It is true

Keenan,

I printed the 624 cell products by 4/3 as well as by 3/2 and all the responses coincide with higher cell frequencies with exactness.

Mario

April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 2:22 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense) > because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either > the exact 3/2 above it or the exact 4/3 above it is missing from the list.
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
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> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

Mario, why do you keep saying you have 624 cells? It sounds like you have
612 per octave.

-Mike

On Apr 7, 2012, at 10:09 PM, Mario Pizarro <piagui@ec-red.com> wrote:

Keenan,

I printed the 624 cell products by 4/3 as well as by 3/2 and all the
responses coincide with higher cell frequencies with exactness.

Mario

April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 2:22 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense)
> because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either
> the exact 3/2 above it or the exact 4/3 above it is missing from the list.
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

Mike,

I studied the secondary school in a military school in Lima. There I heard for the first time about the same question. At that time, 1952, the person who asked me, now Dr. Mario Vargas Llosa, did it. In 2010 he was honored with the Nobel Prize in Literature. We were so young and he was talking about rare themes. His question was not exactly the same as yours but very similar. Of course I couldn´t respond him.

I am worried since I don´t know if you have received the seven pages of the progression.

Coming back to your question. The first pages containing the initial clues on the progression I sent you, show the particularity that in a group of 47 common fractions, working factors with values of 9/8, (9/8)^2, (9/8)^3, ....... (9/8)^6 intervene. I remarked that in my book. The participation of powers of (9/8) happened many centuries in the past and it is probable that people in those times kept the weight of 9/8 in their modest compositions. The fact that nowadays we check six powers of 9/8 in a group of 47 elements and it is also present in the progression in some manner backs the tndency of completing SIX groups of cells instead of 612 / 624. As you know, therewere cultures that used the twelve base for their numeric system. In paralell with these events, music has developed almost independently since number six works there in many ways. The numbers themselves suggest to man what can be done with them.

Would you lke to be informed on the procedure I use to detect rational / irrational numbers?

Mario

April, 8
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Saturday, April 07, 2012 9:19 PM
Subject: Re: [tuning] It is true

Mario, why do you keep saying you have 624 cells? It sounds like you have 612 per octave.

-Mike

On Apr 7, 2012, at 10:09 PM, Mario Pizarro <piagui@ec-red.com> wrote:

Keenan,

I printed the 624 cell products by 4/3 as well as by 3/2 and all the
responses coincide with higher cell frequencies with exactness.

Mario

April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 2:22 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense)
> because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either
> the exact 3/2 above it or the exact 4/3 above it is missing from the list.
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

You have 612 cells per octave. Why do you keep saying 624? 624 cells gets
you to a pythagorean comma sharp of 2/1. 612 gets you to 2/1.

-Mike

On Apr 8, 2012, at 11:51 AM, Mario Pizarro <piagui@...> wrote:

Mike,

I studied the secondary school in a military school in Lima. There I heard
for the first time about the same question. At that time, 1952, the person
who asked me, now Dr. Mario Vargas Llosa, did it. In 2010 he was honored
with the Nobel Prize in Literature. We were so young and he was talking
about rare themes. His question was not exactly the same as yours but very
similar. Of course I couldn´t respond him.

I am worried since I don´t know if you have received the seven pages of the
progression.

Coming back to your question. The first pages containing the initial clues
on the progression I sent you, show the particularity that in a group of 47
common fractions, working factors with values of 9/8, (9/8)^2, (9/8)^3,
....... (9/8)^6 intervene. I remarked that in my book. The participation of
powers of (9/8) happened many centuries in the past and it is probable that
people in those times kept the weight of 9/8 in their modest
compositions. The fact that nowadays we check six powers of 9/8 in a group
of 47 elements and it is also present in the progression in some manner
backs the tndency of completing SIX groups of cells instead of 612 / 624.
As you know, therewere cultures that used the twelve base for their numeric
system. In paralell with these events, music has developed almost
independently since number six works there in many ways. The numbers
themselves suggest to man what can be done with them.

Would you lke to be informed on the procedure I use to detect rational /
irrational numbers?

Mario

April, 8

----- Original Message -----
*From:* Mike Battaglia <battaglia01@...>
*To:* tuning@yahoogroups.com
*Sent:* Saturday, April 07, 2012 9:19 PM
*Subject:* Re: [tuning] It is true

Mario, why do you keep saying you have 624 cells? It sounds like you have
612 per octave.

