btw, notice how in Scala the 45/32 is called the diatonic tritone, and 25/18
the augmented fourth.
Yet when we take the C major scale for instance: C(1/1) D(9/8) E(5/4) F(4/3)
G(3/2) A(5/3) B(15/8) C(2/1)
Normal music theory calls F(4/3) - B(15/8) an augmented fourth, which would
be 45/32.

Again, don't get too hung up giving fixed ratios to certain named intervals.
It doesn't work out (unless you rename everything ever made after
translating something to JI)

Marcel.

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> don't get too hung up giving fixed ratios to certain named intervals.
> It doesn't work out (unless you rename everything ever made after
> translating something to JI)

The interval names used in Scala are largely unsystematic and
cannot be thought of as any kind of standard naming system;
they are a collection of names all mixed up higgledy-piggledy, with
no compelling unifying reason for being that way. A straightforward
systematic approach is much more helpful and useful. Just add 2
modifiers to traditional pitch and interval names to expand the
traditional system to include all possible intervals of any harmonic
limit. Please see here:
Pitches:<http://www.h-pi.com/theory/huntsystem3.html>
Intervals: <http://www.h-pi.com/theory/huntsystem4.html>
(Overview:<http://www.h-pi.com/theory/huntsystem1.html>)

Yours,
AAH
=====

Hello Aaron,

The interval names used in Scala are largely unsystematic and
> cannot be thought of as any kind of standard naming system;
> they are a collection of names all mixed up higgledy-piggledy, with
> no compelling unifying reason for being that way. A straightforward
> systematic approach is much more helpful and useful. Just add 2
> modifiers to traditional pitch and interval names to expand the
> traditional system to include all possible intervals of any harmonic
> limit. Please see here:
> Pitches:<http://www.h-pi.com/theory/huntsystem3.html>
> Intervals: <http://www.h-pi.com/theory/huntsystem4.html>
> (Overview:<http://www.h-pi.com/theory/huntsystem1.html>)
>
> Yours,
> AAH
> =====

Very nice pages you've created!
And I do think a system like this could be usefull.
But in my opinion only when music theory is seriously rewritten and people
would start using a system like this that translates correctly to JI.
But as it stands, such systems do not translate common practice music to
correct JI.
As in common practice notation different JI ratios are written with thesame
name/notation, and notation allows one to get away with things that would
have had to been written completely different for JI.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> Very nice pages you've created!

Thank you, Marcel.

> And I do think a system like this could be usefull.
> But in my opinion only when music theory is seriously rewritten
> and people would start using a system like this that translates
> correctly to JI.

It sounds like here you are confirming that my system does translate
correctly to JI (which it does) ...

> But as it stands, such systems do not translate
> common practice music to correct JI.

... but here it sounds like you are saying that my system doesn't
translate common practice music to correct JI. I think that you
meant to say that the traditional theory is not adequate for translating
common practice tonality into JI, and that's certainly correct.

> As in common practice notation
> different JI ratios are written with the same name/notation, and notation
> allows one to get away with things that would have had to been
> written completely different for JI.

I think this is clarifying your last statement as I rendered it above.
Yes, that's certainly true. That's the whole reason to expand and clarify
the existing system as I do. My system does not disrupt standard music
theory. It rather logically expands and clarifies it. Existing theory doesn't
need to be rewritten, only expanded and clarified. Rewriting it, especially
in a manner as JIMS which invents badly formed interval names that
totally contradict existing history, is nonsensical.

Cheers,
AAH
=====

> What are you doing then with the augmented/diminished seconds, thirds, sixths and sevenths?

Intervals other than the fourth and fifth are named consistently and so their names are retained in JIMS. The fourth's and fifth's interval sizes are named differently (because of the previous reasons) as follows:

The perfect fifth becomes the major fifth, the augmented fifth remains the augmented fifth, the diminished fifth becomes the minor fifth, and the doubly diminished fifth becomes the diminished fifth.

The perfect fourth becomes the minor fourth, the augmented fourth becomes the major fourth, the doubly augmented fourth becomes the augmented fourth, and the diminished fourth remains as named.

