Yahoo Tuning Groups Ultimate Backup tuning The 612 system indorsement

To the tuning list,

Since the absence of a clear argument that confirms the 612 frequency steps of a correct 2/1 octave, let me inform you that recently I made additional analyses on this matter, this message gives a rough idea on what I found . Most musicians know about Julián Carrillo´s announcement on the greater than 2/1 octave relation he defended which was not proved.

The progression of musical cells, as written in my book, states that a musical range is formed by six groups of 104 cells that make a total of 624 cells per cycle and not per octave. Twelve cells before this figure works cell number 612 that equals the accepted octave 2. It is useful to inform that some months ago information on the progression was given to the tuning list including the latest conclusion I arrived, that is, two groups of 46 cells take also part together with the 52 set ones.

Under the explained conditions of the combined work of two types of cell groups in the octave, that is, 104 and 2 identical groups of 46 cells each, the following groups that form the real octave were derived:

104 - 104 - 104 - 46 - 46 - 104 - 104 , the sum of the cells of this combination gives 612 that corresponds to the 2/1 octave, we arrived by analyses to the expected musical octave.

The derivation represents the first valid argument for the indorsement of the 2/1 octave.

Thanks

Mario Pizarro

April, 19

piagui@...

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> To the tuning list,
>
> Since the absence of a clear argument that confirms the 612 frequency steps of a correct 2/1 octave, let me inform you that recently I made additional analyses on this matter, this message gives a rough idea on what I found . Most musicians know about Julián Carrillo´s announcement on the greater than 2/1 octave relation he defended which was not proved.
>
> The progression of musical cells, as written in my book, states that a musical range is formed by six groups of 104 cells that make a total of 624 cells per cycle and not per octave. Twelve cells before this figure works cell number 612 that equals the accepted octave 2. It is useful to inform that some months ago information on the progression was given to the tuning list including the latest conclusion I arrived, that is, two groups of 46 cells take also part together with the 52 set ones.
>
> Under the explained conditions of the combined work of two types of cell groups in the octave, that is, 104 and 2 identical groups of 46 cells each, the following groups that form the real octave were derived:
>
> 104 - 104 - 104 - 46 - 46 - 104 - 104 , the sum of the cells of this combination gives 612 that corresponds to the 2/1 octave, we arrived by analyses to the expected musical octave.
>
> The derivation represents the first valid argument for the indorsement of the 2/1 octave.

I'm sorry, I don't have a clue what this "valid argument" is. What ideas are you starting from? It seems like these numbers are just coming out of nowhere.

I use 2/1 octaves because they sound good to me. Are you saying there's something "invalid" about this?

Keenan

🔗Mario Pizarro <piagui@...>

Keenan Pepper,

Keenan,

I am really sorry for having sent you a copy of the message, it wonï¿½t occur again.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
<I'm sorry, I don't have a clue what this "valid argument" is. What ideas are you starting from? It seems like these numbers are <just coming out of nowhere.

<I use 2/1 octaves because they sound good to me. Are you saying there's something "invalid" about this?
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

The paragraph containing "valid argument" is too short.

When Mr. Carrillo announced in the USA the higher range of the octave, greater than 2/1, he didnï¿½t use solid arguments based on Physics or other convincing demonstrations so that his arguments were not valid for the recognition of his finding.

A paper that demonstrates the correct octave magnitude of 612 steps that is equivalent to the 2/1 range was not presented yet.

About the corrected progression of cells, precisely I am working on that, the idea is to introduce the two sets of 46 cells combined with the 52 x 2 = 104 cell pages.

By the way, when Steve Martin S was receiving full information about the progression, I was working with the combined 52 - 46 cell sets however to simplify the explanations, we only talked about 12 sets of 52 cells only. So that your expression "It seems like these numbers are just coming out of nowhere." is not having sense, however I appreciate your frankness.

Very soon you will have news about the corrected progression and the combined 52/46 sets.

