Yahoo Tuning Groups Ultimate Backup tuning A new equal tempered scale?

Steve,

Mike wrote:

"It has been shown that, if sine waves are used, humans will prefer an octave that is sharp. Furthermore, many instruments will exhibit slight inharmonicity such that their second harmonics are sharp as well. This is just an educated guess, but the tendency to prefer sharp octaves might reflect a tendency towards slightly sharp and inharmonic timbres in general. It may mean that not only do humans prefer sharp octaves, but generally prefer stretched timbres all around. I wouldn't be surprised if this were true in general.

Either way, there's no point arguing over which one is the "true" octave. To deny that our perception of the octave has at least something to do with 2/1 would be unwise. It also makes no sense to pretend that mathematical ratios are inherently important without a stochastic human observer with a stochastic auditory system to perceive them."

I can derive from his words that a sharp octave is what the human prefer to a scale and regarding 2/1, the octave "has at least something to do with 2/1".

Then it would be a wise decision to start using a new equal tempered scale like this one:

1
1.05976223699
1.12309599895
1.19021472821
1.26134462288
1.33672539915
1.41661109924
1.50127094748
1.59099025764
1.68607139446
1.78683479273
1.89362003707
2.00678700656

If we tune the piano and manufacture guitars with this scale there will be a great change.

Mario

Aug. 01

🔗Petr Parízek <petrparizek2000@...>

🔗Mario Pizarro <piagui@...>

Petr,

The interval of a12 tone et scale for a 2/1 octave is as you know 2^(1/12) = 2^(0.0833333....) = 1.05946309436

Similarly, the interval of a 12 tone et scale for a 2.00678700656 / 1 "toctave" equals (2.00678700656)^(1/12) = 1.05976223699 ------- I studied this matter and concluded that the toctave scale shows better harmony (I did and experiment by using a conventional guitar). Mike wrote that most humans prefer stretched octaves, I agree with him when he explained that numbers like 2 or 2.00678700656 are simple numbers. His words express that the better option is an stretched octave.
I add this. "Since numerically I concluded that 2 and 2.006787....... are the only ones that can work as octaves and since Juliï¿½n Carrillo has physically proved that the true octave ratio is higher than 2/1, then it seems that 2.00678700656 I derived satisfies the requirements unless somebody insists on a higher ratio like 2.01587069876 (13.6837 cents higher than 2/1 octave) that is too much I think.

Mario
Aug, 01
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Petr Parï¿½zek" <petrparizek2000@...>
To: <tuning@yahoogroups.com>
Sent: Monday, August 01, 2011 5:13 PM
Subject: Re: [tuning] A new equal tempered scale?

> Hi Mario.
>
> Since I don't know from the top of my head what exact interval sizes your
> decimal factors represent, I can only say that there are already some > people
> who prefer, for example, to use 19 equal divisions of 3/1 instead of 12
> equal divisions of 2/1. I think the loudest promoter of this tuning is
> Bernhard Stopper from Germany.
> And there are, IIRC, some people who also prefer 7 equal divisions of 3/2,
> which makes the octave even sharper than in Stopper's tuning. I only don't
> know right now who those are.
>
> Petr
>
>
>
>
> ------------------------------------
>
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>
>
>
>

🔗petrparizek2000 <petrparizek2000@...>

Mario.
#1. I've said that there were/are other people who already have made instruments tuned to stretched-octave temperaments and you should probably find some info on that to possibly avoid double work.
#2. I'm not saying I don't know what an equal division is or what a 12th root is. I'm saying that you're once again describing the intervals using decimal representations of the factors. I'm sorry to bring up this topic once again, but you seem to be the only person on the tuning list who does this. There are three other ways of describing intervals:
- A) there are exponents of prime numbers,
- B) there are cents,
- C) there are ratios.
Now let's compare these:
- A) Prime exponents clearly tell us what interval it is (i.e. how it was found) but they make it difficult to recognize how large it is from simply looking at the numbers.
- B) Cents say very clearly how large it is but they contain absolutely no information at all about what it is (i.e. how we got it).
- C) Ratios can tell us what it is and with a bit of learning also roughly how large it is.
- D) Your decimal numbers also don't contain any information about what it is and they also don't tell me much how large it is. What's more, if you want to stack intervals upon each other, decimal factors have to be multiplied and divided; in contrast, prime exponents or cents are added or subtracted, which corresponds to the way we understand intervals.
Honestly, in my personal calculations, I often alternate among three different methods of interval description (i.e. prime exponents, cents, and ratios) and I've been able to describe every possible interval that I have ever thought of. So why should I use one more if it's no better than the other three? It's a bit like learning a foreign language spoken by just a few people in the world. If a person who speaks Sámi comes to a country where most people speak English, will those people suddenly start learning Sámi if that language is spoken by about 30,000 people? Of course not.
Petr

🔗Mike Battaglia <battaglia01@...>

On Mon, Aug 1, 2011 at 8:04 PM, Mario Pizarro <piagui@...> wrote:
> Mike wrote that most humans prefer stretched octaves, I agree with him when he
> explained that numbers like 2 or 2.00678700656 are simple numbers. His words
> express that the better option is an stretched octave.

For sine waves. When harmonic timbres come into play, I think most
people would prefer the 2/1, as the stretched octave would then end up
beating terribly. It might be that the tendency towards stretched
octaves is reflective of a general tendency towards stretched harmonic
timbres in general.

> I add this. "Since numerically I concluded that 2 and 2.006787....... are
> the only ones that can work as octaves and since Julián Carrillo has
> physically proved that the true octave ratio is higher than 2/1, then it
> seems that 2.00678700656 I derived satisfies the requirements unless
> somebody insists on a higher ratio like 2.01587069876 (13.6837 cents higher
> than 2/1 octave) that is too much I think.

I'm still not sure why you say that the octave is exactly 2.006787 or
why that exact value is supposed to have special significance.

-Mike

🔗Wolf Peuker <wolfpeuker@...>

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

OK. Well then to answer your question, two sine waves over an octave apart
do not beat. The properties of what causes beating is a line of research that
has been explored extensively in the psychoacoustics literature. For pure
tones, beatlessness corresponds to the tones being far apart, not their
being aligned to some just ratio. Beating is caused by critical band
interactions in the cochlea, not f0 estimation as taking place in the brain.
If you hear beating for two tones that far apart, some additional
nonlinearity is present either in your speakers or in your ears to create
additional combination tones that beat, so you might want to repeat the
experiment at lower volume.

-Mike

On Aug 2, 2011, at 7:34 AM, Steve Parker <steve@pinkrat.co.uk> wrote:

I have tried it. I wouldn't post otherwise.
??

On 2 Aug 2011, at 12:15, Mike Battaglia <battaglia01@...> wrote:

Not with sine waves, no. A lot of people think otherwise until they try it.
You'll see.

Sent from my iPhone

On Aug 2, 2011, at 6:51 AM, Steve Parker < <steve@pinkrat.co.uk>
steve@...> wrote:

On Tue, Aug 2, 2011 at 4:55 AM, Steve Parker <
<steve%40pinkrat.co.uk><steve@...>
steve@pinkrat.co.uk> wrote:
>
> I mean suggest any timbre that will not beat on an interval of 1206 cents?

Let's start with a sine wave...

261.63Hz and 525.04Hz don't beat??

Steve P.

🔗Steve Parker <steve@...>

Ok. Do they wow at all? For me they're not beating
in a piano tuning sense but are regularly wowing.
In pretty confident that my monitoring system is not
introducing anything that bad. My ears may well be.
What I hear though is the same as tuning two piano notes
to the same octave.

Steve P.

On 2 Aug 2011, at 12:45, Mike Battaglia <battaglia01@...> wrote:

> OK. Well then to answer your question, two sine waves over an octave apart do not beat. The properties of what causes beating is a line of research that has been explored extensively in the psychoacoustics literature. For pure tones, beatlessness corresponds to the tones being far apart, not their being aligned to some just ratio. Beating is caused by critical band interactions in the cochlea, not f0 estimation as taking place in the brain. If you hear beating for two tones that far apart, some additional nonlinearity is present either in your speakers or in your ears to create additional combination tones that beat, so you might want to repeat the experiment at lower volume.
>
> -Mike
>
> On Aug 2, 2011, at 7:34 AM, Steve Parker <steve@pinkrat.co.uk> wrote:
>
>>
>> I have tried it. I wouldn't post otherwise.
>> ??
>>
>>
>>
>> On 2 Aug 2011, at 12:15, Mike Battaglia <battaglia01@gmail.com> wrote:
>>
>>>
>>> Not with sine waves, no. A lot of people think otherwise until they try it. You'll see.
>>>
>>> Sent from my iPhone
>>>
>>> On Aug 2, 2011, at 6:51 AM, Steve Parker <steve@...> wrote:
>>>>> On Tue, Aug 2, 2011 at 4:55 AM, Steve Parker <steve@...> wrote:
>>>>> >
>>>>> > I mean suggest any timbre that will not beat on an interval of 1206 cents?
>>>>>
>>>>> Let's start with a sine wave...
>>>>>
>>>>>
>>>>
>>>> 261.63Hz and 525.04Hz don't beat??
>>>>
>>>> Steve P.
>>>>
>>>
>>
>
>

🔗Mario Pizarro <piagui@...>

Hello Wolf,

Here you have it. The only matter you need is the Progression of Musical Cells (about 700 KB). I can send it to you if you want.

