Introducing music Visual set theory

[Music Integrated Solution]

I have spent these few days trying to figure out a way of presenting what I have been experimenting and talking about for some time now and think have a path to follow; communication of original ideas is a challenge, if anyone think what is written (so far) makes a difference with previous explanations or think deserve a comment (any kind), please do it.


Thanks
Enrique.

 

[Keislar, Doug]

Hi Enrique,

Thanks for the URL. It's great to see visual examples from you to help explain some of the things you've been trying to communicate in the recent past.

I believe I understand your system and what you're saying on that page. It took some time to figure it out. If you're interested in making it easier to understand, I would recommend a few things:

1. Start with a chromatic scale from C to C, instead of the John Legend example which most people won't be able to read or understand.
2. Also give the translation of things from your system into the traditional system, to help people understand which pitches are which. This could be done by labeling things with the traditional pitch names and in some cases showing the TN equivalent.
3. Something I recommend from time to time to other people on this list: When you present a piece of music (just as the John Legend excerpt), also present it in TN for comparison. It won't help people who know nothing about TN, but most of on this list have some familiarity with TN (if not fluency).
4. Possibly provide MIDI or MP3 so people can hear the depicted notes.

I have one question about the v-pc bars. I understand their purpose, but I don't understand the need to show all four "reference heads" (or whatever you're calling them these days) every time you show a v-normal order. Wouldn't it suffice to show only the reference heads that are needed to show the pcs in use? For example, for the first v-normal order you show -- dami -- why bother including the black and white rectangular reference heads at the top? Assuming you intend people to draw this notation, it's a lot of extra symbols to draw each time; and even if it's not intended for drawing, the extra symbols seem like an unnecessary distraction that actually make it harder to read in my opinion.

Doug

________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Music Integrated Solution [mtall...@gmail.com]
Sent: Saturday, January 02, 2016 12:28 PM
To: musicnotation
Subject: [MNP] Introducing music Visual set theory

I have spent these few days trying to figure out a way of presenting what I have been experimenting and talking about for some time now and think have a path to follow; communication of original ideas is a challenge, if anyone think what is written (so far)<http://musicintegratedsolution.blogspot.com/2015/12/introducing-music-visual-set-theory.html> makes a difference with previous explanations or think deserve a comment (any kind), please do it.


Thanks
Enrique.


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[Jessifeph John]

This is very neat Enrique. I like the direct translation between set theory terms and their visual counterparts, I like that you actually have a well formulated example to actually refer to, and I like the general goal of making set theory usable. My main issue, and I've brought it up before, is that there is no interval consistency. As far as I can tell, one would have to memorize the positions and their relationships to other positions without any aid. Look at the v-pc symbol for 0 2, 1 3, 2 4, you only gain some sort of consistency at 3 5, 6 8, and 9 11. The beauty of set theory comes when you know the distances between numbers, if not then 0 4 7 and 1 5 8 are not related. Consistent intervals is the visual equivalent of knowing distances between numbers. A rearrangement of your symbols can create the consistency while perhaps looking a bit cluttered:

                            

Now the colors layout the whole tone scale, similar shapes + color the augmented triad, and similar lines the diminished seventh. The only odd balls seem to be 5 and 7 but still have a sort of consistency which is different colors and a line pattern if one memorizes the order the lines go in which isn't hard to do, but in a sense the fact that they are oddballs gives them consistency. I think the ideal condition is one in which each resource (line, color, shape) accents a unique factor of 12 (2, 3, or 4). There are 6 possible permutations. Sadly they all seem to have a downside, I personally think 2col 3line 4shapes is the best.

My other issue is that the piano roll has a voice separation issue that I can't live with.

-Inopa

[Music Integrated Solution]

Doug,
Thanks for the comments, I am aware this draft has to go through several departments; it makes sense that if it claims to be an alternative to the traditional system it should show some graphic comparisons, but on the other hand I am trying to make it as small as possible because there is a lot to say; then I am going to try first communicating 'pitch class notation' with the piano kb and numerical pc notation, which are more universal.
1. I improved the table and moved it to be the first graphic, also made some changes related to your comments.

On Sat, Jan 2, 2016 at 4:34 PM, Keislar, Doug <do...@musclefish.com> wrote:

I have one question about the v-pc bars.....

First it has to do with the mechanical way I do it and showing where they come from, and also it is like a distinction, but yes ultimately an extra step could remove the unnecessary symbols and if handwriting never draw them.

 

[Music Integrated Solution]

Inopa,

Thanks for the comments; the isomorphic relationship is on the positions of the symbols not on their shape; when I go into intervals I hope it could be seen.

 

 

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[Joseph Austin]

Enrique,

As always, I believe your presentation would be more understandable to me if you were to include some examples of it's use for common musical concepts, perhaps comparing it to theTraditional Notation or traditional musical set theory presentation of the same musical examples.

So what concept examples would be relevant?

That is the question I have been asking all along.

Presumably one should be able to illustrate scales, chords, circle of keys, etc.

But beyond that, I've been anticipating examples of applications beyond the mere notation for traditional "music theory" constructs,

to actual application to the analysis or even creation of melodies, harmonies, and more generally, patterns.

For example, I had understood that traditional "scales" are created as sequences of "fifths" (2:3 ratios), followed by "octave" translation (1:2 ratios).

Chords, on the other hand, are constructed from "thirds", (4:5 and 5:6 ratios)--

[which to me has always raised the question of how scale theory and chord theory can be based on ir-rational bases.]

So in PC, one would perhaps say scales are based on 01, 02, and (0 equivalent to Z) [Z being twelve] and chords are based on 03 and 04.

But basing scales on patterns of "whole and half-steps" (01 02 and an occasional 03 steps) has always seemed more ad-hoc than basing them on fifths, i.e. 07.

For my own purposes, I prefer to think of scales as derived from sequences of "alternating major/minor thirds"  (04 03 or 03 04).

But changing terminology does not produce new knowledge or function.

PC seems to be justified by expanding function beyond traditional theory, e.g. atonal music.

I would have hoped, however, that an ET theory would offer results applicable within traditional music theory,

perhaps in areas we might call "multi-tonal" theory or progressions based on extended chords or modulations.

[I suppose the so-called "CIRCLE of fifths" is the principal contribution of ET theory to traditional harmony.]

So, again: what can you DO with your theory, besides transliterate existing scores?

Where are the axioms?  Where are the analyses, the derivations, the theorems, the proofs?

I don't claim to be a music theorist, but I have suggested that the extension of the "scale-forming" operation of "sequence of fifths" 

can produce "just twelve-tone scales" that allow elimination of all accidentals from simple traditional tonic-dominant or major-minor music on a twelve-position staff without creating enharmonic ambiguity or requiring enharmonic equivalence.  This is the sort of insight I might expect from ET theory.

Joe Austin

[Doug Keislar]

Joe,

Re:

I don't claim to be a music theorist, but I have suggested that the extension of the "scale-forming" operation of "sequence of fifths" 

can produce "just twelve-tone scales" that allow elimination of all accidentals from simple traditional tonic-dominant or major-minor music on a twelve-position staff without creating enharmonic ambiguity or requiring enharmonic equivalence.  This is the sort of insight I might expect from ET theory.

Are you aware of the often-discussed "comma shift" problem with just intonation as applied to traditional tonal music?
I haven't studied the following page carefully, but it discusses that problem and has sound examples:
http://www.theory.physics.ubc.ca/341-current/Benedetti/Benedetti.html

Doug

[Music Integrated Solution]

Joe,
Yes, I am working on some comparisons but probably not the usual kind; I intend to make this doc as compact as possible within this kind of format, not as a book or as a chapter of a book.
I wrote this:
“V-set theory has as foundation the most important alternative music theory, and the most important alternative music notation of our times (pc set theory & piano roll notation) as well as the prevailing tuning system of the west (12-TET).
Said foundation is evidence of accepted alternatives, subsequently v-set theory is a continuation of an existing path, aiming to make the piano roll notation and pc set theory or its axioms and concepts more useful.”

 In other words, I do not think necessary to go back and attack TN when the popularity of the PRN is evidence that people appreciate an alternative to TN; something similar could be said of set theory.
On the other hand, the point is: "if said alternatives were more useful it would be better"; and I feel comfortable that I can demonstrate that; though you are right that 'the more useful I can demonstrate it is, the better also'.

Thanks
Enrique.

[Paul Morris]

Hi Enrique,

Thanks for this helpful account of your system.  I think it does a good job of communicating how you’re drawing on and synthesizing piano roll and pitch-class set theory.  I agree with Doug that more illustrations and comparisons would strengthen it – chromatic scales, diatonic scales, series of intervals, etc.  I think Inopa makes a good point about intervals and visual isomorphism, so I’d be interested to see illustrations showing how you’re approaching this.  

Cheers,

-Paul

On Jan 2, 2016, at 3:28 PM, Music Integrated Solution <mtall...@gmail.com> wrote:

[Joseph Austin]

Doug,

Yes, I am aware that, even with twelve tones, the sequence of 2:3 does not form a perfect circle, 

and that the ii and V7 chords  cannot be reconciled.

[As I recall, Bach's WTC starts with this example, showing the "advantage" of ET.]

But I think that is the point of those who insist on distinguishing G# from Ab.

I assume they are trying to preserve the just tuning of the intervals on just-tunable instruments, such as bowed strings and voice.

My point is, that you can assign a default enharmonic to every position of a 12 position staff by selecting a contiguous set of twelve "fifths" that include the tonic and it's dominant or relative minor.  Thus, given a 12-position key signature, "most" accidentals could be removed from the body of many compositions, without any enharmonic ambiguity.

[The convention of "sharp-up flat-down" could still cause problems, but I understand that as a notational kludge, not a musical principle.

As i have discussed elsewhere, I don't believe the concept of "sharping" or "flatting" a given pitch is an harmonic principle,

for according to either scale or chord theory, the "nearest neighbor" notes in a scale are only distantly related according to the circle of fifths,

and "sharping" and "flatting" have no consistent definition in Just Intonation--but then I'm no expert.]

As for "comma migration", could it not be considered a "defect" of composition if the increments and decrements were not matched?