> Redefining terminology that has been established for centuries needs very good reasons (which I did not see so far), otherwise it only results in confusion. What are the reasons that conventional terminology is incompatible

It's incompatibility is in its inconsistency. JIMS is a system of isomorphism (or "same shape"), consistency, and patterns. Same fingering every key and every tuning through isomorphic keyboards. Same terminology for every key using movable do solfeggio. Same notation every key and tuning with chromatic staves.

Should an interval naming system be used with known inconsistencies that make the learning process longer and harder, it would go against everything that JIMS is trying to be: an easier musical system that manages to provide the same musical literacy in (hopefully) one hundredth the time by making all musically relevant patterns more visible and accessible (through isomorphic keyboards and notation), by leaving out all previous musically irrelevant theory (like learning each key differently) regardless of historical relevance, and by making any convoluted or inconsistent theory (like interval naming) consistent.

And though I think that though one can argue that one's system preference is an opinion, as for which system is actually easier is not an opinion. It's like being offered $20 to run either one mile or three. Though whether one would prefer to run a mile or three may be of matter of opinion, but which one is actually easier or more efficient (when taking into account dollars per distance) is not an opinion.

> with your theory?

Just so you know, this isn't my theory; it's Jim Plamondon's system. I do support its use however and have followed its development. It is, even now, still an evolving system.

John Moriarty

Hi Aaron,

Thank you, Marcel.
>
>
> > And I do think a system like this could be usefull.
> > But in my opinion only when music theory is seriously rewritten
> > and people would start using a system like this that translates
> > correctly to JI.
>
> It sounds like here you are confirming that my system does translate
> correctly to JI (which it does) ...
>

Well, your system has a much higher resolution than 12tet so if the music
was written correctly in your system then it would be much easyer to
translate to JI ratios.
But in extreme cases this may not be enough and translation errors would
still occur it seems to me.

It seems to me the only notation system (besides writing the ratios down
themselves) that would work would be a system that indicates a root,
indicates a large set of intervals relevant to that root, and a way to
indicate root changes.

>
> > But as it stands, such systems do not translate
> > common practice music to correct JI.
>
> ... but here it sounds like you are saying that my system doesn't
> translate common practice music to correct JI. I think that you
> meant to say that the traditional theory is not adequate for translating
> common practice tonality into JI, and that's certainly correct.
>

Yes that was was I was mostly saying. Traditional theory isn't adequate for
translating common practice music into JI.

>
>
> > As in common practice notation
> > different JI ratios are written with the same name/notation, and notation
>
> > allows one to get away with things that would have had to been
> > written completely different for JI.
>
> I think this is clarifying your last statement as I rendered it above.
> Yes, that's certainly true. That's the whole reason to expand and clarify
> the existing system as I do. My system does not disrupt standard music
> theory. It rather logically expands and clarifies it. Existing theory
> doesn't
> need to be rewritten, only expanded and clarified. Rewriting it, especially
> in a manner as JIMS which invents badly formed interval names that
> totally contradict existing history, is nonsensical.
>
> Cheers,
> AAH
> =====
>

It all leaves me with one thought.
Why design new notation systems while JI ratios will avoid any confusion
whatsoever and have no limit? (pun intended)
Atleast for JI purposes that is, for temperaments I understand.

Marcel

> The perfect fifth becomes the major fifth, the augmented fifth remains the augmented fifth, the diminished fifth becomes the minor > fifth, and the doubly diminished fifth becomes the diminished fifth.

Sorry, I find this extremely confusing for your students, they will not be able to communicate with the rest of the musical world. IN the end, they then will have to learn both terminologies, not very simplifying.

Besides, only the perfect fifth is consonant, you loose this distinction.

Best,
Torsten

On 1 March 2010 10:10, jlmoriart <JlMoriart@...> wrote:

> It's incompatibility is in its inconsistency. JIMS is a system of isomorphism (or "same shape"), consistency, and patterns. Same fingering every key and every tuning through isomorphic keyboards. Same terminology for every key using movable do solfeggio. Same notation every key and tuning with chromatic staves.