Mario
Aug, 02

TOCTAVE FOUNDATION

This article gives information regarding the derivation of the toctave, that is slightly higher than the 2 octave.
The last group of 18 cells of the progression ends on (9/8)^6 = 2.02728652954 containing the 2 octave
as well as other cells having close frequencies like 2.00678700656 = Cell # 615, called toctave. The whole
progression comprises 624 cells.

The twelfth root of the toctave gives the semitone factor that determines the tone frequencies of an equal
tempered scale detailed below; more information is found in file # 1 which is available in folder
/tuning/files/MarioPizarro/

The Progression is formed by 6 equal groups of cells, each containing 104 cells which comprises six
segments ordained as follows: QRQQRQ.

Set Q comprises 18 cells while Set R works with 16 so (4 x 18) + (2 x 16) .= 104 cells are contained in any
of the 6 segments. Since the progression comprises 6 groups, the total number of cells equals 104 x 6 =
624 cells.

Cell # 612 .= 2 is the octave of the equal tempered scale and is aligned to the third comma of group JMM.
If we analyze the commas distribution along the progression of cells, we can verify that most of them take
part in successive groups of M*M* J * J*M* M and that the third comma of either the group MMJ or JJM is
always aligned to one of the many classic cells that lie in the progression like 9/8, (9/8)^n, 2^(n/2), 3/2,
(4/3), (45/32), (15/8), (16/9), (27/16), 2, ...etc.

The stretched octave should also be considered a classic cell so it is one of the three frequencies that lie
in Segment Q column shown in the table, which are signaled by cell frequencies # 609, # 612 and # 615
that are aligned to the third commas (J, M, J) given in the first column of table.

In the period 1947 to 1967, Juliï¿½n Carrillo has demonstrated that the physical octave is not 2 but a slightly
higher than the 2 ratio.

Therefore, the correct octave is given by cell # 615 = 2.00678700656 = 1205.865 cents

Cell # SEGMENT Q SQ. ROOT THE TOCTAVE SCALE
M 607 1.98873782210 1.41022615991 FREQUENCY
M 608 1.99098340619 1.41102211400 IN DECIMALS CENTS
J 609 1.99323594728 1.41182008318 C 1.00000000000 0
J 610 1.99549103682 1.41261850364 C# 1.05976223699 100.4887
M 611 1.99774424631 1.41341580800 D 1.12309599895 200.9775
M 612 ..2 1.41421356237 Eb 1.19021472820 301.4662
M 613 2.00225830078 1.41501176701 E 1.26134462286 401.955
M 614 2.00451915152 1.41581042217 F 1.33672539913 502.4437
J 615 2.00678700656 1.41661109926 F# 1.41661109923 602.9325
J 616 2.00905742738 1.41741222916 G 1.50127094746 703.4212
M 617 2.01132595536 1.41821223918 Ab 1.59099025761 803.91
M 618 2.01359704486 1.41901270074 A 1.68607139444 904.3987
M 619 2.01587069874 1.41981361408 Bb 1.78683479269 1004.888
M 620 2.01814691994 1.42061497949 B 1.89362003704 1105.376
J 621 2.02043019304 1.42141837368 ? 2.00678700656 1205.865
J 622 2.02271604938 1.42222222222 ?C# 2.12671708713 1306.354
M 623 ..2.025 1.42302494708 ?D 2.25381445770 1406.843
M 624 2.02728652954 1.42382812500 ?Eb 2.38850745145 1507.331
.= (9/8)^6 ?E 2.53125000000 1607.82
?F 2.68252316238 1708.309

<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Wolf Peuker" <wolfpeuker@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, August 02, 2011 2:06 AM
Subject: Re: [tuning] A new equal tempered scale?

> Hello Mario,
>
> Am 02.08.2011 02:04, schrieb Mario Pizarro:
>> Petr,
>>
>> The interval of a12 tone et scale for a 2/1 octave is as you know >> 2^(1/12) =
>> 2^(0.0833333....) = 1.05946309436
>>
>> Similarly, the interval of a 12 tone et scale for a 2.00678700656 / 1
>> "toctave" equals (2.00678700656)^(1/12) = 1.05976223699 ------- > Please tell us /how/ the "toctave" was found, describe your way to this
> (decimal) representation in a comprehensible manner. Thanks in advance!
>
> Best regards,
> Wolf
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>
>
>
>

🔗Mario Pizarro <piagui@...>

Wolf-- The table was garbled. Perhaps this one is ok.

Cell # SEGMENT Q SQ. ROOT THE TOCTAVE SCALE
M 607 1.98873782210 1.41022615991 FREQUENCY
M 608 1.99098340619 1.41102211400 IN DECIMALS CENTS
J 609 1.99323594728 1.41182008318 C 1.00000000000 0
J 610 1.99549103682 1.41261850364 C# 1.05976223699 100.4887
M 611 1.99774424631 1.41341580800 D 1.12309599895 200.9775
M 612 2 1.41421356237 Eb 1.19021472820 301.4662
M 613 2.00225830078 1.41501176701 E 1.26134462286 401.955
M 614 2.00451915152 1.41581042217 F 1.33672539913 502.4437
J 615 2.00678700656 1.41661109926 F# 1.41661109923 602.9325
J 616 2.00905742738 1.41741222916 G 1.50127094746 703.4212
M 617 2.01132595536 1.41821223918 Ab 1.59099025761 803.91
M 618 2.01359704486 1.41901270074 A 1.68607139444 904.3987
M 619 2.01587069874 1.41981361408 Bb 1.78683479269 1004.888
M 620 2.01814691994 1.42061497949 B 1.89362003704 1105.376
J 621 2.02043019304 1.42141837368 π 2.00678700656 1205.865
J 622 2.02271604938 1.42222222222 πC# 2.12671708713 1306.354
M 623 2.025 1.42302494708 πD 2.25381445770 1406.843
M 624 2.02728652954 1.42382812500 πEb 2.38850745145 1507.331
.= (9/8)^6 πE 2.53125000000 1607.82
πF 2.68252316238 1708.309

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Wolf Peuker" <wolfpeuker@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, August 02, 2011 2:06 AM
Subject: Re: [tuning] A new equal tempered scale?

🔗Wolf Peuker <wolfpeuker@...>

🔗Mario Pizarro <piagui@...>

Wolf,

It is 07:00 AM in Lima, I didnï¿½t sleep; at 03:30 AM got the expected expression of the toctave. Since Mike Battaglia is not shure that the toctave with its eleven decimal digits (2.00678700656) is the exact value of the Physics constant, I say that what I am seeing on my desk made me nervous, it was the final group of numbers after hours of fighting:

[(2^26)* 2^(!/4)/(3^13)*(5^2)]*[(3^16)*(5^2)/(2^30)] = [(3^3)*2^(!/4)/ 2^4] = [(27*2^(!/4))/16] = (1.6875*1.189207115) = [(27/16)*2^(1/4)] = (PYTHAGORAS NOTE A)* 2^(1/4) = 2.00678700656 = TOCTAVE

Wolf, there is a copyright, the progression is part of my book. If I send you an email where I give you my permission to study the progression wouldnï¿½t be it all we need?

Mike, the 2/1 is really a numerical octave. Since now we have the musical octave, I expect better harmony. Pythagoras was very close to the toctave. Letï¿½s give out this new.

Mario
AUG. 03-----09:30 AM
----- Original Message ----- From: "Wolf Peuker" <wolfpeuker@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 03, 2011 4:46 AM
Subject: Re: [tuning] A new equal tempered scale?

> Hello Mario,
>
> Am 02.08.2011 21:55, schrieb Mario Pizarro:
>> Hello Wolf,
>>
>> Here you have it. The only matter you need is the Progression of Musical
>> Cells (about 700 KB). I can send it to you if you want.
> Yes, I would like to read it.
> If it is publicly available, a hyperlink would be better.
> If not, I hope there will be no copyright problem.
>
> Thanks in advance!
>
> BTW: I tried to start a xenwiki article stub about the Toctave
> http://xenharmonic.wikispaces.com/Toctave
> Please, could you briefly review it?
>
> Best regards,
> Wolf
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>

🔗genewardsmith <genewardsmith@...>

🔗Mario Pizarro <piagui@...>

Wolf,

It is a nice idea, this way anyone that read it can detect who is not an open minded human.

BTW: Regarding the Progression of Cells: To make the permission document I need your address I think.

Best regards

Mario

Aug. 03--- 02:50 PM
----- Original Message ----- From: "Wolf Peuker" <wolfpeuker@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 03, 2011 4:46 AM
Subject: Re: [tuning] A new equal tempered scale?

🔗Mike Battaglia <battaglia01@...>

I will say that I do like the sound of 12-tet with a stretched octave.
It makes everything sound brighter, and I like that quite a bit. But I
don't understand why this exact value is supposed to be the octave. It
reduces to (27 2^(1/4) / 16), so I'm told. But why is this more
mathematically pure than, say, 1205.00 cents? Or 1204.98 cents? That's
what I don't get.