What would we say of a conventional composition that began in C, modulated to G then D, then ended in D?

It would end a wholetone above where it started! 

[Choir arrangements do such things rather routinely, 

and raising the key a semitone is a common cliche for varying a many-verse hymn tune.]

Am I missing something?

Joe Austin

[Doug Keislar]

Joe,

I guess I don't understand, when you speak of a 12-position staff based on twelve contiguous perfect fifths, whether you're talking about using 12-TET or some kind of just (or Pythagorean) intonation.  I was pointing out a problem with the non-12-TET case.  Pure Pythagorean tuning (a.k.a. 3-limit just intonation) has out-of-tune sounding major thirds (much worse than those of 12-TET).  And if you try to include pure major thirds (5-limit just intonation), you can run into out-of-tune intervals if you're limited to a set of 12 fixed pitches, or the comma shift if not limited to 12 and it's music with traditional tonal harmonic progressions.

Regarding a previous post, my recommendation, as a former piano teacher, would be to rely more on memorization -- and that includes motor/muscle memory as a huge part of the picture, not just cognitive memory -- instead of imagining you'll be able to become a good musician through theoretical understanding.  I am reminded of a former piano student, who was an engineer at a well-known tech company, who came to the piano lesson thinking that he could play the assignment if he concentrated hard enough, when it was clear to me he just hadn't practiced enough.  As an engineer, he was used to approaching things as problems to be solved intellectually.  Music does have that aspect, but it's only one aspect.

Doug

[gguitarwilly]

Enrique,

What I see is a concept very similar to Joe's Chroma Tonnetz, but less clear because there is no interval consistency.

I seem to understand that the only relation to 'set theory' is that notes are clustered visually in various ways. I see no solution for notating rhythm.

For such a rudimentary notation idea, I find the language in which it is presented annoyingly pretentious.

Willem

Op zaterdag 2 januari 2016 21:28:26 UTC+1 schreef Music Integrated Solution:

[Music Integrated Solution]

Hi Paul,
Yes, probably we could go through another round with this issue of “visual isomorphism” but it will require a different mindset to understand what I mean; we have to separate similar-looking, consistency and graph isomorphism, then we can give it try.

Thanks
Enrique.

 

[Music Integrated Solution]

Willem,
I would like to be polite and tell you thank you for your comment and attempt clarifying a wrong perception, but comments out of animosity and petulance have no value and deserve no attention.

Take it easy.

--

[Jessifeph John]

To Willem and Enrique,

Please stop the negativity. We're all similar minded in here and it's only like 10 of us. This can only bring us farther apart. Willem you're post was fine except that last comment. You can say that Enrique is a bit hard to understand but "annoyingly pretentious" is harsh. I think English may not be his native language, Enrique please validate.

-Inopa

[dominique.waller]

I too, think that Willem has been dispising towards Enrique when talking
about "meta-blahblah" and should apologize. I don't share Enrique's
enthousiasm for the Piano Roll Notation, and think he overestimates its
importance, but he has often brought stimulating ideas on this forum. For
example I like his concept of "hybrid notation". We can criticise each
others' ideas without being openly dispising. Dominique

-----Message d'origine-----
From: Jessifeph John
Sent: Wednesday, January 6, 2016 9:15 PM
To: The Music Notation Project | Forum
Subject: Re: [MNP] Re: Introducing music Visual set theory

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[gguitarwilly]

Hi Enrique, Inopa, Dominique,

I appreciate that you are trying to keep things nice on this forum. 

'King of meta-blahblah' is disrespectful, and I should apologise for that, which I do here. Sorry, Enrique.

As to my second comment; I tried to formulate my reaction to the tone of the article on Enrique's blog so that it is clear that it is my personal reaction. It's me that gets annoyed.

I'm told that an 'I message' (does that concept exist in English?) can never be wrong, because one is sharing his/her personal spontaneous reaction.

But if I succeeded somehow in annoying other forum members in return, I'm clearly missing some kind of social antenna here.

This might (to a degree) be a cultural thing; we Dutch are known for our bluntness, and among the Dutch I'm of the blunter kind.

Also, in the eyes of the Dutch, Americans can advertise their own qualities in ways that the Dutch would find insufferably vain.

I believe in honesty over politeness, but you are right one should never become rude.

So if 'annoyingly pretentious' is rude, I also apologise for that.

I'll try to be a good boy, but I make no promises. ;-)

Willem

Op woensdag 6 januari 2016 22:18:24 UTC+1 schreef Dominique Waller:

[Joseph Austin]

On Jan 5, 2016, at 6:17 PM, Doug Keislar <do...@musclefish.com> wrote:

I guess I don't understand, when you speak of a 12-position staff based on twelve contiguous perfect fifths,

whether you're talking about using 12-TET or some kind of just (or Pythagorean) intonation. 

Doug,

Either/both.

I'm just bemused that someone would propose a 12-position "isomorphic" notation 

and then break the isomorphism by re-incorporating the 7-5 pattern.

Joe

[Doug Keislar]

Hi Joe,

Oh.  I misunderstood.  So you're talking about nomenclature rather than tuning?  Do you mean that there should be 12 distinct names in place of the 7 letter names that have possible sharps or flats?  If so, I'm still unclear what you meant by a "default enharmonic" when you wrote:
"you can assign a default enharmonic to every position of a 12 position staff."
and why you were speaking of "just twelve-tone scales".

I'm also unclear on what this question has to do with the system that Enrique proposes.  I don't see any 7-5 pattern there (other than in the traditional piano keyboard that he displays vertically at the beginning of the "staff," which seems just like an aid rather than an intrinsic part of his system).

Sorry if I'm being dense.

Doug

[Music Integrated Solution]

Willem, basically I interpret your selective bluntness as saying: ‘much ado about nothing’ that do not deserve being written in that format or style because it looks like a kid mocking or imitating scholars; is that it?

[Music Integrated Solution]

Willem, I consider myself honest and blunt at such point that could make the Dutch frown.
My problem is that I perceive yours as selective and expressed in a mixture of arrogance and hatred.

Bu I have to confess that it is interesting that a proposal based on accepted alternatives (12-TET, PRN and pc set theory) annoys you so much, while being so enthusiast for others without any evidence of appreciation for a significant community, despite being around for about a couple of centuries. You might argue that it is the way it is presented but I perceive there is something in the message that you disagree or you do not like.

As long as I could be around, I encourage communication based on the message, and being specific as much as possible, one detail at a time otherwise we are wasting our time.

 

 

[Joseph Austin]

On Jan 5, 2016, at 6:17 PM, Doug Keislar <do...@musclefish.com> wrote:

Regarding a previous post, my recommendation, as a former piano teacher, would be to rely more on memorization -- and that includes motor/muscle memory as a huge part of the picture, not just cognitive memory -- instead of imagining you'll be able to become a good musician through theoretical understanding. 

Doug,

I appreciate your voice of experience.

As I am now "starting over" with Janko, and coincidentally it's "New Year's Resolution" time,

I intend to put more emphasis on "practice".

With fewer patterns to memorize, perhaps i will have more success.

Joe

[gguitarwilly]

Hi Enrique,

In answer to your two posts: it's not the system you propose, it's the tone in which it is proposed that caused my reactions.

The saying is 'the truth is in the eye of the beholder': if you write 'My problem is that I perceive yours as selective and expressed in a mixture of arrogance and hatred', I'd like to point out that it is indeed your perception as 'beholder' rather than my intention that is reflected in your interpretation. I find any suggestion that I would in some way be motivated by 'hatred' absurd.

My reaction was 'selective' in that (in mý perception) none of the other forum members shows the kind of self-importance that is conveyed through your style.

However, I may have misinterpreted sincere enthousiasm and attemps to write clearly for self-importance. Messages can get misunderstood both at the sending and at the receiving end.

I propose we leave it at this, and continue our searches for whatever we are searching for on this forum.

Willem

 

Op vrijdag 8 januari 2016 16:46:07 UTC+1 schreef Music Integrated Solution:

[Music Integrated Solution]

Willem, thanks for your feedback, which now makes me think that I should had written some note before providing the link, explaining that this doc is not aimed specifically at this group, but rather for the rest of the world. I just borrowed their style, their language, the one I have found on countless papers, hoping it could contribute in an eventual communication.

Sometimes I have a feeling of being the dissonant chord or a passing note on the group, but never tried to be likable. Perhaps I unnecessarily engaged in the kind of contest that the MNP embodies, while taking a different path that does not seem to lead to the place they originally intended to go.

But the poet seems to be right: ‘caminante no hay camino se hace camino al andar’ (Walker, there is no path, the path is made by walking).

The right path or destination still remains uncertain, meanwhile I want  to thank the MNP for encouraging to walk and for coping with me.

Enrique.

--

[Music Integrated Solution]

On Mon, Jan 4, 2016 at 8:24 PM, Joseph Austin <drtec...@gmail.com> wrote:

So, again: what can you DO with your theory, besides transliterate existing scores?

Joe et al,
Real state says location, location, location.
All I have to say by now is functionality, functionality, functionality.
PRN and set theory already have some functionality, which is the reason why they are popular or appreciated; I will talk mainly what comes “additionally” with v-theory (for short).

() the possibility of representing musical notes “as narrow as a thin line” and improvements related to readability vs. the 7/5 staff that requires wider bands or rectangles.

() the 3x4 and 6x2 schemes and isomorphic capabilities

() unified representation of pc musical notation and pc isolated symbols.

() a consistent graphical relationship between the compact (semi-mergeable) v-pc shapes vs. arbitrary and non-mergeable conventional numeral shapes.

() visual operations in addition to only mathematical ones

() integrated and compact pc-set images vs. isolated circles like pitch-constellations or tone clocks

() visual correlation of notation and pc-set images with important musical instruments

() pronounceable and compact nomenclature that allow a feasible objective description of harmonies.

I will try to put in words how all this (and more) blend to make a positive difference on the musical practice, which is what matters.


 

[Keislar, Doug]

Hi Enrique,

Thanks for that list of functionalities that your system adds to the piano roll and to set theory.