Thanks

Mario

April, 19

--------------------------------

----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, April 19, 2012 2:39 PM
Subject: [tuning] Re: The 612 system indorsement

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> To the tuning list,
>
> Since the absence of a clear argument that confirms the 612 frequency > steps of a correct 2/1 octave, let me inform you that recently I made > additional analyses on this matter, this message gives a rough idea on > what I found . Most musicians know about Juliï¿½n Carrilloï¿½s announcement on > the greater than 2/1 octave relation he defended which was not proved.
>
> The progression of musical cells, as written in my book, states that a > musical range is formed by six groups of 104 cells that make a total of > 624 cells per cycle and not per octave. Twelve cells before this figure > works cell number 612 that equals the accepted octave 2. It is useful to > inform that some months ago information on the progression was given to > the tuning list including the latest conclusion I arrived, that is, two > groups of 46 cells take also part together with the 52 set ones.
>
> Under the explained conditions of the combined work of two types of cell > groups in the octave, that is, 104 and 2 identical groups of 46 cells > each, the following groups that form the real octave were derived:
>
> 104 - 104 - 104 - 46 - 46 - 104 - 104 , the sum of the cells of this > combination gives 612 that corresponds to the 2/1 octave, we arrived by > analyses to the expected musical octave.
>
> The derivation represents the first valid argument for the indorsement of > the 2/1 octave.

I'm sorry, I don't have a clue what this "valid argument" is. What ideas are you starting from? It seems like these numbers are just coming out of nowhere.

I use 2/1 octaves because they sound good to me. Are you saying there's something "invalid" about this?

Keenan

------------------------------------

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🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

So does the progression repeat every 612 cells, or every 624 cells, or what?

-Mike

On Thu, Apr 19, 2012 at 11:59 AM, Mario Pizarro <piagui@ec-red.com> wrote:
> To the tuning list,
>
> Since the absence of a clear argument that confirms the 612 frequency
> steps of a correct 2/1 octave, let me inform you that recently I made
> additional analyses on this matter, this message gives a rough idea on what
> I found . Most musicians know about Julián Carrillo´s announcement on the
> greater than 2/1 octave relation he defended which was not proved.
>
> The progression of musical cells, as written in my book, states that a
> musical range is formed by six groups of 104 cells that make a total of 624
> cells per cycle and not per octave. Twelve cells before this figure works
> cell number 612 that equals the accepted octave 2. It is useful to
> inform that some months ago information on the progression was given to the
> tuning list including the latest conclusion I arrived, that is, two groups
> of 46 cells take also part together with the 52 set ones.
>
> Under the explained conditions of the combined work of two types of cell
> groups in the octave, that is, 104 and 2 identical groups of 46 cells each,
> the following groups that form the real octave were derived:
>
> 104 - 104 - 104 - 46 - 46 - 104 - 104 , the sum of the cells of this
> combination gives 612 that corresponds to the 2/1 octave, we arrived by
> analyses to the expected musical octave.
>
> The derivation represents the first valid argument for the indorsement of
> the 2/1 octave.
>
> Thanks
>
> Mario Pizarro
>
> April, 19
>
> piagui@...
>
>

🔗Mario Pizarro <piagui@...>

To Genewardsmith

Gene,

I already explained to Keenan the meaning of "valid argument" mentioned in a short paragraph, I should have added two

words to cancell the error.

The new subject I started some months ago is quite interesting so as a sharp journalist you will be busy.

Mario

April, 19
<<<<<<<<<<<<<<<<<<<<<<<<<<<<

----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, April 19, 2012 7:28 PM
Subject: [tuning] Re: The 612 system indorsement

>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
>> I'm sorry, I don't have a clue what this "valid argument" is. What ideas >> are you starting from? It seems like these numbers are just coming out of >> nowhere.
>
> The most basic question is what is Mario trying to do, which no one seems > to be able to answer.
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

🔗kraiggrady <kraiggrady@...>

🔗Mario Pizarro <piagui@...>

signature fileTo kraiggrady,

Thanks for your message. Let me ask you why 72 Et is related to Carrillo purposes.

Somebody has written that my expression "valid arguments" I used in my message is not correct and I don´t know why; I would apreciate it if you could reread it and inform me whether I made a mistake or in any case the paragraph is understandable. English language is not my native language, I was born in Perú.

Thanks again

Mario

Lima, April, 20

piagui@...
----- Original Message -----
From: kraiggrady
To: tuning@yahoogroups.com
Sent: Friday, April 20, 2012 5:12 AM
Subject: [tuning] Re: The 612 system indorsement

I think you are correct about Carillo in general. He was less interested in acoustical justification for his divisions of 12. He, for instance, seems to have missed 72 Et while Novaro might be the first proponent of. Carillo did show himself to be an accomplish composer .