-Mike

On Wed, Aug 3, 2011 at 10:44 AM, Mario Pizarro <piagui@...> wrote:
> Wolf,
>
> It is 07:00 AM in Lima, I didn´t sleep; at 03:30 AM got the expected
> expression of the toctave. Since Mike Battaglia is not shure that the
> toctave with its eleven decimal digits (2.00678700656) is the exact value of
> the Physics constant, I say that what I am seeing on my desk made me
> nervous, it was the final group of numbers after hours of fighting:
>
> [(2^26)* 2^(!/4)/(3^13)*(5^2)]*[(3^16)*(5^2)/(2^30)] = [(3^3)*2^(!/4)/ 2^4]
> = [(27*2^(!/4))/16] = (1.6875*1.189207115) = [(27/16)*2^(1/4)] =
> (PYTHAGORAS NOTE A)* 2^(1/4) = 2.00678700656 = TOCTAVE
>
> Wolf, there is a copyright, the progression is part of my book. If I send
> you an email where I give you my permission to study the progression
> wouldn´t be it all we need?
>
> Mike, the 2/1 is really a numerical octave. Since now we have the musical
> octave, I expect better harmony. Pythagoras was very close to the toctave.
> Let´s give out this new.
>
> Mario
> AUG. 03-----09:30 AM
> ----- Original Message ----- From: "Wolf Peuker" <wolfpeuker@...>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, August 03, 2011 4:46 AM
> Subject: Re: [tuning] A new equal tempered scale?
>
>
>> Hello Mario,
>>
>> Am 02.08.2011 21:55, schrieb Mario Pizarro:
>>>
>>> Hello Wolf,
>>>
>>> Here you have it. The only matter you need is the Progression of Musical
>>> Cells (about 700 KB). I can send it to you if you want.
>>
>> Yes, I would like to read it.
>> If it is publicly available, a hyperlink would be better.
>> If not, I hope there will be no copyright problem.
>>
>> Thanks in advance!
>>
>> BTW: I tried to start a xenwiki article stub about the Toctave
>> http://xenharmonic.wikispaces.com/Toctave
>> Please, could you briefly review it?
>>
>> Best regards,
>> Wolf
>>
>>
>> ------------------------------------
>>
>> 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
>>
>>
>>
>>
>
>

🔗Mario Pizarro <piagui@...>

Mike,

If instead of 1205 we use 1206 which is close to 27 (2^1/4)/!6 we would work with 100.5, 200.5, 300.5 .....

Mario

Aug. 03
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 03, 2011 3:06 PM
Subject: Re: [tuning] A new equal tempered scale?

-Mike

On Wed, Aug 3, 2011 at 10:44 AM, Mario Pizarro <piagui@...> wrote:
> Wolf,
>
> It is 07:00 AM in Lima, I didnï¿½t sleep; at 03:30 AM got the expected
> expression of the toctave. Since Mike Battaglia is not shure that the
> toctave with its eleven decimal digits (2.00678700656) is the exact value > of
> the Physics constant, I say that what I am seeing on my desk made me
> nervous, it was the final group of numbers after hours of fighting:
>
> [(2^26)* 2^(!/4)/(3^13)*(5^2)]*[(3^16)*(5^2)/(2^30)] = [(3^3)*2^(!/4)/ > 2^4]
> = [(27*2^(!/4))/16] = (1.6875*1.189207115) = [(27/16)*2^(1/4)] =
> (PYTHAGORAS NOTE A)* 2^(1/4) = 2.00678700656 = TOCTAVE
>
> Wolf, there is a copyright, the progression is part of my book. If I send
> you an email where I give you my permission to study the progression
> wouldnï¿½t be it all we need?
>
> Mike, the 2/1 is really a numerical octave. Since now we have the musical
> octave, I expect better harmony. Pythagoras was very close to the toctave.
> Letï¿½s give out this new.
>
> Mario
> AUG. 03-----09:30 AM
> ----- Original Message ----- From: "Wolf Peuker" > <wolfpeuker@...>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, August 03, 2011 4:46 AM
> Subject: Re: [tuning] A new equal tempered scale?
>
>
>> Hello Mario,
>>
>> Am 02.08.2011 21:55, schrieb Mario Pizarro:
>>>
>>> Hello Wolf,
>>>
>>> Here you have it. The only matter you need is the Progression of Musical
>>> Cells (about 700 KB). I can send it to you if you want.
>>
>> Yes, I would like to read it.
>> If it is publicly available, a hyperlink would be better.
>> If not, I hope there will be no copyright problem.
>>
>> Thanks in advance!
>>
>> BTW: I tried to start a xenwiki article stub about the Toctave
>> http://xenharmonic.wikispaces.com/Toctave
>> Please, could you briefly review it?
>>
>> Best regards,
>> Wolf
>>
>>
>> ------------------------------------
>>
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🔗Mario Pizarro <piagui@...>

Mike,

The progression defined not only the classic pythagorean and JI scales but also all consonant ratios. The sequence MMJ JMM is found anywhere along the set and it is not a coincidence that in all cases major and minor triad components coincide (are aligned to) with the third component of either MMJ or JMM They generate the conventional 2/1 octave which coincides with the third comma of JMM. A half of the last cell frequency gives the phytagorean comma which is obviously aligned to the third comma of the JMM group. If instead of the toctave (Cell # 615 = 27 (2^1/4)/16) that is consonant with 2 frequency (since their ratio gives MMJ), we take Cell # 614 as the toctave, its reduced frequency value is rather complex and dissonant with 2, for one comma of group MMJ is missing.

Our daily occupation deals with analysis, science..... even in this case that you donï¿½t see any trace of science in the progression, the reduced terms of the toctave should be considered.

Mario

Aug. 03

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 03, 2011 3:06 PM
Subject: Re: [tuning] A new equal tempered scale?

-Mike

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

🔗Mike Battaglia <battaglia01@...>

On Wed, Aug 3, 2011 at 8:01 PM, Mario Pizarro <piagui@...> wrote:
>
> Mike,
>
> The progression defined not only the classic pythagorean and JI scales but
> also all consonant ratios. The sequence MMJ JMM is found anywhere along the
> set and it is not a coincidence that in all cases major and minor triad
> components coincide (are aligned to) with the third component of either MMJ
> or JMM They generate the conventional 2/1 octave which coincides with the
> third comma of JMM. A half of the last cell frequency gives the phytagorean
> comma which is obviously aligned to the third comma of the JMM group. If
> instead of the toctave (Cell # 615 = 27 (2^1/4)/16) that is consonant with 2
> frequency (since their ratio gives MMJ), we take Cell # 614 as the toctave,
> its reduced frequency value is rather complex and dissonant with 2, for one
> comma of group MMJ is missing.

I'm completely lost. What's MMJ JMM? What are the Cells? And wouldn't
Cell 614 be flatter than an octave, whereas the toctave is supposed to
be sharper?

> Our daily occupation deals with analysis, science..... even in this case
> that you don´t see any trace of science in the progression, the reduced
> terms of the toctave should be considered.

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> ... What's MMJ JMM? What are the Cells? And wouldn't Cell 614 be flatter than an octave ...?

As it's quiet here, I'll post my summary of what I've managed to glean about this (actually I wrote this about a year ago):

--------------
1) In case it is not obvious, the 612 "cells" are simply 612 different notes, within the octave, relative to an origin or 1/1 note. To me, this is reminiscent of the Indian system, where 22 notes forming JI ratios with the origin are derived by the three different sruti sizes occurring in the right order. In Mario's case there are three much smaller "sruti" (M, J, U) and hence many more notes before the octave is reached. Note also that in the Indian system the sruti are formed of integer powers of 2, 3 and 5, but in Mario's system two of them contain fractional powers of 2 or 3.

2) Mario says that the system is derived using mathematical principles, but I am not sure what they are. However, we can see a number of features in the 612 note set. The 22 Indian notes are all there, and many more notes from the extended "5-limit JI lattice" formed by combining the 2:3 and the 4:5 interval in familiar ways. For example, the Pythagorean diatonic scale is found in cells: (0,) 104, 208, 254, 358, 462, 566, 612; and the JI syntonic scale in (0,) 104, 197, 254, 358, 451, 555, 612.

3) However, in between these "just" intervals there are other positions with fractional powers of 2 or 3. They "fill in" the gaps between the more "just" values. They include the cells 153, 306, 459, which together with 612 (=0) split the octave precisely into quarters, i.e. they form a diminished 7th chord in 12-tET. (NB the other cells that are multiples of 51 give very close approximations to 12-tET notes, but they are not exact.) This diminished chord is a feature in the first three Piagui scales.

4) The three sruti M, J, U are very similar in size, so overall this scheme is very similar to 612-EDO. However, whereas in 612-EDO the JI ratios are approximated, (e.g. 2^(197/612) approx 4:5; 2^(358/612) approx 2:3), in Mario's scheme they are exact (e.g cell 197 = 4:5; cell 358 = 2:3).