When it comes to notation, a picture can be worth a thousand words.  To start with, I'd be particularly interested in pictures that demonstrate the following (as I think others on this list would be):

() the 3x4 and 6x2 schemes and isomorphic capabilities

Doug

---

From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Music Integrated Solution [mtall...@gmail.com]

Sent: Saturday, January 09, 2016 9:30 AM
To: musicnotation
Subject: Re: [MNP] Introducing music Visual set theory

--

[gguitarwilly]

Hi Enrique,

Glad we made peace! ;-)

Willem

Op zaterdag 9 januari 2016 15:32:47 UTC+1 schreef Music Integrated Solution:

[Music Integrated Solution]

On Sat, Jan 9, 2016 at 2:18 PM, Keislar, Doug <do...@musclefish.com> wrote:

When it comes to notation, a picture can be worth a thousand words.  To start with, I'd be particularly interested in pictures that demonstrate the following (as I think others on this list would be):

() the 3x4 and 6x2 schemes and isomorphic capabilities

Doug, Inopa, and all others that have made comments related to this; I am trying to explain it again but I am going to keep the core of the explanation on a page (to keep it small and handy), so that I can improve it or correct it if necessary.

The point is that all relationships: ‘same’, ‘next-to-same’ and ‘previous-to-same’ are equally consistent for visual operations and that is the reason I say they have a theoretical value equivalent to the value of isomorphism on musical instruments.

In other words, what is most important is the isomorphic functionality (capability) of the notation over having a perfect similar look.

The first step is understanding the concept, then we can talk why I consider it more useful than math and numbers for musical purposes, and other issues, take a look.

[Joseph Austin]

On Jan 9, 2016, at 12:30 PM, Music Integrated Solution <mtall...@gmail.com> wrote:

I will try to put in words how all this (and more) blend to make a positive difference on the musical practice, which is what matters.

Enrique,

I'm looking forward to this!

Joe Austin

[Music Integrated Solution]

Joe, I hope you read the last link, which is ‘the key‘(of paramount or crucial importance) to what I call integration, or integrated system, because this concept is an important part of ‘the visual alternative’ to math and numerals in v-set theory.

In other words, there is no back and forth between diatonic TN and duodecimal numerals.

I think a first benefit is ‘the integrated system vs. mixing isolated systems’.

 

--

[Christian]

Hi friends of AN,
thanks for all your comments and ideas on this forum.

Today I want to make a comment on the following statement.

"In other words, there is no back and forth between diatonic TN and duodecimal numerals."

I don´t agree.
I recently found a graphic solution that I called Hamburg Music Pianotype Notation (HMPN)
that allows the use of duodecimal numerals and has a diatonic structure.
The dozenal zero (ten = 1 dozen plus zero) and the primes five and seven of the dozenal system do the trick.
The conventional piano has the solution.
It resembles TN so closely that it could be called "Common duodecimal Notation" if it becomes common use.
It can be written with most free and commercial software but does not play the correct MIDI yet.
It is so simple that it is hard to believe that nobody else has seen it before.
So please tell me if somebody else already found it.
Have a look on www.hamburgmusicnotation.com
More will be published there soon.

A good year for AN and you all
Robert Elisabeth Key
alias Christian Pörksen

[Doug Keislar]

Hello Christian,

Happy New Year to you!

I believe that what Enrique meant by that statement is that the conversion is one-way:
If you have TN containing accidentals, you can convert it to duodecimal numerals, no problem.
But if you try to go back from duodecimal to TN, you have lost the information about whether it was a sharp or a flat, and so that conversion might not be completely accurate (assuming you care about the distinction between sharp and flat).

What he is saying is that with a system like his in place of TN, this problem doesn't exist (because his system is not diatonic and therefore doesn't have a distinction between sharps and flats).  You can go both directions.

If I understand your new system correctly, your staff has eight lines or spaces per octave (four lines, possibly ledger lines, and four spaces).  The cyclic pattern is two octaves rather than one, with alternating octaves using ledger lines for two of the staff lines.  Four of the black keys of the piano use the same space or line as a white key (as in TN).  But G#/Ab (gis/as) has its own space, unlike TN.  So it's not quite a diatonic notation. I'm not aware of another notation system that has a staff like this.

Best wishes,
Doug

[Ivaylo Naydenov]

Hi, Christian
No time for introduction so strict to the questions:

Numbers mixed with letters for note symbols, why... and
Colours, why?

Inversions, how?

Key changes, modulations, how?

[Joseph Austin]

Enrique,

I thought I was following until I got to "la" = previous to same.

I would have thought only 0-11 could be considered "previous to same" starting with 0.

Also, it's not clear to me why you need two "blue" shades but only one "white" shade

(unless there's a subtle color difference that is not showing up on my screen.).

I'm generally unclear on the utility of color vs. position.

I don't think you have demonstrated how "next" and "previous" are sufficient to uniquely identify a pitch or interval 

without somehow invoking the sequence of colors.  

In other words, how big of a "window" around a square must you see to uniquely identify the pitch or interval?

And what if the "row" were in fact a "ring"?  I'd say in general you need 3 squares for blue and 4 for white.

---

Now, let me propose an exercise similar to one I do in my database class.

Exercise 1 (color only)

1. cut off the numbers from your colored row of rectangles.

2. cut each rectangle apart--so you now have 3 dark, 3 medium, and 6 light.

3. put the twelve rectangles in a bag, shake them up, and put them back on a table in arbitrary position.

4a. now, pick any rectangle and tell  it's pitch class

4b. pick any additional rectangle and tell  its interval class with the first.

Or try the following

Exercise 2 (order only)

erase all the colors and numbers, but leave t

1. pick any rectangle and tell  it's pitch class

2. pick any other rectangle and tell  the interval class

I believe you will agree that Exercise 1 can give no answers either pc or ic, 

and Exercise 2 can give no pc answers

but can give all the ic answers your original system gives.

To get pc answers, you would need to distinguish only one of the squares.

Or am I missing something?

Try Experiment 1 with my ChromaTonnetz symbols, and I believe you will find that all pitches and intervals can be determined

by looking at only one (pc)  or two (ic) of the symbols in isolation from any others.

[Note that none of my symbols have "numbers" on them, although I assume the observer "knows" the sequence of colors and orientations,

In effect, logical "position" is encoded into the color+orientation. 

You could think of color and orientation as "digit symbols", 

but it's an unusual number representation, in that the cycles are concurrent rather than nested.]

Joe Austin

On Jan 11, 2016, at 6:33 AM, Music Integrated Solution <mtall...@gmail.com> wrote:

 take a look.

[Joseph Austin]

Yes, that is what my previous post was responding to.

Joe

[John Keller]

Hi Enrique,

In the pitch class names, you have 4 consonants and 3 vowels, starting da, de , di (= C, I, D), then consonants m, f and  t. The vowels are nested within the consonants.

Then for the interval set, you use 3 consonants and 4 vowels, starting sa, na, la. (= 0, 1, 2), then vowels e, i, o. You are nesting these syllables in the other way! Is this a good idea? 

(Also some syllables in each set are identical or similar to the traditional solfege: me, fa, te, and la, so). 

I get that you do not want any of the same names to occur in your pitch set and interval set.

Basically you are dividing the chromatic number by 3 and taking the quotient and remainder to give your pitch or interval name.

If your system is compatible with TN and diatonic numbering, how do you for example get from an interval of a 5th in TN, to the interval name ‘ni’?

Cheers,

John Keller

Express Stave

[Joseph Austin]

Enrique,

I realized later that the critique below does not apply to your actual notation, but only to the "explanatory" document with the colored rectangles.

Your actual notation does have a unique combination of position and background color/shape for each of the twelve tones,

so a given pitch can be determined just from one  trace/ref-head element.

We could debate whether nested or concurrent cycles are better, 

but I conclude that either of our notations should serve as a graphic representation of pitch-class or interval-class sets.

Joe

[Music Integrated Solution]

Joe,
Just wanted to avoid the ‘p’, the ‘l’ is easier to pronounce without moving the mouth, somewhat lazy.
The way I used the colors is just one of many ways of highlighting those clusters, I find this one aesthetic and an efficient way of discriminating 12 elements with three colors.

I changed ‘visual pattern’ for ‘visual scheme’ and ‘positional pattern’ for ‘positional scheme’
I thought that without the symbols explaining the ‘positional scheme’ would be easier to see.

In this example, color does not define the scheme, e.g. 0 & 3 have different color but same position on the positional scheme.

I feel like trying to explain OOP to people that have been writing spaghetti code for many years, and it seems that I have not found a proper way yet; I have explained this to people outside this group and they get it easily; my recommendation is to avoid comparison and approach this with a different mindset.

Thanks

 

[Music Integrated Solution]

Hi John,
Right, pc and pic use different consonants as a necessary distinction. I have tried different combinations of letters and have considered also getting away from solfege as much as possible e.g. using k, p, t, v for the pc, that is something I may change but I am not sure yet.

The system is not compatible with TN or diatonic numbering.

Thanks

[Music Integrated Solution]

Joe,
I made some changes to make it clear that this is a ‘three positional scheme’ and not a three color or shape scheme; also I make it clear that clustering or demarcating is what defines the positional scheme, and colors or shapes are used to produce the clusters.

My point is that the ‘concurrent’ approach does not have more isomorphic capability than the demarcated one.

I do not call it nested because it makes me think of this (((()))), while they are ( ) ( ) ( ) ( ), all clusters have the same level, and positional relationships have the same level also.

We are demarcating creatures, we demarcate everything, and demarcation works.

 It might be better now.

[Joseph Austin]

Enrique,

I realized later that the critique below does not apply to your actual notation, but only to the "explanatory" document with the colored rectangles.

Your actual notation does have a unique combination of position and background color/shape for each of the twelve tones,

so a given pitch can be determined just from one  trace/ref-head element.

We could debate whether nested or concurrent cycles are better, 

but I conclude that either of our notations should serve as a graphic representation of pitch-class or interval-class sets.

Joe

[Music Integrated Solution]

Doug,
You said a picture is worth a thousand words, what is the value of silence? I do not get it.
 

[Joseph Austin]

Enrique,

I realized later that the critique below does not apply to your actual notation, but only to the "explanatory" document with the colored rectangles.

Your actual notation does have a unique combination of position and background color/shape for each of the twelve tones,

so a given pitch can be determined just from one  trace/ref-head element.

