PROGRESSION

Brad Lehman, Tom Dent, Mike Bataglia, A. Sparschuh.....

-- Twenty eight years ago I was not acquainted that musical scales could be designed in a matter of hours, I knew this a few weeks ago by reading emails in tuning yahoo groups. The standard way of research to develop an scale that could be better than the equal tempered put me on the apparent only way to attain my purpose, that is, start and continue with micro-elements of musical sounds and consonance. While I was planning the first steps, I guess that many scales had been designed in tuning yahoo groups and in other places. I don´t know if these efforts are done as pass time or they have defined objectives.

-- In the period 1983 - 1992, the research produced the Piagui system of three scales thanks to the Progression of Musical Cells formed by 612 cell frequencies from Do = 1 up to 2Do = 2. The first cell is the schisma (32805 / 32768) = 1,00112915039,,,,This smallest consonance, distinguishable by the ear of man, after verifying the exactness of all the tones of the Pythagoras and Just Intonation extended scales that emerged in the progression, ratyfies that its value is having a rol in the Physics science, acoustic chapter and more specifically as the basic element of music. Should the first cell of the progression be another value instead of the schisma, none of the fundamental frequencies needed to construct the Piagui system would have been determined. I say more: I do not discard that the Piagui system is a development that is backed by Physics.

-- Actually, cell Nº 612 doesn´t close the progression expansion; its real periodicity is (9/8)(1/2) = 1,06066017178 that never ends and corresponds to the semitone factor K of the Piagui scales, instead, the progression expansion go to an inaudible infinite frequency with respect to Do = 1 which represents any absolute frequency given in cycles per second (Hz). Curiously, from cell Nº 613 a second octave starts its expansion towards cell Nº 612 x 2 = 1224 = 4Do. From here to Nº 612 x 3 = 1836 = 8Do ,,,,, and so forth.

-- Many unknown relations of musical sounds work in the progression and part of them were detected; by now the achieved Piagui system is the real benefit based on the progression, however other benefits could probably be obtained.

-- In case that any member of tuning yahoo groups wants to get the Progression of Musical Cells, just request me to be sent by e-mail.

Lima, Jujy 11, 2008

MARIO PIZARRO

piagui@...

Just wanted to say that, even allowing for something lost in translation, this statement

("32805 / 32768) = 1,00112915039,,,,This smallest consonance, distinguishable by the ear of man...")

seems doubtful.

because:

- at any frequency, 32805/32768 is a unison with beating. If the frequencies were 32805 hz over 32768 hz, these would be inaudible pitches, but they would have an absurdly low difference tone--37 hz. Neither of these supersonic pitches are multiples of 37 hz, and they are some 885 times its pitch--so they aren't comprehensible as harmonics of 37 hz. either. This is around 2 cents, which btw, is around the frequency resolution of a Yamaha tx802 or similar synth.

- because it's a unison with a beating, it's not a consonance. 3/1 is a consonance. a sufficiently high 21/4 (or something) is a sort of consonance, of a funky variety. (64/21 is not a consonance, as I understand the term.)

- a consonance is a simple ratio with a theoretically audible fundamental, or an approximation of same, or it's a psychological term having little precision but meaning "stable" "pleasing" or "familiar"

- "distinguishable by the ear of man" suggests research with subjects, and possibly officious men garbed in white smocks, but i'd wager you haven't been testing this on real people...so what does it mean here?

- if by consonance you mean only "sounding together", then you could say "tone combination" or "simultanaeity" or maybe "unison"

- the smallest distinguishable interval varies from person to person, and would depend on practice, register, timbre, etc.

- in any case, the smallest distinguishable interval is a strange basis for anything. Different amounts of precision are needed depending on what effect you want to achieve. To get the sound of high pitches to "fuse" into a low fundamental without beating, you need precision much greater than 2 cents. To get an octave to sound more or less like an octave, you need somewhat less precision. To get 11/6 to sound like 11 and not like some major 7th (or 15/8) requires maybe 10 cents of precision--I'm just making that up based on the cent difference. In any case, (I believe upon reflection and experience) ratios based on higher primes require more precision than ratios based on lower primes because the intervals are unfamiliar and have less support within the system.

-the best way to win converts to a musical system is to post some music using that system for effect...

-but maybe there's something to get that I'm not getting...

On Jul 11, 2008, at 1:59 PM, Mario Pizarro wrote:

> ...The first cell is the schisma (32805 / 32768) = > 1,00112915039,,,,This smallest consonance, distinguishable by the > ear of man...
>