5) Because the division of the octave is unequal, this means that a constant number of sruti does not always equal the same interval - it depends where you start and end (just as in the Indian system). So we can say that often, but not always, 197sruti=4:5, 358sruti=2:3, 104sruti=8:9, 58sruti=2048:2187, 46sruti=243:256, 12sruti=Pythagorean comma, 11sruti=syntonic comma, 21sruti=diesis, 1sruti=schisma. More precisely, we can express any interval in terms of the number of M, J, U it contains, as a vector. For the intervals in this paragraph, the vectors are (121,68,8), (220,124,14), (64,36,4), (36,20,2), (28,16,2), (8,4,0), (7,4,0), (13,8,0), (1,0,0). This vector is precise for the interval, but may not be available at every point within the octave.

6) The smallest repeating pattern in the order of the srutis is that of the 8:9 interval, that consists of 104 srutis (64 M, 36 J, 4 U). The pattern is also symmetric. Therefore I suspect that Mario intends the pattern not to repeat after the octave (that is 612 sruti) but after 624 sruti, that is the interval (9/8)^6, a Pythagorean comma greater than one octave. This is supported by the fact that he says that he has a full set of 88 notes for a piano. OTOH it is slightly contradicted by the way he describes the sets of 12 notes in Piagui 1, 2, 3.

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

To answer your questions, MMJJMM is a sequence that occurs often within the full sequence; and cell 612 is the octave so 614 is still bigger. None of this means that I understand why 615 is special. In fact I'm still not sure exactly what Carrillo's result was - even if it is to do with harmonics themselves or with human perception ...

Steve.

🔗Mario Pizarro <piagui@...>

Steve,

You can not imagine how happy I feel now after reading your summary. Undoubtely you are a brilliant analyzer. I have offer to Mike Battaglia some basic information regarding MMJJMM and told him that he would need less than 20 minutes to understand it, but after sending him the very very basic information, he responded this:

""" On Thu, Aug 4, 2011 at 1:18 PM, Mario Pizarro <piagui@...> wrote:
> Mike
>
> <I'm completely lost. What's MMJ JMM? What are the Cells? And wouldn't
> <Cell 614 be flatter than an octave, whereas the toctave is supposed to
> <be sharper?
>
> 1) M and J are commas. They were used as factors; M is the schisma (32805 > /
> 32768) = 1.00112915039, while J is a comma (1.00113137110).

Decimal numbers mean nothing to me. Is J a just interval? If so, what
is its ratio?

-Mike"""
------------------------------------------
I responded his email with this:

Mike,

You wrote:

<Decimal numbers mean nothing to me. Is J a just interval? If so, what
<is its ratio?

M and J commas establish two different intervals between two contiguous cells, I gave you the ratio (33554432*2^1/4)/39858075) that gives the J comma. Now I realize that you asked if J is a "just" interval and I donï¿½t have an answer to your question for I donï¿½t know what you mean by "just interval". I thought it is an idiomatical variant of the expression: "Is J just an interval?". Any way, I gave you a correct information, no problem.

I would like to send you a few lines of information on the progression. May I do it?.

Mario

August, 04
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
I didnï¿½t get any answer and today is friday 06.

I noted he refuses to read any information regarding the progression and seems to me that he would prefer not be part of any discussion on this subject, that is what I can see. What did I to face these rough days?

Your message gave me calm. In about two hours I will send a message containing more information.

Thanks to you I feel better know.

Best regards

Mario

🔗Mike Battaglia <battaglia01@...>

Mario, I've been very busy recently, so you'll have to be patient if I
can't reply as quickly as I used to. My comments are:

1) I don't understand why the cells are important.
2) I don't understand why the "toctave" has to align with a cell.

-Mike

On Sat, Aug 6, 2011 at 9:41 AM, Mario Pizarro <piagui@...> wrote:
>
> Steve,
>
> You can not imagine how happy I feel now after reading your summary.
> Undoubtely you are a brilliant analyzer. I have offer to Mike Battaglia some
> basic information regarding MMJJMM and told him that he would need less than
> 20 minutes to understand it, but after sending him the very very basic
> information, he responded this:
>
> """ On Thu, Aug 4, 2011 at 1:18 PM, Mario Pizarro <piagui@...> wrote:
> > Mike
> >
> > <I'm completely lost. What's MMJ JMM? What are the Cells? And wouldn't
> > <Cell 614 be flatter than an octave, whereas the toctave is supposed to
> > <be sharper?
> >
> > 1) M and J are commas. They were used as factors; M is the schisma (32805
> > /
> > 32768) = 1.00112915039, while J is a comma (1.00113137110).
>
> Decimal numbers mean nothing to me. Is J a just interval? If so, what
> is its ratio?
>
> -Mike"""
> ------------------------------------------
> I responded his email with this:
>
> Mike,
>
> You wrote:
>
> <Decimal numbers mean nothing to me. Is J a just interval? If so, what
> <is its ratio?
>
> M and J commas establish two different intervals between two contiguous
> cells, I gave you the ratio (33554432*2^1/4)/39858075) that gives the J
> comma. Now I realize that you asked if J is a "just" interval and I don´t
> have an answer to your question for I don´t know what you mean by "just
> interval". I thought it is an idiomatical variant of the expression: "Is J
> just an interval?". Any way, I gave you a correct information, no problem.
>
> I would like to send you a few lines of information on the progression. May
> I do it?.
>
> Mario
>
> August, 04
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> I didn´t get any answer and today is friday 06.
>
> I noted he refuses to read any information regarding the progression and
> seems to me that he would prefer not be part of any discussion on this
> subject, that is what I can see. What did I to face these rough days?
>
> Your message gave me calm. In about two hours I will send a message
> containing more information.
>
> Thanks to you I feel better know.
>
> Best regards
>
> Mario

🔗Mario Pizarro <piagui@...>

Mike,

For the present just believe me and also believe Steve Martin : THE PROGRESSION OF CELLS IS IMPORTANT.
2) See below---------- The first M is aligned to 1.00112915039. It is also aligned to 32805 / 32768.
TRUST IN GOD------ TRUST ON ME----- MARIO----------AUGUST 06---03:15 PM

CELL Nï¿½ CELL FREQUENCY CELL FREQUENCY
0 1 = Note C (COMMON FRACTION)
M 1 1.00112915039 32805 / 32768
M 2 1.00225957576 18186 / 18145
S J 3 1.00339350328 49083 / 48917
J 4 1.00452871369 36821 / 36655
M 5 1.00566297768 26993 / 26841
M 6 1.00679852243 107662 / 106935
M 7 1.00793534937 20704 / 20541
M 8 1.00907345997 5783 / 5731
S J 9 1.01021509652 38371 / 37983
J 10 1.01135802469 2048 / 2025
M 11 1.01250000000 81 / 80
M 12 1.01364326477 47401 / 46763
M 13 1.01478782046 33694 / 33203
M 14 1.01593366853 54770 / 53911
S J 15 1.01708306652 4763 / 4683
J 16 1.01823376491 31719 / 31151
M 17 1.01938350395 18354 / 18005
M 18 1.02053454123 34938 / 34235

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, August 06, 2011 2:22 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

Mario, I've been very busy recently, so you'll have to be patient if I
can't reply as quickly as I used to. My comments are:

1) I don't understand why the cells are important.
2) I don't understand why the "toctave" has to align with a cell.

-Mike

On Sat, Aug 6, 2011 at 9:41 AM, Mario Pizarro <piagui@...> wrote:
>
> Steve,
>
> You can not imagine how happy I feel now after reading your summary.
> Undoubtely you are a brilliant analyzer. I have offer to Mike Battaglia > some
> basic information regarding MMJJMM and told him that he would need less > than
> 20 minutes to understand it, but after sending him the very very basic
> information, he responded this:
>
> """ On Thu, Aug 4, 2011 at 1:18 PM, Mario Pizarro <piagui@...> > wrote:
> > Mike
> >
> > <I'm completely lost. What's MMJ JMM? What are the Cells? And wouldn't
> > <Cell 614 be flatter than an octave, whereas the toctave is supposed to
> > <be sharper?
> >
> > 1) M and J are commas. They were used as factors; M is the schisma > > (32805
> > /
> > 32768) = 1.00112915039, while J is a comma (1.00113137110).
>
> Decimal numbers mean nothing to me. Is J a just interval? If so, what
> is its ratio?
>
> -Mike"""
> ------------------------------------------
> I responded his email with this:
>
> Mike,
>
> You wrote:
>
> <Decimal numbers mean nothing to me. Is J a just interval? If so, what
> <is its ratio?
>
> M and J commas establish two different intervals between two contiguous
> cells, I gave you the ratio (33554432*2^1/4)/39858075) that gives the J
> comma. Now I realize that you asked if J is a "just" interval and I donï¿½t
> have an answer to your question for I donï¿½t know what you mean by "just
> interval". I thought it is an idiomatical variant of the expression: "Is J
> just an interval?". Any way, I gave you a correct information, no problem.
>
> I would like to send you a few lines of information on the progression. > May
> I do it?.
>
> Mario
>
> August, 04
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> I didnï¿½t get any answer and today is friday 06.
>
> I noted he refuses to read any information regarding the progression and
> seems to me that he would prefer not be part of any discussion on this
> subject, that is what I can see. What did I to face these rough days?
>
> Your message gave me calm. In about two hours I will send a message
> containing more information.
>
> Thanks to you I feel better know.
>
> Best regards
>
> Mario

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

🔗Mike Battaglia <battaglia01@...>

🔗Ryan Avella <domeofatonement@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Mike,
>
> For the present just believe me and also believe Steve Martin : THE
> PROGRESSION OF CELLS IS IMPORTANT.
> 2) See below---------- The first M is aligned to 1.00112915039. It is also
> aligned to 32805 / 32768.
> TRUST IN GOD------ TRUST ON ME----- MARIO----------AUGUST 06---03:15 PM

That is blasphemy; requiring the same trust from us that one would reserve only for God. Do you know the consequences of equating oneself with God, Mario?