We could debate whether nested or concurrent cycles are better, 

but I conclude that either of our notations should serve as a graphic representation of pitch-class or interval-class sets.

Joe

[Doug Keislar]

Hi Enrique,

I gather you are wanting me to respond about http://musicintegratedsolution.blogspot.com/2016/01/visual-patterns-and-visual-set.html.

Sorry; maybe I was distracted by the fact that Joe has responded already.  But, when I wrote I would like to see a picture of this functionality:

      () the 3x4 and 6x2 schemes and isomorphic capabilities

I guess I didn't see everything I was looking for on that page.  Where do we see the 6x2?  Is 6x2 the same thing as what people refer to as 6-6, or would the latter be 2x6?

And in terms of isomorphic capabilities, maybe we are talking about two different things.  Your system has a lot of excellent correlation between notation, nomenclature, and potentially instruments.  So it's isomorphic in that sense.  I was thinking of isomorphism in the sense that Paul has discussed: when a given intervallic pattern (chord, etc.) looks similar in all transpositions.  So I was hoping to see, for example, a major triad or a dominant seventh chord in all 12 transpositions, and to notice a pattern that helps identify all transpositions as being the same intervallic structure.  Is this is a goal of yours?

Doug

On 1/12/16 4:26 PM, Music Integrated Solution wrote:

Doug,
You said a picture is worth a thousand words, what is the value of silence? I do not get it.
 

[Music Integrated Solution]

Doug,
There is a line:
"A 6x2 scheme is also highlighted as in 0->6, 4->10, 2->8, 5->11, 9->3"
For me the 6/6 is the 2x6 scheme.
I gathered you were disappointed, and it did not surprise me.

On Tue, Jan 12, 2016 at 7:56 PM, Doug Keislar <do...@musclefish.com> wrote:

And in terms of isomorphic capabilities, maybe we are talking about two different things. 

Yes, we are; I am trying to explain and showing a table with isomorphic functionality and you are expecting to see a score with similar looking chords.

I am aware that the 2x6 produces more similar-looking chords, I do not argue that, but is it better?

I am leaving this picture for when I can return to the conversation.

Thanks.

[Joseph Austin]

On Jan 12, 2016, at 9:58 AM, Music Integrated Solution <mtall...@gmail.com> wrote:

I feel like trying to explain OOP to people that have been writing spaghetti code for many years, and it seems that I have not found a proper way yet;

Enrique--I assume this is an analogy, or do you really think music is "Object Oriented"? That's a subject I would be interested in  exploring at some depth.

I have taught classes in OOP, and it's easier with a graphics environment like Visual Basic or Alice or Scratch, or even Robotics, where you can totally divorce the coding from the execution.

Joe

[Doug Keislar]

I assume it was just a translation glitch and that Enrique meant "I feel like someone who is trying to explain...," whereas a native English speaker reads it as "I am considering trying to explain...."

Doug

[Joseph Austin]

Or perhaps Enrique is saying, it would be like me trying to explain OOP?

In any case, my problem with "musical" set theory is the same problem I had when studying set theory in school.

Set theory would always be presented at the beginning of a math course.

We got a lot of definitions, did a page of exercises, and never used it again for the rest of the term!

When my kids were in school--same story.  They would have a week of homework on sets, then never use them again!

There's only so much you can do with sets, and I'm not convinced that composing or performing music is one of them.

But I'm willing to be proved wrong!

In computers, for example, set theory is isomorphic to boolean logic, and you can do a lot with that!

I just haven't seen musicians taking it in such a direction.

Joe Austin

[Music Integrated Solution]

Joe,
That is an analogy; I have read that people that have never programmed computers understand or learn faster OOP that some people that have been programming in primitive languages for many years.

The analogy comes because it seems to me that communicating the notion of ‘isomorphic functionality’ on the v-pc notation to people that only relate isomorphism on music notation to similar-looking is more difficult. The analogy is like if previous knowledge is obstructing new knowledge.

Isomorphic functionality on the v-pc notation is not about similar-looking, but about how or what we DO through the notation.

LEARNING TO NAME ‘ONE’ PITCH INTERVAL CLASS (PIC MOD 12) APPLIES TO NAMING EVERYTHING ELSE (other than the pc). Does it sound familiar?

All pic are named with the same method (relationship + distance) and as this is an objective method, any pic name generates the other pc that produces the interval.

There is more to say but I would like to know, how it is going before moving on.

 

--

[Music Integrated Solution]

In other words, if learning how to name one pic, we name them all, all normal forms, all pc-sets with the same interval pattern (equivalent to generic chord names), transpose, some types of inversions and more.

[Joseph Austin]

So I could consider your pic scheme a "distance" measure in a mix-radix number system (color, position) modulo "4,3".

00 01 02 10 11 12 20 21 22 30 31 32

where the digits are actually letters with a different set of digits for each base:

as an al es en el is in il os on ol,

except that you write the numerals in "reverse" of the traditional system, least significant digit leftmost.

In which case, it's not clear that the "colors" have any relevance to the pic scheme,

except perhaps for naming the pc.

So suppose you name the pc's similarly.

Then you should be able to establish a point:line duality relationship between pc and pic such that:

a pic can be "computed" as the difference of (distance between)  two pcs,

and  pc and be computed as the sum/difference of a pc and a pic,

using mixed radix modular arithmetic.

Am I getting it?

So next,  how does the 3x4 scheme specifically figure in?

Of course, I still favor concurrent cycles instead of nested cycles:

00 11 22 03 10 21 02 13 20 01 12 23

as I believe they are "more" isomorphic.

In this [Pertchik] case, the 3 and 4  factors relate directly to harmonious intervals of "three" and "four" (or their multiples).

It's not clear to me what intuitive significance to assign to your 3x4 nested scheme.

---

Re the analogy: Yes, it's easier to learn OOP from scratch that to convert from procedural.

I've been offering a similar argument for AN all along:

that is, AN should be directed to the new student "tabula rasa".

Don't introduce 7-5, or sharps and flats, or CDEFGABC, or ii IV vi I iii V viiº at all.

If they don't already know it, they won't ever need it.

And if the do already know it, as Sherlock Holmes would say,

they should do their best to forget it,

as it merely clutters the mind with distracting and confusing information.

Joe

[Jessifeph John]

MIS,

After a bit of struggling, I finally see how the intervals have consistency. However, it might be beneficial to use a simpler language than "previous-to-same" etc.. Since they're all relative to 'same' then why not just use Previous, Same, Next.

And while now I understand that there is interval consistency, I still don't think it's as strong as other systems but strength might not be necessary since in this case it makes other aspects of your system weaker such as the v-bars.

Now my issue that remains is that PR has difficulty in distinguishing voices. We can use color on computers but doing so excludes handwritability.

Solutions?

-Inopa

[Joseph Austin]

OK, but you get all those advantages just using integers mod twelve.

So I need to give more thought to the "visual" aspects;

learn how to do "visual" arithmetic as it were.

It seems that puts "trace and ref-heads" in competition with "clock" notation.

Although for set discussions, it would work to arrange your system into a circle or "clock".

It seems what you have is actually a 2x2x3 system: (shape,color,position).

But as I mentioned elsewhere, it turns out for Janko it is most convenient to have the least-significant (most often changing) factor be 2, like a twelve-sector dart board.  

Joe

[Music Integrated Solution]

On Wed, Jan 13, 2016 at 11:16 PM, Joseph Austin <drtec...@gmail.com> wrote:

So I could consider your pic scheme a "distance" measure in a mix-radix number system (color, position) modulo "4,3".

00 01 02 10 11 12 20 21 22 30 31 32

Joe, my effort is to make you see it in this way

(a) 00 10 20_01 11 21_02 12 22_03 13 23

when represented with numerals it blurs the clusters, so I put the underscore. This could make no sense to the mathematician but this is not rocket science just a visual positional scheme.

(b) “Any method of clustering or demarcating three positions may produce 'the three positional scheme', whether we use symbols, shapes or bands to produce them. Colors or shapes are used to produce the clusters and any resulting color or shape scheme is secondary or of no importance”.

(c) Learn to name a pic as explained.

With a, b, c in mind, put your mindset in learning mode, not in inventing mode (and that is for everybody) and please read slowly v.2.0.

When I have the time will go over other comments.

Thanks

[John Keller]

Enrique, 

While your intervals go:    00 10 20   01 11 21 ( sa na la   se ne le),

your pitches (notes) go:   00 01 02   10 11 12 ( da de di   ma me mi) etc

How do we pronounce these syllables? the vowels?

Do you want to ditch chord names such as “C major”, and replace by "Da saneni” ?

What would be the chord symbol instead of “C"?

JohnK

[Doug Keislar]

On 1/14/16 2:47 PM, John Keller wrote:

Enrique, 

While your intervals go:    00 10 20   01 11 21 ( sa na la   se ne le),

your pitches (notes) go:   00 01 02   10 11 12 ( da de di   ma me mi) etc

How do we pronounce these syllables? the vowels?

While waiting for Enrique to reply, I'll guess that these are pronounced as in Spanish and Italian.
English equivalent sounds:
a -> ah
e -> ay
i -> ee

Do you want to ditch chord names such as “C major”, and replace by "Da saneni” ?

I think it could just be Daneni.  No need for sa, because intervals imply two pitches already.  Daneni has the same number of syllables as C major.
The very nice thing about this approach is ANY three-note chord has just three syllables, ANY four-note chord has four, etc.  (Here, "note" means "pitch class.")
And the generic form is shorter, e.g., "major triad" would have only two syllables: neni.
I think there's a lot of potential in this kind of approach (whether using Enrique's specific syllable scheme or a similar one, such as one for Joe's non-nested 4x3).  Did Ivaylo also come up with something like this?

What would be the chord symbol instead of “C"?

Good question.  "Da" is not quite as compact as "C", but maybe Enrique would use a graphical symbol instead.

[Joseph Austin]

observations:

* for persons not familiar with pitch class set theory, it might be worth a brief review of the basic concepts:

* I'm not sure "consistent" is the word you want.  I'm trying to figure out exactly what concept you mean by this:  something like: same distance, same pic, same name?