,',',', Kraig Grady ,',',',
Mesotonal Music from:
''''''' North/Western Hemisphere:
North American Embassy of Anaphoria Island

''''''' South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

🔗Keenan Pepper <keenanpepper@...>

🔗Mike Battaglia <battaglia01@...>

🔗Andy <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>... 612 frequency steps of a correct 2/1 octave,....

Hola Mario,
in deed 612-edo is an reasonable choice, because:

1. on the one hand in the 5-limit case::
http://www.huygens-fokker.org/docs/measures.html
Quote:
"
schisma

Like comma, also an interval: the difference between the Pythagorean and syntonic comma. Because it is so small it is also useful as a measure. The syntonic comma is 11.008 schismas, the Pythagorean comma 12.008, and the minor diesis 21.016 schismas, so practically 11, 12 and 21. There are also temperaments with the fifth tempered by a fraction of a schisma. There are 614.21264 schismas in an octave. A similar useful unit is 1/612 part of an octave, or one step of 612-tone equal temperament, because this temperament has extremely accurate approximations of fifth and thirds, and because 612 is divisible by 12. So one step is also very close to 1/12 of a Pythagorean comma and the schisma.

2. on the other hand, wihin 3-limit
Study the series of
https://oeis.org/search?q=5+7+12+53+306+665&language=english&go=Search
'A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of two tones of musical harmony: the perfect 4th, 4/3 and its complement the perfect 5th, 3/2.
'
Consider there:
"1, 2, 3, 5, 7, 12, 29, 41, 53, 200, 253, 306, 359, 665,...."
Here it turns out, that "306" is the 12th convergent of the series.

Hence you's choice 612:=306*2 makes sense -alike-Newton's- preference.

3. That famous '612'-edo works also well for the higher
5- or 7-limit, see:
https://oeis.org/A060526
"
A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of six simple musical tones:
8/7 5/4 4/3 3/2 8/5 7/4:
attend the convergents:
1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 21, 22, 31, 53, 84, 87, 94, 99, 118, 130, 140, 171, 270, 410, 441, "612",...." &ct...

4. 612-edo turns out to be apt for 11-limit too:
https://oeis.org/A060527
"
A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the ratios of 8 musical tones:
8/7 16/11 5/4 4/3 3/2 8/5 11/8 7/4.
with the convergents:
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 15, 22, 26, 31, 41, 63, 72, 87, 109, 161, 202, 224, 270, 494, "612", .....

http://tonalsoft.com/enc/w/werckmeister.aspx
"
612-edo gives a superb approximation of Werckmeister III, the maximum deviation being only ~1/29-cent. Below is a graph of Werckmeister III tuning as a scale within one octave, given as 612-edo degrees. The major divisions on the y-axis quantize it into the 612-edo representations of 12-edo for comparison. Note that 612-edo divides exactly into 12, so it provides an excellent means of comparison between 12-edo and Werckmeister III without the need for decimal or fractional parts.
Werckmeister III: 612-edo approximation

~12edo ~612edo skhismas
note degrees correction ~cents error of 612edo from Werckmeister

B 11 -4 -1/43
Bb 10 -2 -1/86
A 9 -6 -1/29
Ab/G# 8 -4 -1/43
G 7 -2 -1/86
F# 6 -6 -1/29
F 5 -1 -1/173
E 4 -5 -1/35
Eb 3 -3 -1/58
D 2 -4 -1/43
C# 1 -5 -1/35
C 0 0 0

Finally remember again about:
/tuning/topicId_75743.html#75773?l=1
Even already Sir Isaac Newton considered 612-EDO.
Literature: New Grove (2001) Vol.17 p.815

bye
Andy

🔗Mario Pizarro <piagui@...>

Mike Battaglia

Mike,

As I said before, we donï¿½t need to use the word "repeat" because it facilitates to write or to read wrongly I think.
Any chain of cells works statically. When I wrote the book I could end the progression list on cell # 612 = 2 without including the 12 pythagorean cells. It was a doubtful decision, since the final 12 pythagorean cells do not take part of the first cycle , the following arrangement is being considered

104 ---- final cell = 1.125 = 9/8
104 ---- final cell = 1.265625 = (9/8)^2
104 ---- final cell = 1.423828125 = (9/8)^3
46------ final cell = 3/2
46------ final cell = 128/81
104 ---- final cell = 16/9
104 ---- final cell = 2 = Cell # 612

When we couple 12 sets of pure 52 cells each we get 12 * 52 = 624 cells per cycle
This also complies with 6*104 = 624 cells per cycle. Its final cell is (9/8)^6 while the former arrangement ends on 2 which is a better ending.

