Re: Wrong statements

Steve,

I wrote wrong statements when responded your message given below.

> Mario,
>I have not listened to the two chords, but I am a bit confused about what >they are intended to show.
>(1) why add a third note ("G") into the comparison - can't we just simply >compare the 1 - 2 dyad with the 1 - & dyad?
>(2) if there is to be a third note, why make the above tuning choices? e.g. >why not use the pure 3/2 interval in both cases? If >you say the 3/2 is >not available in the equal tempered system with 2/1, well it is not >available in the toctave system either, is >it? Just as the "equal >tempered" G is 2^(7/12), so the "Toctaved G" is not 3/2*C but &^(7/12)*C, >isn't it?
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(1) You are correct. I shouldn�t use G into the comparison since e. t. G is not 3/2 but 1.4983.... A fast response was the cause. Before I should had explained that since the 12 tet scale is most used in occident despite its tone frequency imperfecctions, IMO the better options are those scales that work with stretched octaves.

You asked the following:

>"e.g. why not use the pure 3/2 interval in both cases?".
It was an error to use 3/2 for G tempered so it would also be an error to use it in both cases. About your question (2):

>(2) >you say the 3/2 is not available in the equal tempered system with >2/1, well it is not available in the toctave system either, is >it? ----- >and: >"Toctaved G" is not 3/2*C but &^(7/12)*C, isn't it?--
When responding these points I was keeping in mind that in no case "tempered G" is 3/2 while "toctaved G" does it as we can see it in the attached file. (I admit that I didn�t balance the conditions)

I attached a toctaved scale where D/C# = P interval factor = (8/9)*2^(1/4) =
1.05705299111 and C#/C = K interval = (9/8)^(1/2) = 1.06066017178. Both K
and P intervals are the Piagui scale semitone factors.

P and K factors are cells # 49 and # 52 respectively, their ratio gives the MMJ product.

Starting with K factor, the tone intervals follow the sequence K P K K K K P P K K K K =
(K^9)*(P^3) that surprisingly gives the toctave & = Cell # 615 = 2.00678700656.

Since K and P are the basic elements to develope the Piagui scales, they may reinforce
the validity of the mentioned toctave, isn�t it?.

Regards

Mario

September, 18