* clarify the meaning of "i-position" when the term is first introduced.

Later you refer to "next" and "previous" but "previous is illustrated as "next-next".

Clarify the distinction between "previous/same/next" and "left/center/right".

* pic naming

- i get the consonant,

but I don't understand the "consistency" of the vowel

- for n, couldn't the vowel be either e or o for the same distance, depending on i-position

- similarly, for p (l), couldn't the vowel be either a or e for the same distance?

This seems to be a fundamental problem wth any NxM nested system.

Joe

[Philip Rhoades]

People,

On 2016-01-15 14:47, Joseph Austin wrote:
> observations:
> * for persons not familiar with pitch class set theory, it might be
> worth a brief review of the basic concepts:
>
> * I'm not sure "consistent" is the word you want. I'm trying to
> figure out exactly what concept you mean by this: something like:
> same distance, same pic, same name?
>
> * clarify the meaning of "i-position" when the term is first
> introduced.
> Later you refer to "next" and "previous" but "previous is illustrated
> as "next-next".
> Clarify the distinction between "previous/same/next" and
> "left/center/right".
>
> * pic naming
> - i get the consonant,
> but I don't understand the "consistency" of the vowel
>
> - for n, couldn't the vowel be either e or o for the same distance,
> depending on i-position
> - similarly, for p (l), couldn't the vowel be either a or e for the
> same distance?
>
> This seems to be a fundamental problem wth any NxM nested system.

I have not been keeping up with stuff here for quite a while due to
other life events intervening however I would dearly love to get back to
spending more time on MNP discussions. In my next life (after being
thawed out) I will be classical guitarist . .

It looks like smart people here are taking Enrique's proposal seriously,
so I have to assume that there is, indeed, something interesting to talk
about here - HOWEVER, I am not sure if I am by myself on this, but, I
have NO BLOODY CLUE what this discussion is all about. Yes, I am a
wannabe musician but I do have SOME clues about maths and physics etc as
well as a general idea about how traditional notation works so I am left
to wonder: is my cognitive decline accelerating or is this stuff
seriously complex or something - I am just not getting it - and so far,
I have NO IDEA about how this might be useful to a child, or anyone else
for that matter, trying to learn music in a more natural and logical way
- that allows for more rapid progress than the traditional method . .

Am I alone? If so, I guess I will just wait till I am thawed out . .
and have a look at the state of things then . .

Regards,

Phil.

> Joe
>
>> On Jan 14, 2016, at 4:15 PM, Music Integrated Solution
>> <mtall...@gmail.com> wrote:
>>
>> On Wed, Jan 13, 2016 at 11:16 PM, Joseph Austin
>> <drtec...@gmail.com> wrote:
>>
>>> So I could consider your pic scheme a "distance" measure in a
>>> mix-radix number system (color, position) modulo "4,3".
>>> 00 01 02 10 11 12 20 21 22 30 31 32
>>
>> Joe, my effort is to make you see it in this way
>>
>> (a) 00 10 20_01 11 21_02 12 22_03 13 23
>>
>> when represented with numerals it blurs the clusters, so I put the
>> underscore. This could make no sense to the mathematician but this
>> is not rocket science just a visual positional scheme.
>>

>> (b) _“Any method of clustering or demarcating three positions may

>> produce 'the three positional scheme', whether we use symbols,
>> shapes or bands to produce them. Colors or shapes are used to
>> produce the clusters and any resulting color or shape scheme is

>> secondary or of no importance”._

>>
>> (c) Learn to name a pic as explained.
>>
>> With a, b, c in mind, put your mindset in learning mode, not in
>> inventing mode (and that is for everybody) and please read slowly

>> v.2.0 [1].

> Links:
> ------
> [1]
> http://musicintegratedsolution.blogspot.com/2016/01/visual-patterns-and-visual-set.html

--
Philip Rhoades

PO Box 896
Cowra NSW 2794
Australia
E-mail: ph...@pricom.com.au

[John Keller]

Philip,

My advice would be follow the threads that do make sense to you, and don’t worry about the ones that don’t! A few of the posters here could be described as being radical, even to the others who follow and understand. And this is not being derogatory.

I find that although I may not agree with certain ideas, I do find an occasional point worth considering that makes me rethink an aspect of my own system or teaching method.

Cheers,
John Keller
Express Stave

[John Keller]

This is a topic I have wanted to start for a while.

Comparing 7/5 layout to the Janko 6/6, I feel there are certain points actually favouring 7/5.

1 There is only one key to press for each pitch.

2 It is a layout which, without artificial colour or tactual markings, allows facility of finding notes by feel without having to look.

3 The distance between notes of the chromatic scale is even if you look at the back of the keys. This allows me to place my 'degree card' behind the keys on the keyboard to show the diatonic scale, the chords, the interval distances etc, and so we can easily associate relative solfa when playing the 7/5 piano.  

4 With Janko, there is consistency in fingering of every major scale starting on the tonic, but then you must learn a different fingering for minor or dorian or lydian modes etc. But the 7/5 piano has a consistency of its own: - 

In all 'right hand scales' (key signatures on the right of the clock) your right hand plays 4th finger on B or H, 3rd finger on E or J. You just add more black keys on the right of the groups of two and three as you go through the keys. So although the tonics change, the fingering doesn’t, and the modes also keep the same fingering, just adjusting to more or less of the black keys. 

The 'left hand scales' on the left of the clock have this same consistency for the left hand fingering. 

I teach kids to improvise on all scales progressing around the clock using this method. It is easy to explain, and even young kids get quite fluent at it. 

5 Even 6/6 AN advocates on this forum use note terminology which keeps the distinction between the naturals and ‘extras’. Traditional musicians on all instruments have this concept. For example, wind instruments have the naturals as easy linear fingering, with the accidentals fingering being more tricky. For violin and viola we have a similar concept in that consecutive fingers play diatonically and fingers are raised or lowered (inflected) to pitch the accidentals.  So for ease of conversing with other musicians, it is good to keep the 7/5 distinction. 

Although I teach the black key names H I J K L as well, I can easily point out that these are the ‘extras' and they may be referred to as sharps or flats of the naturals. And my Express Stave notation can be used with just the naturals if you want, using accidentals and key signatures as in TN, because the naturals and extras are clearly delineated by the (reverse) 7/5 note-head colour. 

Cheers,

John K

[Music Integrated Solution]

On Wed, Jan 13, 2016 at 11:36 PM, Jessifeph John <myle...@gmail.com> wrote:

MIS, 

it might be beneficial to use a simpler language than "previous-to-same" etc..

yes, it is redundant, but first time readers might wonder next or previous to what.

 About your other issues, the PRN is what it is, there options and workarounds but overall I prefer it as an alternative.

Enrique.

 

[Music Integrated Solution]

On Thu, Jan 14, 2016 at 5:47 PM, John Keller <jko...@bigpond.net.au> wrote:

How do we pronounce these syllables? the vowels?

I pronounce them as in Spanish where there are only five vowel sounds.

 

Do you want to ditch chord names such as “C major”, and replace by "Da saneni” ?

Yes, (rather da_nese) because this is an objective alternative

 

What would be the chord symbol instead of “C"?

There are generic chord names and specific chord names
For specific chords, I prefer the ‘v-normal order’, which use the pc names, as shown in J. Legend intro; then any Cmaj variant would be ‘damefi‘, but usually I use a bit more detailed variant for successions of harmonies e.g. in ‘All of me’ intro:

dami   demi   damafi   mafite  mafefi  I write optionally:

da/mí  /démi  dama/fí  mafíte  maféfi

The ‘/’ before the pc name indicates that the note is repeated on the chord, and the acute on the vowels indicates the lowest note or bass note; then the words can be pronounced with different stress according to the order used.

A map of v-normal orders is a form of objective description of harmonies, which is also a type of alternative to the full detailed scores, related to memory and freedom.

A specific chord can also be named with the format ‘pc_interval pattern’ e.g. Cmaj in normal order is da_nese or ‘pc_v-normal form’ but v-normal form has not been explained yet.

A generic name is shorter e.g. major is nese and minor is sene, a triad is named with the two successive pic concatenated.  

In a few words, I would describe all this as ‘A visual alternative to music set theory’ that in a more pretentious language it is suggesting a branch of set theory.

There are many reasons for having an objective alternative of describing harmonies and one of them is related to the use of chromatic notation, which I prefer to call pc musical notation meaning there are no sharps or flats.

On the other hand I am following (in my opinion) a solid path that has been created by many composers and scholars, and translating it through a visual scheme, the translation is not literal, there are differences to make it more useful and closer to tonal music.

If you notice I have avoided the words 'easy', or 'improvement over' for me it is 'a justified and necessary alternative' in our times that I am finally putting together while experiencing the difference.

Thanks

Enrique.

 

 

[Music Integrated Solution]

Doug, Joe,

Thanks for the comments/suggestions, I hope the previous post could be of help, anyway I will answer some of the questions that I see more necessary.

Thanks.

[Music Integrated Solution]

John,

Actually I talked about names and not symbols because now I am not using such compact form, there is an appeal describing with one letter, but first I have to go over with details then I will see if it is justified using some short version of the names.

In the traditional system it is more than justified because it uses very long names that anyway do not have the details of the chords, but these are short and have the details, actually I do not see a significant reason for having additionally symbols.

[Music Integrated Solution]

On Thu, Jan 14, 2016 at 10:47 PM, Joseph Austin <drtec...@gmail.com> wrote:

observations:

* clarify the meaning of "i-position" when the term is first introduced.

 

Joe, I emphasized more in the clusters, which is what define the positions, as a matter of fact symbols are small clusters, then changed i for c from cluster.

"Each rectangle in fig.1 correlates with a pc, which is indicated with pc conventional numerical notation; fig.1 shows four visually distinctive clusters with three pitch classes each.
Each pc occupies a distinctive and unique position on said clusters, so that we can see that e.g. pc 0, 3, 6 and 9 are in the same position of the clusters, said positions will be called the c-position.

 

* pic naming

- i get the consonant,

but I don't understand the "consistency" of the vowel

"The vowels a,e,i,o will indicate the specific physical distance (of the four possible) between c-positions, where 'a' is the closer and 'o' is the further as shown in fig. 2."