Mike, the latest paragraphs advocate the election of 5 sets with 104 cells plus one set with 92 cells (2*46) that make Cell 612 = 2 unless my reasoning is wrong..

Mario

April, 20

02:00 PM
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: "Mario Pizarro" <piagui@...>
Sent: Friday, April 20, 2012 10:27 AM
Subject: Re: [tuning] Re: The 612 system indorsement

But you just said on the tuning list that it repeats every 624 cells.
Is it that it repeats every 612 cells, every 624 cells, or both?

-Mike

On Apr 20, 2012, at 11:13 AM, Mario Pizarro <piagui@...> wrote:

> Mike,
>
> When your question includes the verb "repeat", appears the confusion. A > much
> better way to explain the cell extension process is to avail the data > given
> in my book as follows:
>
> 1) The final cells of the FIRST CYCLE of the progression, approximately 12
> or 6 cells, will be copied from the book. The final one of this cycle is
> cell # 612 = 2. The attached page presents an extension of 12 cells from
> number 613 to 624 which coincidently or as a progression property, this
> extension comprises the pythagorean comma.
>
> 2) From Cell 613 a SECOND CYCLE of cells works. NOTE that the interval
> factor sequence along this extension starting from cell 613 is MM JJ MMMM > JJ
> MM which coincides with the first twelve intervals of the progression. It
> means that the initial 12 cells of the second cycle is already coupled.
>
> 3) First cycle........ From (Cell # 0) = 1 up to (Cell # 612) = 2
>
> 4) Second cycle ......[From (Cell # 612) = 2 up to (Cell # 2* 612)] = > (From
> 2 up to 2*2) = From 2 to 4
>
> 5) To continue the Second Cycle from Cell 624 we use the interval sequence
> starting on cell # 13 since the first 12 cells are already known.
>
> CONCLUSION
>
> THE PROGRESSION REPEAT EVERY 612 CELLS.
>
> Mario
>
> April, 20------------Please see the attachment
>
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> ----- Original Message -----
> From: "Mike Battaglia" <battaglia01@...>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, April 19, 2012 7:30 PM
> Subject: [tuning] Re: The 612 system indorsement
>
>
> So does the progression repeat every 612 cells, or every 624 cells, or > what?
>
> -Mike
>
>
>
> On Thu, Apr 19, 2012 at 11:59 AM, Mario Pizarro <piagui@...> wrote:
>> To the tuning list,
>>
>> Since the absence of a clear argument that confirms the 612 frequency
>> steps of a correct 2/1 octave, let me inform you that recently I made
>> additional analyses on this matter, this message gives a rough idea on
>> what
>> I found . Most musicians know about Juliï¿½n Carrilloï¿½s announcement on the
>> greater than 2/1 octave relation he defended which was not proved.
>>
>> The progression of musical cells, as written in my book, states that a
>> musical range is formed by six groups of 104 cells that make a total of
>> 624
>> cells per cycle and not per octave. Twelve cells before this figure works
>> cell number 612 that equals the accepted octave 2. It is useful to
>> inform that some months ago information on the progression was given to
>> the
>> tuning list including the latest conclusion I arrived, that is, two >> groups
>> of 46 cells take also part together with the 52 set ones.
>>
>> Under the explained conditions of the combined work of two types of cell
>> groups in the octave, that is, 104 and 2 identical groups of 46 cells
>> each,
>> the following groups that form the real octave were derived:
>>
>> 104 - 104 - 104 - 46 - 46 - 104 - 104 , the sum of the cells of this
>> combination gives 612 that corresponds to the 2/1 octave, we arrived by
>> analyses to the expected musical octave.
>>
>> The derivation represents the first valid argument for the indorsement of
>> the 2/1 octave.
>>
>> Thanks
>>
>> Mario Pizarro
>>
>> April, 19
>>
>> piagui@...
>>
>>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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>
>
>
> <For Mike.doc>

🔗Mike Battaglia <battaglia01@...>

🔗Mario Pizarro <piagui@...>

Keenan,

I donï¿½t understand why you are rigurously checking my messages, I donï¿½t do that with yours. It is clear that they only contain common talking. I ask you not to interfer with my personal communications. During the whole day my messages were responses to those I received. Despite all this I still keep my frienship with you.