When you tell us to accept the "truth" based on faith alone, you are playing God. How can we know that you are not lying? How can we know your motives?

If you want some credibility among us, I suggest you show us proof that the progression of cells are important. Even God doesn't demand blind faith; he supplies signs wherever they are necessary. You should know this of all people.

I am apologize in advance if I sound angry. I only want to know why. I want to see proof. I am an analytical person, and concepts do not make sense to me unless if I can see them with my own eyes, and hear them with my ears.

Ryan

🔗genewardsmith <genewardsmith@...>

🔗Mario Pizarro <piagui@...>

Ryan,

It is not a blasphemy. I used hyphens ---- to indicate that my trust in GOD is something apart of Mario, that is why I put the hyphens. Only crazy people intend to equate with GOD.
------------------------------------------------------------------------------------------------------
> That is blasphemy; requiring the same trust from us that one would reserve > only for God. Do you know the consequences of equating oneself with God, > Mario? ---NO RYAN IT WAS A MISUNDERSTANDING, PLEASE SEE MY MESSAGE
----------------------------------------------------------------------------------------------------------
Another point: I was asked to explain why the progression is important. Since the explanation might take hours due to the complexity of the subject, I wrote "For the present.....".In every country these three words mean that I asked Mike just to believe me and also believe Steve Martin that the Progression of cells contains the needed data for determining the octave. It has no sense to talk on cell # 614 but cells #609, #612, #615, #618.....#624. This is the first time that the progression is classified as important, Ididnï¿½t do it.
--------------------------------------------------------------
> When you tell us to accept the "truth" based on faith alone, you are > playing God. How can we know that you are not lying? How can we know > your motives? I NEVER ASKED TO ANYONE TO ACCEPT SOMETHING BASED ON FAITH > ALONE. WHO INVENTED THIS SILLY DECLARATION?. I DIDNï¿½T USE THE WORD "TRUTH"
-----------------------------------------------------------------------------------------------------------------------
> If you want some credibility among us, I suggest you show us proof that > the progression of cells are important. Even God doesn't demand blind > faith; he supplies signs wherever they are necessary. You should know > this of all people. I REPEAT THAT I CONFIRM THAT THE PROGRESSION OF CELLS > ARE IMPORTANT. ARE YOU TRYING TO CANCELL MY RIGHT OF GIVING AN OPINION?-- > YOU OFFEND ME
----------------------------------------------------------------------------------------------------------------------
Fortunately, Mike just told me to be patient. Since I know why cell 615 and not cell 614 is the natural octave, it is expected that not only Mike but also Steve Martin arrive to the same conclussion I arrived. Steve made an analysis of the progression, he also entered to some topics I bypassed. The main step is to understand and recognize that the third comma of MMJ, that is J and the third comma of JMM, that is M, when are seen in the progression tables, are always aligned (placed in the same row) either to a triad tone, a consonant cell like 3/2, 4/3.... or to the musical octave. It would be a wrong decision to choose a different value.

Mario
August, 06
------------------------------------------------------------------------------------------------
----- Original Message ----- From: "Ryan Avella" <domeofatonement@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, August 06, 2011 4:08 PM
Subject: [tuning] Re: A new equal tempered scale?

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> Mike,
>>
>> For the present just believe me and also believe Steve Martin : THE
>> PROGRESSION OF CELLS IS IMPORTANT.
>> 2) See below---------- The first M is aligned to 1.00112915039. It is >> also
>> aligned to 32805 / 32768.
>> TRUST IN GOD------ TRUST ON ME----- MARIO----------AUGUST 06---03:15 PM
>
> That is blasphemy; requiring the same trust from us that one would reserve > only for God. Do you know the consequences of equating oneself with God, > Mario? ---NO RYAN IT WAS A MISUNDERSTANDING, PLEASE READ MY MESSAGE
>
> When you tell us to accept the "truth" based on faith alone, you are > playing God. How can we know that you are not lying? How can we know > your motives? I ASKED MIKE TO BELIEVE ME AND ALSO BELIEVE STEVE MARTIN > THAT THE PROGRESSION IS IMPORTANT. AS A MATTER OF FACT STEVE IS PAYING > ATTENTION TO IT. I DID NOT FORCED MIKE TO BELIEVE THAT. IT IS UP TO HIM TO > BELIEVE OR NOT ON THAT. MY TARGET IS TO GIVEOUT THE FEATURES OF THE > PROGRESSION. UNLESS MIKE AND STEVE ARE NOT SUFFICIENTLY INFORMED ON THIS > MATTER WE CANNOT AVAIL ITS PROPERTIES. "FAITH" HAS NOTHING TO DO ON THIS > SUBJECT.
>
> If you want some credibility among us, I suggest you show us proof that > the progression of cells are important. Even God doesn't demand blind > faith; he supplies signs wherever they are necessary. You should know > this of all people. I CONFIRM THAT THE PROGRESSION OF > CELLS ARE IMPORTANT. ARE YOU TRYING TO CANCELL MY RIGHT OF GIVING AN > OPINION?-- YOU OFFEND ME
>
>
> I am apologize in advance if I sound angry. I only want to know why. I > want to see proof. I am an analytical person, and concepts do not make > sense to me unless if I can see them with my own eyes, and hear them with > my ears. I AM DISCUSSING THIS MATTER WITH MIKE AND STEVE AND DONï¿½T NEED > YOUR ADVISE. REGARDING YOUR ABILITIES, YOUï¿½D BETTER OFFER YOUR SERVICES TO > SOMEBODY WHO NEEDS YOU.
>
>
>
> Ryan
>
>
>
> ------------------------------------
>
> 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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> Yahoo! Groups Links
>
>
>
>

🔗Mario Pizarro <piagui@...>

Steve,

You wrote:
---------------------------------------------------------------------------
> To answer your questions, MMJJMM is a sequence that occurs often within > the full sequence; and cell 612 is the octave so 614 is still bigger. None > of this means that I understand why 615 is special.

Me neither...

-Mike
--------------------------------------------------------------------
To make clear some aspects like sequence MMJJMM we would need some talking by emails. If you would be here in Lima, I could give you a copy of the book I wrote where you could see the role of the third comma "J" in group MMJ or the interval "M" in group JMM.
---------------------------------------------------------------
Perhaps you can detect some of these interesting features if you mark in the progression some of the MMJ and JMM groups. This way you could verify that well known triad tone frequencies lie in the same row and the other two commas either MM or JM make possible the consonance of MMJ and JMM with former and contiguous elements.

Regarding Ryan Avellaï¿½s message, he inserted words which I didnï¿½t write and also availed my own words. It was an unfair message.

Mario
August, 6

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, August 06, 2011 3:23 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

> On Sat, Aug 6, 2011 at 5:17 AM, martinsj013 <martinsj@...> wrote:
>>
>> 3) However, in between these "just" intervals there are other positions >> with fractional powers of 2 or 3. They "fill in" the gaps between the >> more "just" values. They include the cells 153, 306, 459, which together >> with 612 (=0) split the octave precisely into quarters, i.e. they form a >> diminished 7th chord in 12-tET. (NB the other cells that are multiples of >> 51 give very close approximations to 12-tET notes, but they are not >> exact.) This diminished chord is a feature in the first three Piagui >> scales.
>
> So is this some kind of rank-2 temperament then where the period is
> 1/4-oct and the generator is a schisma? Are the cells MOS?
>
>> To answer your questions, MMJJMM is a sequence that occurs often within >> the full sequence; and cell 612 is the octave so 614 is still bigger. >> None of this means that I understand why 615 is special.
>
> Me neither...
>
> -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
>
>
>
>

🔗Mario Pizarro <piagui@...>

Dear friends,

Ryan Avella sent me a message having phrases near to insults against me. Most of them are based on the fact that in my response to Mike message given below, I wrote that the progression of cells are important, where the word "important" had to be included whereas it was used in Mikeï¿½s question, who wrote:

1) I don't understand why the cells are important.

It is evident that Avella needs some lessons on how to practice respect. If we would be living in times of the Three musketeers, this weekend my godfather would be given instructions to his horse while I would be warming my powered legs to be used once we find the villain.

Mario

August, 07
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, August 06, 2011 2:22 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

Mario, I've been very busy recently, so you'll have to be patient if I
can't reply as quickly as I used to. My comments are:

1) I don't understand why the cells are important.
2) I don't understand why the "toctave" has to align with a cell.