Thanks

[Ivaylo Naydenov]

Hi, John

I would like to give more wide spread over the subject you affect above as a comparison between standard 7-5 (black-n-white) piano keyboard and the janko 6-6, 6-5, 6-4 or 6-2 keyboard.

1. So... Yes, I there are design of a 6-2 janko keyboard. As a fact origianly Janko has designed 6-6 keyboard that only visualy appeared to be 6-6 whilst in reality it is 6-2 keyboard.

It is called internal bridge connection between the rows. But that is purely design and mechanical relevant so no need to say more on that.

2. Black and white are colours so standard piano keyboard also relies on colour. Tha tactile marks are the actual shapes and elevation of the keys between the two rows as well. Without that elevation standard piano is even worse than the janko one.

But it should be mentioned that like the standard piano kbd, also the original janko piano kbd and all its derivates till today (humbled reminder of my Plain Piano Keyboard) are designed to have elevated rows of keys respectively... which is bad (at least to me).

3. The distance between notes of the chromatic scale on the 7-5 kbd is not even... though they differ in a really small value, but they are not even. Yes you can "even" them with a purpously made ruler, that is not a problem. I have explained that in my "Treatise of Pentatonics".

4. Both keyboards have their own strenghts and weaknesses on that point. Mostly weaknesses... because their keys are separatet into elevated rows. Which sends us back to point 2.

I have no idea what you explain here. First I am not a standard piano kbd player and it sounds complicated to me.

5. I do advocate AN (Alternative Notations), because I have designed one (Plain Notation System), and I do not use terminology which distinguishes naturals, sharps, bflats, double flats, etc.! I am a traditional guitar player and I use Tabulature (which is the best Alternative Notation system for any fretted music instruments). This refers to Nomenclature of Music "theory" and as an advocate of an AN, I completely abandon the old (traditional, standard) way of approaching the notes, cleffs, intervals, chords, "octaves", etc.!

It is a very interesting subject to discuss the so called "musical alphabet: A, B, C, D, E, F, G. Why exactly those notes, who said that, and many other questions. Maybe it is the case like with the psalm Sancte Iohannes (Hymnus in Ioannem). Hence all that is a special case. And as such they do not fit well in a new Alternative Notation, Nomenclature and "theory". Not al all.

[Music Integrated Solution]

On Thu, Jan 14, 2016 at 10:47 PM, Joseph Austin <drtec...@gmail.com> wrote:

observations:

* I'm not sure "consistent" is the word you want.

"The demarcated groups of three rectangles on fig.1 create a ‘three positional scheme’, meaning that despite whatever color those rectangles may have what is consistent is their position on the demarcated clusters."

Joe, I know this is turning dense but I started the conversation and feel the responsibility that what I am saying is understood.

For me the conversation has been worth the time in helping me to improve communicating what does not seem to be obvious.

Thanks.

[Joseph Austin]

PS,

To be clear, my concern is that two intervals with the number of steps could have two different pic names using the "visual" method, and the same pic name could represent intervals of different size.

For example:

01 = na (one step)

12 = na (one step)

but

23 = ne, (also one step)  "e" because the color-group changes: starts in blue, ends in white.

Also:

08 = li (7 steps) [previous in three; two color changes away]

but

16 = li (5 steps)

Or else I don't understand how the "visual" identification via the color groups works.

Joe Austin

[Music Integrated Solution]

Phil,
I assume you have read the provided links as well as some complementary comments.
I have to say that everything do not have to be made with the only purpose of being simple and easy, or for kids.
Can you imagine what it would be of computer programming if the only purpose were to make it simple and easy?

Alternative music notation has been mostly projected from the ‘look and push’ point of view.
Though we can certainly look and push with the v-pc musical notation, this is projected as an integrated system that is additionally very concerned with the alternative (objective) description of harmonies and with the alternative (set theoretical) manipulation of harmonic materials.
But, first it has to be understood to realize if it could be of any use for you.

On the surface a conclusion could be a starting point:
“concluding that the v-pc musical notation and its visual scheme is more convenient than conventional numerical pc notation for musical purposes, and more convenient than the traditional diatonic notation for set theoretical purposes”.

Enrique.

[Music Integrated Solution]

On Fri, Jan 15, 2016 at 7:45 PM, Joseph Austin <drtec...@gmail.com> wrote:

PS,

To be clear, my concern is that two intervals with the number of steps could have two different pic names using the "visual" method, and the same pic name could represent intervals of different size.

No, that is not the case

 

For example:

01 = na (one step)

12 = na (one step)

but

23 = ne, (also one step)  "e" because the color-group changes: starts in blue, ends in white.

On the table and looking left to right, from 2 to 3 is na for two reasons:

() The only meaning and purpose of color is to produce visual clusters, the only thing that is next is the c-position on the cluster.

() The distance expressed with a,e,i,o is measure starting (equally) from every pc.

 

[Music Integrated Solution]

Joe,
I am calling it 3x4 because it highlights (most distinctive) the cycle of 3 positions, which is repeated 4 times, or it can be seen also as three types are repeated 4 times
while you are calling 3x4 two concurrent cycles, one of 3 types and another of 4
If I may, I would call chroma tonnetz scheme 3x4&4x3, while v-pc notation is 3x4&6x2

The problem is that dictionaries usually do not include definitions of irrelevance.

On the other hand, if all intervals were in some way highlighted then it will result no highlighting at all.
I have taken back some variant of naming pc that I considered a while ago, now I see it fits perfect to the set theoretical approach, because it includes also the 6x2 scheme on the pc names, it is more efficient because it uses only 3 consonants, and has some other advantages.

Now e.g. the name ba and bla reflect both the second minor and tritone relationship.

 

[John Keller]

Enrique,

Now e.g. the name ba and bla reflect both the second minor and tritone relationship.

You say "second minor", but mean “unison”!

You have simply changed your pitch class names.

The following table shows 

Express Stave pitch names

Old MIS pitch names

New MIS pitch names

C   I   D   J   E   F   K   G   L   A   H   B   C

da de di ma me mi fa  fe   fi   ta  te   ti   da

ba be bi  fa  fe   fi  bla ble bli fla  fle  fli  ba

Is this correct?

I suggest that you could express yourself more simply, so as to be better understood :)

Cheers, 

John K

 

[Music Integrated Solution]

Hi John,

What I should had typed is that with this kind of arrangement the succession of some names continues reflecting the minor third, e.g. ba fa (the vowels remain the same), but the tritone is now as distinctive as in the notation e.g. ba bla, fe fle.... 

I think overall it is better; I am generating by computer several combinations of this type, like instead of using the 'l' adding a vowel at the end, e.g. instead of fla or ble it would be fau or beu, not sure what is the best yet.

But what it is important is that all this (I call a visual implementation of pc set theory) has produced a spark that is leading me to a way of understanding or explaining what tonal music is, and this is a more serious stuff. Now I find more meaningful the words of the poet "walker there is no path, the path is made by walking". 

Thanks.

[Joseph Austin]

PS,

To be clear, my concern is that two intervals with the number of steps could have two different pic names using the "visual" method, and the same pic name could represent intervals of different size.

For example:

01 = na (one step)

12 = na (one step)

but

23 = ne, (also one step)  "e" because the color-group changes: starts in blue, ends in white.

Also:

08 = li (7 steps) [previous in three; two color changes away]

but

16 = li (5 steps)

Or else I don't understand how the "visual" identification via the color groups works.

Joe Austin

[Joseph Austin]

PS,

To be clear, my concern is that two intervals with the number of steps could have two different pic names using the "visual" method, and the same pic name could represent intervals of different size.

For example:

01 = na (one step)

12 = na (one step)

but

23 = ne, (also one step)  "e" because the color-group changes: starts in blue, ends in white.

Also:

08 = li (7 steps) [previous in three; two color changes away]

but

16 = li (5 steps)

Or else I don't understand how the "visual" identification via the color groups works.

Joe Austin

[Joseph Austin]

Sorry for the duplicates--I had email issues causing some to be resent.

Joe

[Joseph Austin]

So you are saying the vowel cannot be read directly from the colors,

but must be "counted"?

In that case, in what sense is your naming scheme  "visual"?

Joe

[Joseph Austin]

Enrique,

I don't doubt that your system provides unique names.

And your "reference heads" are an effective alternative to a staff for PRN music.

But we already have a well-trodden analysis path of "stacked thirds", i.e. chromatic "3"s and "4"s.

And in fact all intervals and chords can be described with number strings (use letters or syllables for the "digits" it you prefer, and use twelve or twenty-four (for larger intervals) distinct syllables if you want compaction.

The root-interval-interval... form is quite compact and meaningful,

without the necessity of learning new names (although I would not object to going dozenal).

e.g. 043 = C major,, 

034= C minor, 

0433= C7

0343= Cmin7

0434=Cmaj7 

044=Caug

0333=Cdim7

etc.

And alternative voicings could also be represented this way if desired.

I keep saying the "proof of the pudding" will be more evident in the examples than in the definitions.

When can we expect to see meaningful musical concepts like chord progressions explicated in terms of the new theory?

For example, I've suggested that "Circle of fifths" progressions can be understood as descending chromatic tritones, which become evident in a notation like Chromatonnetz in which tritones exhibit an isomorphic visual similarity (same color, opposite orientation) and the progression exhibits continuous color-orientation movement along an intuitive sequence (rotation, incremental color change)

Joe

[Joseph Austin]

John,

You may be correct, but I think it's worthwhile continuing to experiment with Janko.

From my limited experience with Janko, I miss the lack of "tactile orientation" of the 7-5 keyboard.

But I had assumed "feeling for the black keys" on piano was a beginner crutch whose need would disappear with practice (just as, for example, it disappears when reaching for pedals on the organ).

Paul V's differentiated-surface keys may help somewhat, but I have no experience with that.

Also, I am now convinced that "janko" is a "different instrument" from piano, 

as for example a ukulele or banjo is not a guitar,

and requires a different technique and pedagogy to master.  

Whether Janko is in fact easier to learn and play than piano is still an open question, in my opinion.