How do chromatic staves get you the same notation for every key and
tuning? I don't see it. I can see that chromatic scales get you the
same notation for every subset of the chromatic scale. But enforcing
that means you lose tuning isomorphism. This isn't in the PDFs and
you haven't addressed it here.

> And though I think that though one can argue that one's system preference is an opinion, as for which system is actually easier is not an opinion. It's like being offered $20 to run either one mile or three. Though whether one would prefer to run a mile or three may be of matter of opinion, but which one is actually easier or more efficient (when taking into account dollars per distance) is not an opinion.

Which system's easier is an opinion and will remain so until there are
properly controlled studies establishing it. Carving the musical
world up into two competing systems is not a fact. Which system of
notation (the topic here) is based on a larger scale is a fact. That
staff notation and jianpu are already consistent with meantone, and
work with different tunings, is also a fact. That existing, acoustic
instruments require different fingerings for different scales is a
fact.

Graham

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> It all leaves me with one thought.
> Why design new notation systems while JI ratios will avoid any
> confusion whatsoever and have no limit? (pun intended)
> Atleast for JI purposes that is, for temperaments I understand.

If ratios alone suit your needs, then by all means use them. But
if you want something in a so-called musical notation, it's another
problem. You may be interested in my H-Chroma which allows
combinatorial 47-Limit JI to me notated. It has all those things
you mention, allowing 38,245 possible JI ratios per octave to be
easily notated. I don't have web pages for this yet, but will be
giving a presentation on it at the Ben Johnston symposium
at Wright State. I also have invented an instrument that uses this
system. It's been developed since 10 years ago. I lent the prototype,
'The Goose', to Jacob Barton and Andrew Heathwaite at OddMusic
in Champaign-Urbana, but recently picked it up before my move
and I will have it with me at the symposium. See the OddMusic photo:
<http://oddmusicuc.wordpress.com/2009/06/15/oddmusic-office-hours/>

Cheers,
AAH
=====

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
Steve>> And, wait - minor 2nd = 256/243 and augmented unison = 25/24 - that implies major 2nd = 800/729 ... ?
Marcel> 12tet notation does not translate to correct 5-limit JI. You cannot say an augmented something is allways x/x. ...
> 5: 2 36/25 631.283 cents classic diminished fifth ...
> Again, don't get too hung up giving fixed ratios to certain named intervals.

That was my point; I thought that Carl was saying that the 256/243 and 25/24 were the fixed ratios - but I see that in other posts he says that the nomenclature (perfect/diminished) is worth preserving as it originated in a different place (from major/minor) and in any case the ratios can be varied by a comma or so (depending on context, I assume).

Steve.

> How do chromatic staves get you the same notation for every key and
> tuning?

The same way you get it with traditional notation. You add another dimension
to the notation not having to to with vertical position. In traditional
notation, sharps and flats give you isomorphism across all tunings in the
syntonic temperament, but they're a nightmare to read. In JIMS notation,
alternate noteheads are used for seven of the chromatic locations to tell
apart enharmonic equivalents (this giving you the 19 notes that JIMS uses at
once for any given tonic), then arrows are used to notate transposition of
the entire staff for when modulation occurs and the tonal center of the
entire piece changes.

One reason chromatic staves are used is because they are simply more
ergonomic; there is less inherent mental load to the system because for each
location on the staff there are less possible notes possibly being
represented:
In traditional notation, any given staff location can represent an
*infinite* number of notes through sharps and flats, though traditionally
it's likely to represent one of maybe 5.
With a chromatic staff using alternate noteheads a given staff location will
only ever represent one or two notes. Less cognitive load.

The more technichal reason that a chromatic staff is used (as opposed to an
enharmonic staff with 19 staff locations which would give a unique staff
location to each note that JIMS defines as functionally relevant to a given
tonic) is that the enharmonic notes will sometimes be higher and sometimes
be lower that their counterpart depending on the tuning. If each enharmonic
note were given a unique line or space, the intuitive one dimensional aspect
of the staff locations corresponding to pitch would become void. Because Eb,
depending on the tuning, maybe be higher than, lower than, or equivalent to
D#, they must be put on the same line and differentiated between by some
other means. Also, the chromatic scale is the scale over which there is no
overlapping of function across the entire syntonic temperament. In other
words, though Eb and D# overlap across the syntonic temperament, D and Eb
will never cross. F# and Gb may cross each other, but F# will not cross over
F.