-Mike

On Sat, Aug 6, 2011 at 9:41 AM, Mario Pizarro <piagui@...> wrote:
>
> Steve,
>
> You can not imagine how happy I feel now after reading your summary.
> Undoubtely you are a brilliant analyzer. I have offer to Mike Battaglia > some
> basic information regarding MMJJMM and told him that he would need less > than
> 20 minutes to understand it, but after sending him the very very basic
> information, he responded this:
>
> """ On Thu, Aug 4, 2011 at 1:18 PM, Mario Pizarro <piagui@...> > wrote:
> > Mike
> >
> > <I'm completely lost. What's MMJ JMM? What are the Cells? And wouldn't
> > <Cell 614 be flatter than an octave, whereas the toctave is supposed to
> > <be sharper?
> >
> > 1) M and J are commas. They were used as factors; M is the schisma > > (32805
> > /
> > 32768) = 1.00112915039, while J is a comma (1.00113137110).
>
> Decimal numbers mean nothing to me. Is J a just interval? If so, what
> is its ratio?
>
> -Mike"""
> ------------------------------------------
> I responded his email with this:
>
> Mike,
>
> You wrote:
>
> <Decimal numbers mean nothing to me. Is J a just interval? If so, what
> <is its ratio?
>
> M and J commas establish two different intervals between two contiguous
> cells, I gave you the ratio (33554432*2^1/4)/39858075) that gives the J
> comma. Now I realize that you asked if J is a "just" interval and I donï¿½t
> have an answer to your question for I donï¿½t know what you mean by "just
> interval". I thought it is an idiomatical variant of the expression: "Is J
> just an interval?". Any way, I gave you a correct information, no problem.
>
> I would like to send you a few lines of information on the progression. > May
> I do it?.
>
> Mario
>
> August, 04
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> I didnï¿½t get any answer and today is friday 06.
>
> I noted he refuses to read any information regarding the progression and
> seems to me that he would prefer not be part of any discussion on this
> subject, that is what I can see. What did I to face these rough days?
>
> Your message gave me calm. In about two hours I will send a message
> containing more information.
>
> Thanks to you I feel better know.
>
> Best regards
>
> Mario

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

🔗Mike Battaglia <battaglia01@...>

On Aug 7, 2011, at 1:36 AM, "Mario Pizarro" <piagui@...> wrote:

Dear friends,

Ryan Avella sent me a message having phrases near to insults against me.
Most of them are based on the fact that in my response to Mike message given

below, I wrote that the progression of cells are important, where the word
"important" had to be included whereas it was used in Mike´s question, who
wrote:

1) I don't understand why the cells are important.

Why don't you discuss it with him offlist, or block his emails? I moderate
this list but can't stop what people do offlist, and I don't want to burden
the folks on this list with disputes that happen off of it.

It is evident that Avella needs some lessons on how to practice respect. If
we would be living in times of the Three musketeers, this weekend my
godfather would be given instructions to his horse while I would be warming
my powered legs to be used once we find the villain.

???????

Mario, I reiterate my questions:
1) How do you claim the cells are involved in the perception of music?
2) Why is the "toctave" supposedly related to the cells?

-Mike

🔗Steve Parker <steve@...>

🔗Mario Pizarro <piagui@...>

Steve,

Yes, it appears that I am acting on the contrary. Regarding the sound, "we" (the tuner, the grand piano owner and I) donï¿½t understand why you got irregular sound. If I would be the only person who did the evaluation I would contract another tuner despite I am very sensible to inharmony and beating.

This morning I realize that if the progression itself is the only mean we use to arrive to a serious conclussion, we are lost. The convincing way to conclude that the progression of cells is a trusty mean that can serve as a reference to choose cell # 615 as the real musical octave provided we recognize the unquestionable Carrilloï¿½s statement that the octave is slightly higher than 2, I repeat, the convincing way is to revise Chapter IV of my book. You have this chapter in my folder. Besides that, the great number of cases that are shown in my book where the third J comma of group MMJ and the third M comma of JMM share the same row of the cellï¿½s data where also lie either well known consonances like 3/2, 4/3, 5/4, 81/80, 256/243, 25/24, 27/25, 135/128, 16/15, 9/8, (9/8)^(n/2),.....etc or a triad frequency like 27/16 (E), 45/32, ....ETC

In no case cell # 614 is the searched octave for it does not share the row of data with the third comma.

This afternoon I will post one toctave scale that shows interesting features never shown by 2 /1octave.

Mario
August, 07

----- Original Message ----- From: "Steve Parker" <steve@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, August 07, 2011 5:26 AM
Subject: Re: [tuning] Re: A new equal tempered scale?

> Mario,
>
> one would normally expect the discovery of the 'quality' of the true > octave and then the sums to justify it.
> You seem to have started with the sums and come to a 'better' judgement > without any statement as to why it is better, especially given that when > tuned it sounds like a honky-tonk piano.
> I have nothing against the sound whatsoever but it is a non-starter as a > serious tuning for common practice repertoire.
>
> A lot of people on the list could make mathematically satisfying comma > schemes but would then supply reasons as to their usefulness, lack of > beats etc.
>
> Steve P.
>
> ------------------------------------
>
> 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
>
>
>
>

🔗Steve Parker <steve@...>

🔗genewardsmith <genewardsmith@...>

🔗Mario Pizarro <piagui@...>

Steve,

Thousands of people, including universitary teachers and authorities congratulated Julián Carrillo for he demonstrated that the real octave is greater than 2/1. I have his declaration on two pages in spanish, if you want I can translate it into the english language and send it to you, if you ask that does not mean that you agree with him, just read it.

He was nominated to the Nobel prize, and this only ocurr when the nominated person has really did something important.

It is also true that he didn´t find the magnitude of the difference regarding 2/1, however he did experiments in NY with the presence of physicians who signed a declaration confirming all they have appreciated.

Are you thinking that many distinguished people of the US are defending a lying?

Mario

August, 07
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Sunday, August 07, 2011 5:04 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

On 7 Aug 2011, at 16:20, Mario Pizarro wrote:

provided we
recognize the unquestionable Carrillo´s statement that the octave is
slightly higher than 2

I'm not at all sure that this was Carrillo's statement.

Steve P.

🔗genewardsmith <genewardsmith@...>

🔗Fabrice Lengronne <fabrice.lengronne@...>

Dear Mario,

Could you send to the group the original spanish text of Julián
Carrillo, so we can have a reference and the text of what he said or
wrote? It would be great for this debate...

Fabrice Lengronne

On 07/08/2011, at 11:54 p.m., Mario Pizarro wrote:

>
> Steve,
>
> Thousands of people, including universitary teachers and authorities
> congratulated Julián Carrillo for he demonstrated that the real
> octave is greater than 2/1. I have his declaration on two pages in
> spanish, if you want I can translate it into the english language
> and send it to you, if you ask that does not mean that you agree
> with him, just read it.
>
> He was nominated to the Nobel prize, and this only ocurr when the
> nominated person has really did something important.
>
> It is also true that he didn´t find the magnitude of the difference
> regarding 2/1, however he did experiments in NY with the presence of
> physicians who signed a declaration confirming all they have
> appreciated.
>
> Are you thinking that many distinguished people of the US are
> defending a lying?
>
> Mario
>
> August, 07
> ----- Original Message -----
> From: Steve Parker
> To: tuning@yahoogroups.com
> Sent: Sunday, August 07, 2011 5:04 PM
> Subject: Re: [tuning] Re: A new equal tempered scale?
>
>
> On 7 Aug 2011, at 16:20, Mario Pizarro wrote:
>
>> provided we
>> recognize the unquestionable Carrillo´s statement that the octave is
>> slightly higher than 2
>
> I'm not at all sure that this was Carrillo's statement.
>
> Steve P.
>
>
>

🔗Mike Battaglia <battaglia01@...>

On Sun, Aug 7, 2011 at 10:54 PM, Mario Pizarro <piagui@...> wrote:
>
> Steve,
>
> Thousands of people, including universitary teachers and authorities congratulated Julián Carrillo for he demonstrated that the real octave is greater than 2/1. I have his declaration on two pages in spanish, if you want I can translate it into the english language and send it to you, if you ask that does not mean that you agree with him, just read it.
>
> He was nominated to the Nobel prize, and this only ocurr when the nominated person has really did something important.

He seems to have discovered some important property of string
inharmonicity, which he was nominated for the Nobel Prize in Physics
for. Wikipedia's a bit unclear as to what, specifically, he
discovered.

Either way, yes, as of 2011, it's widely known that plucked or struck
strings will exhibit some degree of inharmonicity. And it's also known
that humans seem to have a subjective preference for stretched
octaves. It is reasonable to hypothesize some sort of causative
relationship from the first to the second. However, something like a
brass instrument or a bowed string will -NOT- exhibit inharmonicity.

The point we're making is that you keep using this phrase "the true
octave is sharp of 2/1," but it's impossible to determine what you
mean by "true octave" (the perceptual "equivalence point" between two
pitches? The second mode of vibration of a plucked stiff string?).
Secondly, since you keep citing Carrillo's work on the latter, then to
define the stretched octave as 2/1 * two schismas and a tiny
irrational comma doesn't sync up, as the inharmonicity coefficient is
going to depend on properties such as the tension and thickness of the
string.