It is easy enough to "play by ear" by the "hunt and peck" method, 

at least if one uses an isomorphic coloring,

but I'm not persuaded that it is "easy" to play by sight-reading notation.

A typical 5-finger exercise like Hanon #1 requires continual vigilance and change of pattern in locating thumb and fingers on the proper rows for each motif (which could be somewhat aided by an alternating-color notation such as Clairnote).  It's like playing in the "most difficult" piano key all the time!

I'm suspecting part of my difficulty is due to the small, typewriter-style buttons of the Chromatone 

as opposed to larger rectangular surfaces of the original Janko or some other modern implementations.

The other part of the difficulty is lack of suitable beginner material.

We have found some "Molineux" lessons that move at a leisurely pace, but I have not yet gotten into them.

First, I need to convert them to isomorphic chromatic notation!

[The first set of lessons focus on timing notation, which I believe is the right approach,

but not particularly relevant to janko vs. piano.]

Another significant advantage of piano: they are everywhere.

If you play Janko, you must take your own instrument along wherever you want to play it!

Joe Austin

[Joseph Austin]

Enrique,

I'm not sure what to call my system, because I'm not aware of a conventional numeral system that uses concurrent cycles.

Incidentally, I've been toying with a representation of the Tonnetz as a 24-point space,

basically a major+minor circles-of-fifths, where each triangle has intervals 3,4,7

 g d a e b F C G D A E B 

e b F C G D A E B f c g

or dozenally:

 6 1 8 3 E 5 0 7 2 9 4 X 

3 E 5 0 7 2 9 4 X 6 1 8

-----

I'm thinking about what your system would look like if implemented in Synthesia.

I'm imagining the traces in groups of three against four color bands per your graphic,

e.g. blue white green white.

Now for purposes of Janko I might prefer the two-factor to be the more apparent,

e.g. two colors of traces, or three bands of four rather than four bands of three.

This would essentially become a Synthesia version of Clairnote.

Joe

[Music Integrated Solution]

On Wed, Jan 20, 2016 at 3:48 PM, Joseph Austin <drtec...@gmail.com> wrote:

So you are saying the vowel cannot be read directly from the colors,

but must be "counted"?

In that case, in what sense is your naming scheme  "visual"?

As you can 'see' four pitch classes on the same cluster-position, and see the different distances between them; some vowels are used according to the distance, formerly ‘a’ for the closer and ‘o’ for the further.

However, adjusting to the set theoretical approach, where ic (mod 6) is used over pic (mod 12), then the tritone ‘special distinction’ on the notation, now is reflected on the pic names,  e.g.

sa na la se ne le - sai nai lai sei nei lei

I think, overall these type of pic names are better

 

Same for pc names

da de di a e i - dar der dir ar er ir

[Music Integrated Solution]

The three-color scheme and three-positional scheme have some similarity but they are different.
The 3-color is like an obvious way of using three colors, but the 3-position has important advantages, e.g. 12 pc orientation (very efficient way of using 3 colors) and can be expressed with symbols, even without different colors.

[roy pertchik]

I've been advocating this system for years: three colors rotating on a 6+6 layout, 3x4 names using three consonants and four vowels.

Roy Pertchik

Design and Construction Consultant
NYS Arch., NCARB

2130 Birch Street

Palo Alto, CA 94306

917 294 6605

Let's make the world a little better

[Music Integrated Solution]

On Sat, Jan 23, 2016 at 2:21 PM, roy pertchik <roype...@gmail.com> wrote:

I've been advocating this system for years: three colors rotating on a 6+6 layout, 3x4 names using three consonants and four vowels.

Hi Roy,

I know; your system has been praised and frequently quoted here, but from my point of view it is not enough, to say the best, and sort of stuck on its way to somewhere, that is what I see; you know, in this group there is no policy against unsolicited opinions:)

Regards

Enrique.

[Joseph Austin]

Roy,

I don't think  Enrique's system is "factored" the same way as yours.

FWIW, I'm finding my 12 shapes are quite useful interpreted as scale degrees in moveable-do,

especially for the Janko in which the scale shape, hence fingering, is the same in all keys regardless of absolute pitches.

So I "play" by scale degrees, not by pitch names.

But the 3x4 aspect is quite useful for recognizing chords and harmonies,

especially in hymn music which it typically scored in 4 parts.

So what I'm saying is,

traditional pitch notation is useful for "laying bricks";

3x4 tri-color is more useful for "building walls" and "building cathedrals".

Joe Austin

[Music Integrated Solution]

On Mon, Jan 25, 2016 at 7:49 PM, Joseph Austin <drtec...@gmail.com> wrote:

Roy,

I don't think  Enrique's system is "factored" the same way as yours.

Joe,
I have to agree, the MIS stands (is factored?) on the most relevant and important of the related alternative world, on what is accepted and appreciated by a huge international community of musicians and composers.

What I see is that the concurrency of 3/4 (or 3x4C to give it a name) is rather an experiment in a deadlock that is given more value than what it actually has, or in other words, the idea is asociated by its proponensts with having some unique or exclusive value and subsequently it has to be implemented at any cost, but what I see is that the resulsts does not justify the cost and do not see a real unique value.

Enrique.

[Joseph Austin]

Enrique,

I don't know whether Roy has statistics regarding tri-color implementations, 

but I for one do find it useful, especially for identifying chord intervals.  

Of course, no one has to implement anything they don't find useful,

[although many of us must settle for what "the market" does choose to implement]

but I offer no apology for promoting tri-color advantages as I see them.

Of course I couple it with a 2x2 factor which results in:

* 12 unique symbols, comprising a "shape-note" system for identifying chromatic scale degrees,

* odd-even differentiation for distinguishing Janko keyboard rows.

* visual identification of major-minor thirds/sixths and tritones.

* no discontinuities in either sequence, resulting in a "more perfect" isomorphism among keys.

* The interval distance can be computed from Color,Angle with the formula =3*(C-A)mod4 + C,

where C = {0,1,2} and A = {0,1,2,3}

C-A is the amount the color cycle is "ahead" of the orientation cycle.

I surmise that this is the sort of "visual arithmetic" you were striving for,

and it actually works with concurrent cycles!  

I would say, for Janko, your "color-band" system would be more useful with 3 bands of 4 than 4 bands of 3, 

as one needs an even-odd factor to distinguish janko rows.

I'd use caution using popularity of adoption as the measure of goodness.

By that criterion, TN would be the "best" system!

(Of course, some would argue that that is correct.)

Joe

[Joseph Austin]

PS, here is the color-orientation calculation

[Jessifeph John]

What would we do to orient ourselves in 19tet? Is there any pattern to be had from a prime number?

[Keislar, Doug]

Interesting question. Obviously a prime number by definition has no factors, so there are no simple cycles like the 6x2, 4x3, etc. in 12-TET.
In terms of tonality, the whole step in 19-TET is 3/19 of an octave and the diatonic half-step is 2/19, so a major scale is these intervals (measured in units of 1/19 octave): 3, 3, 2, 3, 3, 3, 2. Music theorists would call the distribution of the 3s and 2s "maximally even."

https://en.m.wikipedia.org/wiki/19_equal_temperament

Unless one wants to learn a different notation system for every conceivable tuning system of interest, it seems one has to adopt a certain tuning as the reference point and measure others as deviations from it, perhaps using the same notation system but adding some sort of accidentals or other indicators. That reference tuning could be 12-TET and the notation could be a chromatic, 12-degree system such as those on the Music Notation Project site. On the other hand, quite a few microtonal enthusiasts have stuck with TN and used various accidentals for the microtones.

Doug
________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Jessifeph John [myle...@gmail.com]
Sent: Tuesday, January 26, 2016 9:06 PM
To: The Music Notation Project | Forum
Subject: Re: [MNP] Introducing music Visual set theory

What would we do to orient ourselves in 19tet? Is there any pattern to be had from a prime number?

[Doug Keislar]

I'm changing the subject line, since the topic here has departed from the original thread.

Regarding how to notate 19-TET, as asked by Inopa below, I had replied that we could consider using a 12-degree staff with alterations such as accidentals to accommodate the other seven tones.  Then today I remembered that Joseph Yasser had already done this back in 1932, as you can see in the attached picture:



Yasser's book A Theory of Evolving Tonality advocated 19-TET.  He was taken with the idea that just as 12-TET had a grouping of 7 diatonic tones plus 5 ancillary chromatic tones, 19-TET could be considered as a group of 12 plus an ancillary group of 7.  (A sort of Fibonacci series.  The next in the series would be 31, which is also a popular microtonal scale.)  As you can see above, he designed both a notation system (having 12 degrees per octave -- six lines and six spaces) and a keyboard (but not an isomorphic one!).  The top staff above shows the 12 pitches in TN.  The bottom staff shows all 19 pitches on his 12-degree staff, with the group of 7 indicated as both sharps and flats that alter neighboring pitches in the main group of 12.

Yasser's group of 12 notes are selected from 19-TET, thus they don't have the same tuning as the 12 notes of 12-TET.  I was wondering whether his grouping also reflects the 12 pitches that are closest to 12-TET.  The tuning, in cents, of 19-TET is shown here:

https://en.m.wikipedia.org/wiki/19_equal_temperament#Scale_diagram

Here are the degrees that are furthest from 12-TET (in other words, furthest in cents from a multiple of 100, which also means the closest to a quarter-tone):

2.  63 (-37)
5.  253 (-47)
8.  442 (+42)
10.  568 (-32)
11.  632 (+32) - Yasser chose this to be a "white key"
13.  758 (-42)
16.  947 (+47)
19.  1137 (+37)

The first column is the scale degree, using 1-based counting, rather than 0-based.  The second column is the interval size in cents, and the number in parentheses is the deviation in cents from the closest 12-TET pitch.  As you can see, there are eight of these outliers, and their deviations form a symmetrical series.  For example, the first in the list has a deviation of -37, while the last has +37, and so on.  Yasser needed only 7 pitches, not 8, so he chose scale degree #11 to be a "white key" (part of the group of 12).  He could have equally well chosen #10, I think.  Other than that one scale degree that's part of his 12, his grouping is indeed the same as the list of outliers above.  So in fact he did choose the 12 closest to 12-TET (with one choice being arbitrary).