-Mike

On Apr 7, 2012, at 10:09 PM, Mario Pizarro <piagui@ec-red.com> wrote:

Keenan,

I printed the 624 cell products by 4/3 as well as by 3/2 and all the
responses coincide with higher cell frequencies with exactness.

Mario

April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 2:22 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense)
> because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either
> the exact 3/2 above it or the exact 4/3 above it is missing from the list.
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan,
>
> I printed the 624 cell products by 4/3 as well as by 3/2 and all the
> responses coincide with higher cell frequencies with exactness.

I still maintain that this is impossible, because of a mathematical truth called the Fundamental Theorem of Arithmetic, and that you must be mistaken.

You said you were going to send me the list of all the cell frequencies, but I haven't received anything yet.

Keenan

Mike,

Theoretically, the progression is an endless set. I think what we can do is to left an empty row jusr after cell 612. Do you agree?

Did you receive the 7 pages of the progression ?

Mario
April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Sunday, April 08, 2012 11:39 AM
Subject: Re: [tuning] It is true

You have 612 cells per octave. Why do you keep saying 624? 624 cells gets you to a pythagorean comma sharp of 2/1. 612 gets you to 2/1.

-Mike

On Apr 8, 2012, at 11:51 AM, Mario Pizarro <piagui@...> wrote:

Mike,

I studied the secondary school in a military school in Lima. There I heard for the first time about the same question. At that time, 1952, the person who asked me, now Dr. Mario Vargas Llosa, did it. In 2010 he was honored with the Nobel Prize in Literature. We were so young and he was talking about rare themes. His question was not exactly the same as yours but very similar. Of course I couldn´t respond him.

I am worried since I don´t know if you have received the seven pages of the progression.

Coming back to your question. The first pages containing the initial clues on the progression I sent you, show the particularity that in a group of 47 common fractions, working factors with values of 9/8, (9/8)^2, (9/8)^3, ....... (9/8)^6 intervene. I remarked that in my book. The participation of powers of (9/8) happened many centuries in the past and it is probable that people in those times kept the weight of 9/8 in their modest compositions. The fact that nowadays we check six powers of 9/8 in a group of 47 elements and it is also present in the progression in some manner backs the tndency of completing SIX groups of cells instead of 612 / 624. As you know, therewere cultures that used the twelve base for their numeric system. In paralell with these events, music has developed almost independently since number six works there in many ways. The numbers themselves suggest to man what can be done with them.

Would you lke to be informed on the procedure I use to detect rational / irrational numbers?

Mario

April, 8
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Saturday, April 07, 2012 9:19 PM
Subject: Re: [tuning] It is true

Mario, why do you keep saying you have 624 cells? It sounds like you have 612 per octave.

-Mike

On Apr 7, 2012, at 10:09 PM, Mario Pizarro <piagui@...> wrote:

Keenan,

I printed the 624 cell products by 4/3 as well as by 3/2 and all the
responses coincide with higher cell frequencies with exactness.

Mario

April 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 2:22 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense)
> because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either
> the exact 3/2 above it or the exact 4/3 above it is missing from the list.
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

On Sun, Apr 8, 2012 at 6:10 PM, Mario Pizarro <piagui@...> wrote:
>
> Mike,
>
> Theoretically, the progression is an endless set. I think what we can do
> is to left an empty row jusr after cell 612. Do you agree?
>
> Did you receive the 7 pages of the progression ?

Yes, I received it.

Does your progression of cells repeat every 2/1 octave?

-Mike

Mike,

If you examine the M,J,U ordaining along the pythagorean comma that works just after Cell 612 you will see the following order:MMJJ MMMM JJMM. This sequence is equal to the sequence of the first 12 cells-- From cell #1 to cell #12.

Therefore the second cycle of the progression starts on cell 612 = 2. --- The last 12 cells (Cell 613 to Cel 624) replace the first 12 cells mentioned in the former paragraph. That means that in order to continue the progression to a second cycle we couple the order that starts on Cell 13, that is MMJJ MMMM JJUU and continue the pack Cell 25 up to the new end.

I suggesr you Mike to do the operations explained above; the second end will be 4.

Mario

April, 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, April 08, 2012 5:18 PM
Subject: Re: [tuning] It is true

> On Sun, Apr 8, 2012 at 6:10 PM, Mario Pizarro <piagui@...> wrote:
>>
>> Mike,
>>
>> Theoretically, the progression is an endless set. I think what we can do
>> is to left an empty row jusr after cell 612. Do you agree?
>>
>> Did you receive the 7 pages of the progression ?
>
> Yes, I received it.
>
> Does your progression of cells repeat every 2/1 octave?
>
> -Mike
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>