> Which system's easier is an opinion and will remain so until there are
> properly controlled studies establishing it.

I was more-so trying to avoid the counter-argument that there is no
continuous load imposed on a user by any system, as long as he understands
the system. This seems obviously wrong to me because I understand
traditional notation but have a very hard time reading it, whereas I have
far less experience with chromatic notation but find it immensely easier to
read. I just wanted to point out that personal preference to a notation does
not affect its actual definable difficulty in its imposed load on a user.

> That existing, acoustic
> instruments require different fingerings for different scales is a
> fact.

Though true, the fact that instruments require different fingerings for each
scale doesn't support, I don't think, that traditional notation is any
more-so fit for standard instruments than chromatic notation. In fact, I
think chromatic notations are necessary to reveal to a musician with such an
instrument that in each key they are merely playing the same combinations of
intervals. I've played some (very little admittedly) chromatically notated
music on my trumpet, and still found it easier to read, just like it was
easier to read on my isomorphic keyboard.

For an interesting example, take any 12-edo instrument, isomorphic or not,
and imagine reading a song from both diatonic and chromatic notation without
regard to anything but staff position. Reading that song in diatonic
notation would result in as many mistakes as accidentals, whereas reading
that same song in a chromatic notation will result in exactly the desired
result.

John M

On 12 March 2010 06:55, John Moriarty <JlMoriart@...> wrote:
>
>
> > How do chromatic staves get you the same notation for every key and
> > tuning?
> The same way you get it with traditional notation. You add
> another dimension to the notation not having to to with
> vertical position. In traditional notation, sharps and flats give you
> isomorphism across all tunings in the syntonic temperament,
> but they're a nightmare to read. In JIMS notation, alternate
> noteheads are used for seven of the chromatic locations to tell apart
> enharmonic equivalents (this giving you the 19 notes that JIMS
> uses at once for any given tonic), then arrows are used to notate
> transposition of the entire staff for when modulation occurs and
> the tonal center of the entire piece changes.

So it's the same as what we have already ... by which you presumably
mean staff notation. But it's somehow an advance. And accidentals
are nightmare to read despite all the people who put themselves
through this nightmare over the centuries.

Only 19 notes at a time? That's not much for microtonal work.

> One reason chromatic staves are used is because they are
> simply more ergonomic; there is less inherent mental load to
> the system because for each location on the staff there are
> less possible notes possibly being represented:

But jianpu has all the notes in one location, so why doesn't that have
an intolerable mental load? Guitar tabulature also has a whole scale
crammed into each location. Why do guitarists put up with it?

> In traditional notation, any given staff location can represent an
> *infinite* number of notes through sharps and flats, though
> traditionally it's likely to represent one of maybe 5.

Only two or three at any time, with reasonable music. No more than
three if you have a 19 note limit.

> With a chromatic staff using alternate noteheads a given staff location
> will only ever represent one or two notes. Less cognitive load.

But there are also more locations. And the "one or two" is assuming
your 19 note restriction. Traditional notations work very well if you
restrict the music to a 7 note gamut.

> The more technichal reason that a chromatic staff is used
> (as opposed to an enharmonic staff with 19 staff locations which
> would give a unique staff location to each note that JIMS defines
> as functionally relevant to a given tonic) is that the enharmonic notes
> will sometimes be higher and sometimes be lower that their
> counterpart depending on the tuning. If each enharmonic note were
> given a unique line or space, the intuitive one dimensional aspect of
> the staff locations corresponding to pitch would become void.
> Because Eb, depending on the tuning, maybe be higher than,
> lower than, or equivalent to D#, they must be put on the same line
> and differentiated between by some other means. Also, the
> chromatic scale is the scale over which there is no overlapping of
> function across the entire syntonic temperament. In other words,
> though Eb and D# overlap across the syntonic temperament,
> D and Eb will never cross. F# and Gb may cross each other,
> but F# will not cross over F.