For the 12-note scale, he chose a series starting with C, just as on the traditional keyboard.  The choice is completely arbitrary, other than retaining compatibility with traditional names, but I would tend to base the series instead on D, which is the central point of the circle of fifths in terms of the numbers of sharps and flats.  In the traditional system, there are 7 diatonic pitches, and D is the centermost pitch of these on the circle of fifths.  Similarly, in 19-TET, the circle of fifths is seen here:

https://en.m.wikipedia.org/wiki/19_equal_temperament#Scale_diagram

but since 12 is an even number, unlike 7, there are two choices for a group of 12 that have D near the center:
Ab Eb Bb F C G D A E B F# C#
or
Eb Bb F C G D A E B F# C# G#

As you can also see in the circle of fifths at the above URL, D is diametrically opposite the pair B#/Cb and E#/Fb, which (as you can see in the scale diagram) are the only two pitches of 19-TET in which a sharp and a flat are enharmonically equivalent.

If I were designing a notation system for 19-TET based on a 12-degree staff, I wouldn't choose to use both sharps and flats to indicate each of the 7 ancillary tones, as Yasser did.  I'd probably choose just one new symbol.  Or maybe I'd use two -- such as an up arrow and a down arrow -- but only one for a given scale degree, depending on whether the pitch is closer to the 12-TET pitch above or the 12-TET pitch below.

-- Doug

[Joseph Austin]

Why choose just 12 "chromatic" pitches instead of, say, 13?

I had suggested extending the diatonic scales with 5 additional fifths when using a 12-position staff.

But it does lead to an ambiguity, in the key of C, for G# vs Ab. Adding both would solve the problem,

but of course would require an accidental to distinguish only those two pitches in a given "13-fifths key" on a 12-position staff.

I've not studied this extensively, but off the top of my head, I'm wondering whether instead of attempting to notate absolute pitch, when scoring "justly tuned" music, we should rather notate intervals.

This is essentially a "mathematically dual" notation:

given two pitches, one can compute the interval,

but given one pitch and an interval, one can compute the other pitch.

BTW, TN notates absolute pitch and relative time.

I've been advocating for notating absolute time.

But why not relative pitch?

Has anybody ever proposed an intervalic or relative-pitch notation?

Joe Austin

[Keislar, Doug]

Joe,

The reason to choose 12 quasi-diatonic (not "chromatic") pitches, rather than 13, is that there are 12 positions on a chromatic staff that was designed for 12-TET (such as most of the ANs discussed in this forum). The point is to consider if we can start from one standard AN (such as 12-degree one) and accomodate microtonal scales that have more than 12 pitch classes. In the case 19-TET, it works well to choose a group of 12 main pitches (what I'm calling "quasi-diatonic" here), with 7 ancillary ones. For some other microtonal scales, deciding on 12 would probably be more difficult.

Regarding whether anyone has proposed a relative-pitch AN, see:
http://musicnotation.org/system/thumline-notation-by-jim-plamondon/
Ignore the fact that the chromatic scale is illustrated there using fixed note names; I believe that's just a side effect of the Web programming.
Not sure whether this is what you had in mind. Obviously, any pitch-proportional AN can in principle be used either in an absolute or a relative manner.

-- Doug
________________________________________
From: musicn...@googlegroups.com [musicn...@googlegroups.com] on behalf of Joseph Austin [drtec...@gmail.com]
Sent: Wednesday, January 27, 2016 6:33 PM
To: musicn...@googlegroups.com
Subject: Re: [MNP] accommodating microtonal scales

Why choose just 12 "chromatic" pitches instead of, say, 13?
I had suggested extending the diatonic scales with 5 additional fifths when using a 12-position staff.
But it does lead to an ambiguity, in the key of C, for G# vs Ab. Adding both would solve the problem,
but of course would require an accidental to distinguish only those two pitches in a given "13-fifths key" on a 12-position staff.

I've not studied this extensively, but off the top of my head, I'm wondering whether instead of attempting to notate absolute pitch, when scoring "justly tuned" music, we should rather notate intervals.
This is essentially a "mathematically dual" notation:
given two pitches, one can compute the interval,
but given one pitch and an interval, one can compute the other pitch.

BTW, TN notates absolute pitch and relative time.
I've been advocating for notating absolute time.
But why not relative pitch?

Has anybody ever proposed an intervalic or relative-pitch notation?

Joe Austin

On Jan 27, 2016, at 8:24 PM, Doug Keislar <do...@musclefish.com<mailto:do...@musclefish.com>> wrote:

I'm changing the subject line, since the topic here has departed from the original thread.

Regarding how to notate 19-TET, as asked by Inopa below, I had replied that we could consider using a 12-degree staff with alterations such as accidentals to accommodate the other seven tones. Then today I remembered that Joseph Yasser had already done this back in 1932, as you can see in the attached picture:

[cid:part1.06090...@musclefish.com]

You received this message because you are subscribed to the Google Groups "<https://en.m.wikipedia.org/wiki/19_equal_temperamentUnlessonewantstolearnadifferentnotationsystemforeveryconceivabletuningsystemofinterest,itseemsonehastoadoptacertaintuningasthereferencepointandmeasureothersasdeviationsfromit,perhapsusingthesamenotationsystembutaddingsomesortofaccidentalsorotherindicators.Thatreferencetuningcouldbe12-TETandthenotationcouldbeachromatic,12-degreesystemsuchasthoseontheMusicNotationProjectsite.Ontheotherhand,quiteafewmicrotonalenthusiastshavestuckwithTNandusedvariousaccidentalsforthemicrotones.Doug________________________________________From:musicn...@googlegroups.com[musicn...@googlegroups.com]onbehalfofJessifephJohn[myle...@gmail.com]Sent:Tuesday,January26,20169:06PMTo:TheMusicNotationProject|ForumSubject:Re:[MNP]IntroducingmusicVisualsettheoryWhatwouldwedotoorientourselvesin19tet?Isthereanypatterntobehadfromaprimenumber?--YoureceivedthismessagebecauseyouaresubscribedtotheforumoftheMusicNotationProject(hostedbyGoogleGroups).Toposttothisgroup,sendemailtom...@googlegroups.comTounsubscribefromthisgroup,sendemailtomusicno...@googlegroups.comFormoreoptions,visitthisgroupathttp://groups.google.com/group/musicnotation?hl=en---YoureceivedthismessagebecauseyouaresubscribedtotheGoogleGroups>The Music Notation Project | Forum" group.
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[Jessifeph John]

Doug, thanks so much for your response.

I realize now that I'm too obsessed with the factors of 12. I need to update my framework. I want to get down to the essence of it. I want my framework to be descriptive not predictive, and I want it to allow for easy orientation and getting around. I think I could start with some overarching foundation that can be simplified for particulars. Maybe the foundation should be the ratios of intervals, but I don't know how to get from there to simplified descriptions. I'll come up with something eventually.

Doug, what exactly do you mean by "I'd probably choose just one new symbol."

-Inopa

[Doug Keislar]

Re:

> Doug, what exactly do you mean by "I'd probably choose just one new symbol."

I just meant that I thought it was unnecessary for Yasser to use both
sharps and flats for everything in the set of 7 pitch classes (the black
keys on his keyboard). He was trying to follow the model of TN. I
meant that for a given pitch class in 19-TET (one of the 7 that required
an "accidental" on a 12-degree staff), I would use just one symbol (such
as an up arrow or a down arrow) -- not two enharmonic equivalents. For
example, for A# (in the nomenclature used at
https://en.m.wikipedia.org/wiki/19_equal_temperament#Scale_diagram) I
might use a downward-pointing arrow in front of a notehead on the line
that would normally be used for A# on a 12-degree staff. The arrow
would be downward pointing to reflect the fact that the pitch is 37
cents lower than a 12-TET A#.

For total clarity, we could also put "accidentals" in front of all the
pitches that are different from 12-TET, such as an upward or downward
arrow along with the number of cents deviation. Or that could go in a
"tuning signature" (like a key signature) at the beginning of the staff.

Doug

[Michael Johnston]

http://www.classicalmpr.org/story/2016/01/25/the-sibelius-academy-acquires-a-new-quartertone-piano

There's a nice photo of their quarter-tone piano.

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"

[Doug Keislar]

Thanks, Michael! Very interesting.

On further reading, it seems that the photo at that URL is actually a
photo of an old quarter-tone piano, probably from the early 20th century.
The Academy's own Web site has a photo of their new keyboard, which is
quite different:
http://www.uniarts.fi/en/newsroom/new-quarter-tone-piano-acquired-sibelius-academy
It apparently has MIDI output, so that the sound can be either
computer-generated or acoustically generated on a pair of conventional
MIDI-equipped pianos.

Doug

[Music Integrated Solution]

Joe,
I appreciate your comments; it is interesting to see your enthusiasm for a less efficient use of tri-colors or dependency on them, the 3/4C concurrency of schemes and the pure symbolic notation of pc(s). It made sense because of the spreadsheet and word processor story.
There is a lot going on, I wish I had the time to make it happen, so let’s see.

 

[Jessifeph John]

I'm frustrated. I spent the last 4 hours trying to understand the ratios of just intonation. I don't know where I'm getting tripped up. Can someone help me? Why is 3/2, which is 1.5, not halfway between the octave? Why is it 2/3 from the base note? Is 2 not the octave, and 1 the reference point, hence 2/1? I'm clearly just misunderstanding something. God this is driving me nuts.

-Inopa

P.S halp.

[Doug Keislar]

Yes, it's confusing.  Frequency is linear, but pitch is the log of frequency, so it's a log scale. 
The piano keyboard is a logarithmic scale of frequency.  Octaves are powers of 2 in terms of frequency (but multiples of 12 in terms of log frequency).  Half of an octave is 2 to the 6/12 power (which is the square root of two, which is not 1.5).

Maybe these will help:

https://en.wikipedia.org/wiki/Interval_%28music%29#Frequency_ratios
"For instance, an equal-tempered fifth has a frequency ratio of 2^7/12:1, approximately equal to 1.498:1, or 2.997:2 (very close to 3:2)."

https://en.wikipedia.org/wiki/Music_and_mathematics#Frequency_and_harmony

-- Doug

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