Mario

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Friday, April 20, 2012 12:58 PM
Subject: [tuning] Re: The 612 system indorsement

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> signature fileTo kraiggrady,
>
> Thanks for your message. Let me ask you why 72 Et is related to Carrillo > purposes.
>
> Somebody has written that my expression "valid arguments" I used in my > message is not correct and I donï¿½t know why; I would apreciate it if you > could reread it and inform me whether I made a mistake or in any case the > paragraph is understandable. English language is not my native language, I > was born in Perï¿½.

You can explain in Spanish, if that helps. I can read Spanish fine, or even translate it into English. I'm just bad at expressing myself in it.

Keenan

------------------------------------

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan,
>
> I don´t understand why you are rigurously checking my messages, I don´t do
> that with yours. It is clear that they only contain common talking. I ask
> you not to interfer with my personal communications. During the whole day my
> messages were responses to those I received. Despite all this I still keep
> my frienship with you.

I don't think I could possibly be more confused with what you're saying at this point. Let's take these issues one at a time.

> I don´t understand why you are rigurously checking my messages

I don't understand what you mean by this. I'm merely reading your messages, trying (so far unsuccessfully) to understand what you're saying, and then asking you questions. Am I doing something wrong?

> I ask you not to interfer with my personal communications.

How can I possibly be doing this? I've only replied to posts you've made to the tuning list, which is the opposite of "personal" - it is a public forum, archived on the Internet where anyone in the world can continue to see it. What "personal communications" are you referring to?

> During the whole day my
> messages were responses to those I received. Despite all this I still keep
> my frienship with you.

I still have no idea what I'm doing wrong. When have I acted impolitely?

Keenan

🔗Mario Pizarro <piagui@...>

To Mike Battaglia

Mike,

I always do what you ask and now you are angry. If you specifically tell me what you want and I can do it, I will do it provided you give me enough informarion. At the moment I think that I don´t understand quite well "repeat this, repeat that". We are intelligent people so it is unbelievable that we cannot understand ourselves.

Mario.

----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Friday, April 20, 2012 2:35 PM
Subject: Re: [tuning] Re: The 612 system indorsement

On Apr 20, 2012, at 3:18 PM, Mario Pizarro <piagui@ec-red.com> wrote:
Mike Battaglia

Mike,

As I said before, we don´t need to use the word "repeat" because it
facilitates to write or to read wrongly I think. Any chain of cells works statically.

Why?? Why does it facilitate me to read wrongly? I asked you exactly the information I need to know, and I keep asking you, and you won't tell me!!

Do you understand what I mean when I ask about it repeating? Most scales repeat every octave. Your progression of cells is a scale, right? Does it also repeat every octave?

Is it that you can configure the progression to repeat in more than one way, depending on what you want? Is that what "every chain of cells works statically" means, that I can set up different chains differently depending on what I want?

-Mike

🔗Keenan Pepper <keenanpepper@...>

🔗Mario Pizarro <piagui@...>

Mike Battaglia,

Mike,

I have the progression of cells version 6 x 104 and in three days will also have version 5 x 104 + (2 x 46). Please tell me what information you want from these documents. In any case I can send you the latest version.

Mario

April, 21

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Friday, April 20, 2012 2:35 PM
Subject: Re: [tuning] Re: The 612 system indorsement

On Apr 20, 2012, at 3:18 PM, Mario Pizarro <piagui@...> wrote:
Mike Battaglia

Mike,

As I said before, we don´t need to use the word "repeat" because it
facilitates to write or to read wrongly I think. Any chain of cells works statically.

Why?? Why does it facilitate me to read wrongly? I asked you exactly the information I need to know, and I keep asking you, and you won't tell me!!

Do you understand what I mean when I ask about it repeating? Most scales repeat every octave. Your progression of cells is a scale, right? Does it also repeat every octave?

-Mike