Eb and D# will not overlap for typical syntonic temperaments
(meantones). They will for a schismatic temperament, which is one
valid reason for using chromatic scales for microtonality, which the
papers you cited don't mention.

It helps to define your "entire syntonic temperament" so that this is
true. Switch to mavila and it doesn't work.

> > That existing, acoustic
> > instruments require different fingerings for different scales is a
> > fact.
> Though true, the fact that instruments require different fingerings
> for each scale doesn't support, I don't think, that traditional notation
> is any more-so fit for standard instruments than chromatic notation.
> In fact, I think chromatic notations are necessary to reveal to a
> musician with such an instrument that in each key they are merely
> playing the same combinations of intervals. I've played some
> (very little admittedly) chromatically notated music on my trumpet,
> and still found it easier to read, just like it was easier to read on
> my isomorphic keyboard.

I've played some jianpu-notated music on my dizi. It's easy to read
but you have to learn each key separately. That's always been the
problem with movable-do systems. It means your rule about not
learning new fingerings only works for the isomorphic keyboard. Which
is great for the keyboard, but you could also use jianpu with it,
which is a traditional notation.

> For an interesting example, take any 12-edo instrument, isomorphic
> or not, and imagine reading a song from both diatonic and chromatic
> notation without regard to anything but staff position. Reading that
> song in diatonic notation would result in as many mistakes as
> accidentals, whereas reading that same song in a chromatic notation
> will result in exactly the desired result.

Right, 12-edo. Chromatic notation would obviously be a good fit for
12-edo, but for all the years that 12-edo has been the standard, it
didn't catch on outside guitar tablature. Somehow you think it's good
for microtonality anyway. I don't see anything new here.

Graham

I'm in danger of getting dragged into small arguments here, so I'll
state my main point. What a lot of us would like, and what JIMS sort
of claims, is a notation with the following properties:

* transpositional isomorphism
* tuning isomorphism
* rank 2 tuning

I'll now define them.

Transpositional isomorphism: move a tune or chord to start on another
note, and in so far as it sounds the same, it looks the same.

Tuning isomorphism: you notate the structure, not the tuning, so the
same piece can be played with different tunings.

Rank 2 tuning: this is more than a simple division of the octave.

Now, if there's a notation system that can deliver on all of these at
the same time, I haven't seen it. I'd be very interested if somebody
can come up with one. But, there are basic problems with traditional
notations that JIMS doesn't overcome.

It is possible to have the two kinds of isomorphism if you use an
equal temperament. So, as 12-equal is a very important temperament,
chromatic notations are a valid way to get it to work isomorphically.
But if you transpose in a chromatic scale without it being equally
tempered, it's going to sound different, so you lose tuning
isomorphism. And if you have to add marks to say which tuning each
chromatic note should have, you lose transpositional isomorphism.
This isn't to say that the notation won't work, or isn't practical for
microtonality, only that the problems it has are exactly the same as
diatonic-based notations when you move to more general tunings.

All this wouldn't matter if the notation weren't being pushed along
with an isomorphic keyboard. It claims to solve problems with staff
notation. It also claims to be conceptually simpler. And then it
claims to work with arbitrary syntonic/meantone tunings. Once again
we have three claims that can't be true together.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> I'm in danger of getting dragged into small arguments here, so
> I'll state my main point. What a lot of us would like, and what
> JIMS sort of claims, is a notation with the following properties:
>
> * transpositional isomorphism
> * tuning isomorphism
> * rank 2 tuning
>
> I'll now define them.
>
> Transpositional isomorphism: move a tune or chord to start on
> another note, and in so far as it sounds the same, it looks
> the same.

I think this is always a good property for keyboards, but in
one important case, a bad property for notations. That one case
is generalized diatonic music. Projecting into consecutive
degrees of a generalized diatonic scale is important. In this
view, major and minor triads 'sound the same' in their native
positions the diatonic scale.

Of course this is an interjection, because if one isn't writing
generalized diatonic music, then an isomorphic notation is
desirable. So, carry on!

-Carl