Really quite Meloquial, this!

Well, with some suitably clever marketing you should both become affluent!

Here's a portion of it. Still a work in progress, and not intended for church use.

Recording (synth) at https://soundcloud.com/williamcopper/0582_melofluent

Pdf below. J

I find this micro-notation easier to read and play.

Unless I'm mistaken:
CB's example is of micro-tonal music - that is, music with deliberately more then 24 (mas o menos) named pitch classes- essentially "extended technique" with regards available pitches.
This is in contrast to Mr. C's system, which is a (more or less) traditional understanding of music theory and harmony, except wherein an understanding of intonation may inform the course of the composer's craft and the performer's execution.

That is to say, I don't think that CB's and Mr. C's notational systems are in conflict/competition, but rather that they have wholly different purposes.

Mr copper, is there a sideways picture on my comment in your browser?

Kathy's photo, got it now, ty Chonak.

Wow.... I never heard of Newband or the zoomoozophone. I thought Mr. Bass was just making up words.

This is for Chuck and anyone else with a math background and/or weird interests, just speculation:

Let's represent Melofluent's melody in the traditional pitchclass interval format:
[357230] (first four bars).

One improvement, signed intervals: [-3 5 7 -2 -3 0 ]

Now, these intervals are themselves ratios: [ -6/5, 4/3, 3/2, -10/9, -6/5, 1/1 ]

And these ratios can be represented by real numbers:

[ -1.2000, 1.3333, 1.5000, -1.1111, 1.2000, 1.0000 ] or subtracting 1

[ -0.2000, 0.3333, 0.5000, -0.1111, 0.2000, 0.0000 ]

The question: are there ways to manipulate a set of real numbers in a meaningful way musically?

And another question: is is conceivable to get the rhythm combined with the set somehow: simplistically, for example, 2 for the half note, 1 for the quarter and multiply, gives

[ -2.4000, 1.3333, 3.0000, -1.1111, 2.4000, 3.000 ]

And another question: the set is ordered. Might one use the ordinal number itself in some recursive way?

Um, a few comments, although I am not sure just how relevant they are.

1) "Ratios" such as -6/5 are real numbers: -6/5 = -1.2.

2) You didn't actually subtract 1 from the (signed) numbers: you subtracted 1 from the positive numbers and added 1 to the negative numbers. At any rate, since succession of pitch ratios behaves multiplicatively (not additively), any such subtraction (or addition) is, on the whole, meaningless, except to distort the nature of the ratios themselves.

3) Actually, signed numbers (ratios) is not really what should be considered here, anyway. It is the (positive) ratio of the (absolute) frequencies <2nd freq>/<1st freq>, so that a descending interval will have a ratio less than one, while an ascending interval will have a pitch greater than one. Thus, in your example the ratios would be:

[5/6, 4/3, 3/2, 9/10, 5/6, 1]

Now, once we have the sequence in 3), it is easy to see what the ratios are when one skips over notes (eg. this might be reasonable for skipping over "passing" notes). Thus (while the 2nd, 4th and 6th notes are not passing notes in your example, they are not the downbeat notes, so to get the pitch ratios for the intervals from the 1st to 3rd to 5th to 7th notes, just multiply pairs of ratios:

[5/6*4/3, 3/2*9/10, 5/6*1] =[ 10/9, 27/20, 5/6]

which fits with the pitchclass interval sequence [2, 5, -3] for the intervals of successive downbeats. Note the crooked fourth ratio 27/20, which suggests that the somewhat narrow 9/10 descending major second ratio would be better served by using a the wider ratio of 8/9 ... for then the second downbeat ratio would be 3/2*8/9 = 4/3, namely that of a perfect fourth. This makes the downbeat ratio for the first measure to the third measure equal to 10/9*4/3 = 40/27, which is, of course, a crooked fifth, where originally this ratio was 10/9*27/20 = 3/2, a perfect fifth.

Put differently, the absolute pitches (taking G=1) of the notes, in your original sequence are:

[1, 5/6, 10/9, 5/3, 3/2, 5/4, 5/4] = [G, E, A, E, D, B, B];

of course, these are part of the G-major scale with absolute pitch ratios:

[G, A, B, (C), D, E] = [1, 10/9, 5/4, (4/3), 3/2, 5/3].

I have noticed that the first four measures of your melody are entirely pentatonic, which prompts some further thoughts. But more about that later.

CharlesW ... i am a mathematician, as well as a musician. For some it may seem idle hands and too much free time. But this is in the nature of scholarly research and application, all in a quest for a better understanding and practice of our compositional and performance art and craft.

Interesting. CharlesW, this is WORK, btw, fun tho it may be.

I like the idea of the array (x,y) with pitch, rhythm kept separate, and yes, the correction of my ratios to greater or less than 1 for up or down is definitely an improvement. Forcing downbeats to pure tuning would be wrong however: it's a feature of the melody that the downbeats do NOT make a pure fifth/fourth. Or perhaps that the melody is in 6/4 with the pure fifth at the third bar ... but see Kathy's comment re 6 in another thread, not that I agree with that.

Great thoughts, I'm still working through these ideas. If only Melo himself can play them ...

Quite true. I already know, though, that Act IV of this little piece is going be all about DO SI RE, with the high tuned A. That's music analysis, not math. I'd just like to get there in a mathematically interesting way.

Without mathematical realities as they relate to physics we would have no music.
But!, thankfully, we don't have to understand mathematics or physics to make beautiful music; and, likely, make it with more poetry than of which a mathematician ever dreamed. (Poetry, fortunately, is not reducable to mathematical formulae, and, is a spiritual, rather than a physical, phenomenon.)

Yes, carelessness, and unfamiliarity with treating the intervals as ratios. Corrected now. My expansion of the melody was a simple matter of making each interval one diatonic step larger (major or minor second, whichever leaves the interval in the same diatonic scale).

It's important to the piece, as I imagined it, that the second bar A be tuned low: I've worked before on the notion of Shenkerian second scale step being brought into play only when its tuning changes from low to high, ie from subdominant to dominant harmony. So that's going to be the overriding structure: G (low A) B (high A) G.

[edit] removed most recent update; a few more days it should be done but the bridge is out right now ...

Almost done. Tentative new title "The Enchanted Circle". Also toyed with "Golden Drop of Sun" since it is kind of a study on the tuning of RE.

https://soundcloud.com/williamcopper/0582_enchanted_circle

WIP Score attached. Edit: finished score attached. May need one more pass of revision to get more smoothly to the end.

Thanks, Francis... still working on it. Also posted a couple of the 10 or so flute quartets I've written recently, at https://soundcloud.com/williamcopper

And an arrangement of O Danny Boy for Flute and Strings: https://soundcloud.com/williamcopper/0547_danny_boy