Keenan Pepper

Keenan,

In the past century some musicians by themselves or assisted by
mathematicians, intended to demonstrate that the musical octave, that is,
the true musical octave, slightly differs from the range 1 up to 2. One of
them, the mexican Julián Carrillo has written the book titled "Sonido 13";
he was a distinguished person and notable musician who firmly declared that
he can detect by ear that tiny discrepance asserting that the higher figure
is slightly greater than 2. I had the comments written by Joaquin Zamaçois
in his book titled "Teoría de la Música" and recall that he commented that
J. Carrillo directed an orchestra that played pieces using a slightly
stretched octave. I also read that J. Z. wrote that Carrillo´s nephew was
the mathematician who assisted to him. As far as I recall, the comments
refer that J. Carrillo didn´t deduce the discrepant value.

I missed the group of photocopied pages that contain the comments.

Obviously, I didn´t try to detect by ear such a true musical octave.
Recently, I asked to myself: ¿ what indorses the 2 exactness of the octave?.
There might be a scientific reason for asserting that it is really 2
exactly. Probably some institution in this planet has already measured this
natural range. ¿Nobody proved that 2 is the exact musical octave or this
range was measured with inapropriated instrumentation / procedures?.

I examined the progression of musical cells given in my book "The Piagui
Musical Scale: Perfecting Harmony" (Author: C. Mario Pizarro). The
progression contains 624 frequency steps comprised in the range C = 1 up to
cell # 624 that equals to (9/8)^6 = 2.02728652954098. It is a geometrical
progression since any cell value equals to the product of the preceding cell
multiplied by one of the M, J, U commas (M = Smallest interval or schisma =
(32805 / 32768)).

The first and last groups of 12 cells make a product of 1.01364326477... =
Pythagorean comma. What a coincidence.

The analysis of the progression properties led to the obtainment of the true
musical octave. In a few days, (July 16), a grand piano will be tuned and
adjusted to this octave.

Thanks
Mario
Lima, July 09

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----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 09, 2011 1:44 PM
Subject: [tuning] Re: The importance of latency

Hey Mario,
You might want to check with Pythagoras...just saying...
 
Tim

--- On Sat, 7/9/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] Keenan Pepper
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Date: Saturday, July 9, 2011, 11:51 PM

Keenan,

In the past century some musicians by themselves or assisted by
mathematicians, intended to demonstrate that the musical octave, that is,
the true musical octave, slightly differs from the range 1 up to 2. One of
them, the mexican Julián Carrillo has written the book titled "Sonido 13";
he was a distinguished person and notable musician who firmly declared that
he can detect by ear that tiny discrepance asserting that the higher figure
is slightly greater than 2. I had the comments written by Joaquin Zamaçois
in his book titled "Teoría de la Música" and recall that he commented that
J. Carrillo directed an orchestra that played pieces using a slightly
stretched octave. I also read that J. Z. wrote that Carrillo´s nephew was
the mathematician who assisted to him. As far as I recall, the comments
refer that J. Carrillo didn´t deduce the discrepant value.

I missed the group of photocopied pages that contain the comments.

Obviously, I didn´t try to detect by ear such a true musical octave.
Recently, I asked to myself: ¿ what indorses the 2 exactness of the octave?.
There might be a scientific reason for asserting that it is really 2
exactly. Probably some institution in this planet has already measured this
natural range. ¿Nobody proved that 2 is the exact musical octave or this
range was measured with inapropriated instrumentation / procedures?.

I examined the progression of musical cells given in my book "The Piagui
Musical Scale: Perfecting Harmony" (Author: C. Mario Pizarro). The
progression contains 624 frequency steps comprised in the range C = 1 up to
cell # 624 that equals to (9/8)^6 = 2.02728652954098. It is a geometrical
progression since any cell value equals to the product of the preceding cell
multiplied by one of the M, J, U commas (M = Smallest interval or schisma =
(32805 / 32768)).

The first and last groups of 12 cells make a product of 1.01364326477... =
Pythagorean comma. What a coincidence.

The analysis of the progression properties led to the obtainment of the true
musical octave. In a few days, (July 16), a grand piano will be tuned and
adjusted to this octave.

Thanks
Mario
Lima, July 09

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 09, 2011 1:44 PM
Subject: [tuning] Re: The importance of latency

What does that mean?

-Mike

On Sat, Jul 9, 2011 at 10:49 PM, Tim Reeves <reevest360@...> wrote:
>
> Hey Mario,
> You might want to check with Pythagoras...just saying...
>
> Tim