Findings

Margo,

Your message exhibits how deep you use to be when you investigate
these matters.

This is my chance to know your opinons on the Piagui tuning, When I
started to write my book, my music theory knowledge was almost poor, I
dared to write my own common sense ideas, availing the fact that there
were no punishments for dared writers.

Years before, after reading the classic Pythagoras scale with his
spaced seven tones, I thought why he only worked with seven tones?. My
neighbor said that singers cannot sing more than seven tones per
octave. So I inserted notes PI, AG, UK, between C/D, D/E, F/G and
started to practice the ten tone solfeo, there was no problem.

Next morning I brought the idea of much many tones within the octave
where seven should be the pytagorean ones, the concept of a
progression of cells started to born, its provisional name was derived
from the inserted tones given above: PIAGUI.

At that time I went to the National Library of Lima where I did a
selection of books containing musical chords information, I started to
"talk" with Zarlino, Holder, Delezenne and other well known
researchers on the improvement of musical scales. One of my findings
was the "schidsma", (32805/32768). It was clear that the progression
tone spaces should not be equal and very small consonances were called
to take part of it.

Now I will study your tentative findings on the Piagui tuning. Before,
I have to pray to all the saints. Mr. Neidhardt, Mr. Marpurg, please
accompany me.!!!

I admit that it seems that people had problems understanding some of
my mathematical concepts instead of using simple procedures, which are
compatible to the group.

Let me say that the half of a 9/8 tone equals (9/8)^(1/2) =101.955
cents = K and not P, a nonimportant mistake. K and P were writen
inversely.

You correctly wrote that K^8 * P^4 make sense due to numerical
relations. Let me add that on pages 72, 73, 74, 75 of my book, without
going to any chord property, that is, by pure arithmetical and
algebraic reasoning, just by starting with the equations:

(A) .....K^m P^n = 2

(B) ..... m + n = 12

...........and once the two equations with four variables were solved,
the three variants of Piagui scales were derived.

Regarding Chris Vaisvil pattern KKKKPPKKKKPP, it sins of being an
asymmetrical set that might have been derived from the symmetric
Piagui scales, otherwise he would have given the mathematical
procedure that has been applied to get his arrangement.

In my opinion, any scale proposal should be backed by a mathematical
demonstration.

I left for tomorrow the remaining analysis.

This evening I will sleep very well because I dialogued with a really lady.

Bye

Mario

November 08

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