I'm certainly open to see where you go with this and I think that your
progression of 612 cells certainly is rather interesting if it syncs
up with as many JI intervals as you claim (and isn't 612-equal some
kind of magic number?), but I simply ask that we be clear in the
language we use, that's all.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

Hi Mario,

> Thousands of people, including universitary teachers and authorities congratulated Julián Carrillo for he demonstrated that the real octave is greater than 2/1.
> I have his declaration on two pages in spanish, if you want I can translate it into the english language and send it to you, if you ask that does not mean that you agree with him, just read it.

I've read it. The Spanish is not too bad at all. I'm familiar with Carrillo (as no doubt are plenty of others here). His own writing used 1/4 and 1/16 tones - divisions of 1200 cents not 1206.

> He was nominated to the Nobel prize, and this only ocurr when the nominated person has really did something important.

He did not win anything for showing that the octave was greater than 2. He showed that the half of a string (as a physical entity) vibrated higher than 2 for physical reasons.
On a guitar for example this is dealt with easily so that you end up with an octave of 2 (i.e. 220 - 110).

> It is also true that he didn´t find the magnitude of the difference regarding 2/1, however he did experiments in NY with the presence of physicians who signed a declaration confirming all they have appreciated.
>
> Are you thinking that many distinguished people of the US are defending a lying?

I'm not sure you understand how science, maths or peer review work at all.

I can't imagine any distinguished person in the US lying.............

Steve P.

🔗Steve Parker <steve@...>

> it's widely known that plucked or struck
> strings will exhibit some degree of inharmonicity. And it's also known
> that humans seem to have a subjective preference for stretched
> octaves.

I play different pianos every day and often feel that the octaves are sharp although I can stop strings and hear the tuning of harmonics that has led to it.
My perfect pitch includes no stretch - I can pick out 5 cents sharp over the range of a piano.

> It is reasonable to hypothesize some sort of causative
> relationship from the first to the second. However, something like a
> brass instrument or a bowed string will -NOT- exhibit inharmonicity.

I often find brass players to flatten octave leaps, but not when sounded together.

> The point we're making is that you keep using this phrase "the true
> octave is sharp of 2/1," but it's impossible to determine what you
> mean by "true octave" (the perceptual "equivalence point" between two
> pitches? The second mode of vibration of a plucked stiff string?).
> Secondly, since you keep citing Carrillo's work on the latter, then to
> define the stretched octave as 2/1 * two schismas and a tiny
> irrational comma doesn't sync up, as the inharmonicity coefficient is
> going to depend on properties such as the tension and thickness of the
> string.

This is what makes Mario's work unrelated to Carrillo's, either from misinterpretation or misunderstanding.

Steve P.

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> He seems to have discovered some important property of string
> inharmonicity, which he was nominated for the Nobel Prize in Physics
> for. Wikipedia's a bit unclear as to what, specifically, he
> discovered.
>
> Either way, yes, as of 2011, it's widely known that plucked or struck
> strings will exhibit some degree of inharmonicity. And it's also known
> that humans seem to have a subjective preference for stretched
> octaves. It is reasonable to hypothesize some sort of causative
> relationship from the first to the second. However, something like a
> brass instrument or a bowed string will -NOT- exhibit inharmonicity.
>
> The point we're making is that you keep using this phrase "the true
> octave is sharp of 2/1," but it's impossible to determine what you
> mean by "true octave" (the perceptual "equivalence point" between two
> pitches? The second mode of vibration of a plucked stiff string?).
> Secondly, since you keep citing Carrillo's work on the latter, then to
> define the stretched octave as 2/1 * two schismas and a tiny
> irrational comma doesn't sync up, as the inharmonicity coefficient is
> going to depend on properties such as the tension and thickness of the
> string.
>
> I'm certainly open to see where you go with this and I think that your
> progression of 612 cells certainly is rather interesting if it syncs
> up with as many JI intervals as you claim (and isn't 612-equal some
> kind of magic number?), but I simply ask that we be clear in the
> language we use, that's all.

Great summary, IMO. Two small points:

* yes, the Wikipedia article talks about stopped strings, but Carrillo's own (presumably "dumbed down") words only talk of trumpeters and an oboist. (unless I and the automatic translation service have completely misread the Spanish).

* all three of Mario's commas are similar in size (yes, one is the schisma, but none is "tiny"), so the scheme is indeed close to 612EDO.

Steve.

🔗Mario Pizarro <piagui@...>

Geneward,

I was talking on Juliï¿½n Carrillo and now you mention the true octave or toctave. No doubt these negative critics are the poissons you need to live and at the end, when you hide your bitterness and realize that you were wrong neither a church nor a dog will cure your repentance. You know nothing of the foundations of the toctave, you only dare to give just a bit of ridiculous comments instead of extending your music knowledges which are notable.

----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, August 07, 2011 10:13 PM
Subject: [tuning] Re: A new equal tempered scale?

>
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
>> He was nominated to the Nobel prize, and this only ocurr when the >> nominated person has really did something important.
>
> Hundreds of people are nominated for any given Nobel prize. The prize > committee does not keep records of nominations, so this isn't something > which is usually known; it becomes known only when the nominator makes it > known and in any case it means little. Adolf Hitler, for instance, was > nominated for a Nobel Peace Prize.
>
>> Are you thinking that many distinguished people of the US are defending a >> lying?
>
> I think many of us are thinking that claiming "true octave" means > something other than a ratio of 2 is wrong *by definition*.
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

🔗Steve Parker <steve@...>

Ok. Now I believe this whole thing is a troll.

Steve P.

On 8 Aug 2011, at 14:06, "Mario Pizarro" <piagui@...> wrote:

> Geneward,
>
> I was talking on Julián Carrillo and now you mention the true octave or
> toctave. No doubt these negative critics are the poissons you need to live
> and at the end, when you hide your bitterness and realize that you were
> wrong neither a church nor a dog will cure your repentance. You know nothing
> of the foundations of the toctave, you only dare to give just a bit of
> ridiculous comments instead of extending your music knowledges which are
> notable.
>
> ----- Original Message -----
> From: "genewardsmith" <genewardsmith@...>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, August 07, 2011 10:13 PM
> Subject: [tuning] Re: A new equal tempered scale?
>
> >
> >
> > --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> >
> >> He was nominated to the Nobel prize, and this only ocurr when the
> >> nominated person has really did something important.
> >
> > Hundreds of people are nominated for any given Nobel prize. The prize
> > committee does not keep records of nominations, so this isn't something
> > which is usually known; it becomes known only when the nominator makes it
> > known and in any case it means little. Adolf Hitler, for instance, was
> > nominated for a Nobel Peace Prize.
> >
> >> Are you thinking that many distinguished people of the US are defending a
> >> lying?
> >
> > I think many of us are thinking that claiming "true octave" means
> > something other than a ratio of 2 is wrong *by definition*.
> >
> >
> >
> > ------------------------------------
> >
> > 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
> >
> >
> >
> >
>
>

🔗Michael <djtrancendance@...>

>"Ok. Now I believe this whole thing is a troll. "
Correct me if I'm wrong, but everything I have seen Mario Pizarro publish has resolved around the idea of improving 12EDO by correcting notes by a couple of cents IE a barely audible, if audible at all, measure. This discussion, low and behold, seems to be the idea of correcting the octave itself by a couple of cents. It's the tuning equivalent of "pinching pennies"...vying for very little advantage...and I could see how someone could interpret going for such a simple goal and considering it a revolution would label it as trolling.

Let me try to put it more productively...I hope you/Mario will graduate to thinking about tuning improvement on a larger scale than improving 12EDO by a couple of
cents.

"Even" people like myself can at least say they have tried various types of fifths, sixths acting as fifths, both JI and temperaments...all often representing structure many cents different than 12EDO...even if people don't like our results. It's safe to say sticking with something very close to 12EDO isn't going to be argued much against, because it's like saying x = x...but it isn't going to make a significant difference or evolution from what has already been done with 12EDO either.

🔗hstraub64 <straub@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Ok. Now I believe this whole thing is a troll. "
> ï¿½ Correct me if I'm wrong, but everything I have seen Mario
> Pizarro publish has resolved around the idea of improving 12EDO by
> correcting notes by a couple of cents IE a barely audible, if
> audible at all, measure.ï¿½ This discussion, low and behold, seems
> to be the idea of correcting the octave itself by a couple of
> cents.ï¿½ It's the tuning equivalent of "pinching pennies"...vying
> for very little advantage...and I could see how someone could
> interpret going for such a simple goal and considering it a
> revolution would label it as trolling.ï¿½
>

As far as I see, it was not "going for such a simple goal and considering it a revolution" that was labeled as trolling. It was this:

> > No doubt these negative critics are the poissons you need to live
> > and at the end, when you hide your bitterness and realize that
> > you were wrong neither a church nor a dog will cure your
> > repentance. You know nothing of the foundations of the toctave,
> > you only dare to give just a bit of ridiculous comments

This is simply insulting. And it's not the first time.
--
Hans Straub

🔗Steve Parker <steve@...>

I'm definitely not trying to improve on 12ET.
I am no fan of it at all..
So far I think I'm the only person who has actually
tuned to Mario's prescription and I don't find
the difference between it and 12ET barely audible.
Steve P.

On 8 Aug 2011, at 16:15, Michael <djtrancendance@...> wrote:

> >"Ok. Now I believe this whole thing is a troll. "
> Correct me if I'm wrong, but everything I have seen Mario Pizarro publish has resolved around the idea of improving 12EDO by correcting notes by a couple of cents IE a barely audible, if audible at all, measure. This discussion, low and behold, seems to be the idea of correcting the octave itself by a couple of cents. It's the tuning equivalent of "pinching pennies"...vying for very little advantage...and I could see how someone could interpret going for such a simple goal and considering it a revolution would label it as trolling.
>
> Let me try to put it more productively...I hope you/Mario will graduate to thinking about tuning improvement on a larger scale than improving 12EDO by a couple of
> cents.
>
> "Even" people like myself can at least say they have tried various types of fifths, sixths acting as fifths, both JI and temperaments...all often representing structure many cents different than 12EDO...even if people don't like our results. It's safe to say sticking with something very close to 12EDO isn't going to be argued much against, because it's like saying x = x...but it isn't going to make a significant difference or evolution from what has already been done with 12EDO either.
>
>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

Mario, this type of response is unacceptable. We're all just trying to
understand the big picture of your cells, string inharmonicity, the toctave,
etc.

I've left a number of pertinent questions that have been echoed by others,
and haven't seen them answered. Here's another one: If the "toctave" is
sharp because of inharmonicity, then there's also a "tfifth" and a "tmajor
third" as well. And while I did like the sound of the stretched 12-equal
tuning, I still don't get why the toctave is 2 * (PC)^(1/4).

There's no need to get defensive to questions about your work in the way
that you are, or to resort to personal attacks. Why not take a step back and
reconsider if your reaction to criticism may be too harsh?

Sent from my iPhone

On Aug 8, 2011, at 9:07 AM, Mario Pizarro <piagui@...> wrote:

Geneward,

of the foundations of the toctave, you only dare to give just a bit of
ridiculous comments instead of extending your music knowledges which are
notable.

🔗Mike Battaglia <battaglia01@...>

🔗Steve Parker <steve@...>

🔗Michael <djtrancendance@...>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Mario Pizarro <piagui@...>

Mike,

As soon as I read that some members of the list disapprove the terms "true octave" that I had been using, I changed to "toctave", I needed to use a name related with octaves and at the same time gives the idea that it´s not the 2/1 octave. This change was done about 8 days ago.

As respect to the response I sent to Gene Ward, I admit that part of it contains inapropriated words that probably came out for he uses to write short and polite scoffs on the toctave. Since he will read this message, I avail these lines to say that I am sure that this kind of response he won´t receive from me again. Some times he makes me remember a playful friend.

Regarding the toctave and since you said that I didn´t respond your questions around the following:

"Why Cell # 615 should be the stretched octave the humans apparently want to hear." , I hope you understand the following:

Recently I informed you that I have done experiments on the guitar by a slight frequency raise of the 6th, 4th and 1st open strings,
The result was a clear harmony improvement. The microphone/electronic counter (a very precise Gl counter) measured an average frequency raise of 1.00437 times respect to the 2 octave (Average ratio for the three strings). So 2*1.00437 = 2.00874 assumes the unavoidable error of harmony appreciation and not of the instrument since its exactness is far better fhan 1/50 of the frequency intervals showed by cells # 612 / # 613 / # 614 / # 615.

Whereas Cell # 612 = 2 and Cell # 615 = 2.006787....we see that Cell # 615 is slightly lower than the measured 2.00874; since none of the Cells # 616 and # 617 is the third comma either in group MMJ or JMM and also their frequencies are much higher than 2.006787, I conclude that Cell # 615 is a good choice for a stretched octave.

There is a great number of cases that are shown in my book where the third J comma of group
MMJ and the third M comma of JMM share the same row of well known consonances like 3/2, 4/3, 5/4, 81/80, 256/243,
25/24, 27/25, 135/128, 16/15, 9/8, (9/8)^(n/2),.....etc or a triad frequencies llike 27/16 (E), 45/32, ....ETC

I caused disgusts in tuning, from now and on I will only send messages provided they contain useful information. Most of the list are prepared to choice the stretched value for the octave.

Regards

Mario

August, 08
<<<<<<<<<<<<<<<<<

----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Monday, August 08, 2011 1:43 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

Mario, this type of response is unacceptable. We're all just trying to understand the big picture of your cells, string inharmonicity, the toctave, etc.

I've left a number of pertinent questions that have been echoed by others, and haven't seen them answered. Here's another one: If the "toctave" is sharp because of inharmonicity, then there's also a "tfifth" and a "tmajor third" as well. And while I did like the sound of the stretched 12-equal tuning, I still don't get why the toctave is 2 * (PC)^(1/4).

There's no need to get defensive to questions about your work in the way that you are, or to resort to personal attacks. Why not take a step back and reconsider if your reaction to criticism may be too harsh?

Sent from my iPhone

On Aug 8, 2011, at 9:07 AM, Mario Pizarro <piagui@...> wrote:

Geneward,

I was talking on Julián Carrillo and now you mention the true octave or
toctave. No doubt these negative critics are the poissons you need to live
and at the end, when you hide your bitterness and realize that you were
wrong neither a church nor a dog will cure your repentance. You know nothing
of the foundations of the toctave, you only dare to give just a bit of
ridiculous comments instead of extending your music knowledges which are
notable.

🔗Mike Battaglia <battaglia01@...>

Mario,

Would I be correct in stating your position?

1) The "octave" harmonic for most strings is slightly sharp because of
string inharmonicity
2) People have been shown to prefer octaves sharp of 2/1
3) You did some personal experiments on a guitar and found you
preferred an octave of ~1207.5 cents
4) The closest match to this is Cell 615
5) You think that the cells are important because the third cell of
each group of three tends to be some just ratio like 3/2, 4/3, 5/4,
6/5, etc

Right?

-Mike

On Mon, Aug 8, 2011 at 8:48 PM, Mario Pizarro <piagui@...> wrote:
>
> Mike,
>
> As soon as I read that some members of the list disapprove the terms "true octave" that I had been using, I changed to "toctave", I needed to use a name related with octaves and at the same time gives the idea that it´s not the 2/1 octave. This change was done about 8 days ago.
>
> As respect to the response I sent to Gene Ward, I admit that part of it contains inapropriated words that probably came out for he uses to write short and polite scoffs on the toctave. Since he will read this message, I avail these lines to say that I am sure that this kind of response he won´t receive from me again. Some times he makes me remember a playful friend.
>
> Regarding the toctave and since you said that I didn´t respond your questions around the following:
>
> "Why Cell # 615 should be the stretched octave the humans apparently want to hear." , I hope you understand the following:
>
> Recently I informed you that I have done experiments on the guitar by a slight frequency raise of the 6th, 4th and 1st open strings,
> The result was a clear harmony improvement. The microphone/electronic counter (a very precise Gl counter) measured an average frequency raise of 1.00437 times respect to the 2 octave (Average ratio for the three strings). So 2*1.00437 = 2.00874 assumes the unavoidable error of harmony appreciation and not of the instrument since its exactness is far better fhan 1/50 of the frequency intervals showed by cells # 612 / # 613 / # 614 / # 615.
>
> Whereas Cell # 612 = 2 and Cell # 615 = 2.006787....we see that Cell # 615 is slightly lower than the measured 2.00874; since none of the Cells # 616 and # 617 is the third comma either in group MMJ or JMM and also their frequencies are much higher than 2.006787, I conclude that Cell # 615 is a good choice for a stretched octave.
>
> There is a great number of cases that are shown in my book where the third J comma of group
> MMJ and the third M comma of JMM share the same row of well known consonances like 3/2, 4/3, 5/4, 81/80, 256/243,
> 25/24, 27/25, 135/128, 16/15, 9/8, (9/8)^(n/2),.....etc or a triad frequencies llike 27/16 (E), 45/32, ....ETC
>
> I caused disgusts in tuning, from now and on I will only send messages provided they contain useful information. Most of the list are prepared to choice the stretched value for the octave.

🔗Steve Parker <steve@...>

🔗Mario Pizarro <piagui@...>

Mike,

Right!!! Right!!!!

I just completed 1 and a half pages of a table containing three coupled toctaves. If I place this table on this page you will received it garbled, so I will also send it to your personal email.

Thanks

Mario

August, 09
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Number Cell
of added Decimal cell frequencies THREE TOCTAVES
FIFTHS cells Cell # frequencies (Cents)
0 0 C 1.00000000000 0
K
696.09 52 52 C# 1.06066017178 101.955 .+ 600 = G = 701.955
P
701.955 49 101 D 1.12119522033 198.045 .+ 600 = Ab = 798.045
K
701.955 52 153 Eb 1.189207115 300 .+ 600 = A = 900 cents
K
701.955 52 205 E 1.26134462288 401.955 .+ 600 = Bb = 1001.955
K
701.955 52 257 F 1.33785800438 503.91 .+ 600 = B = 1103.91
K
701.955 52 309 F# 1.41901270074 605.865 .+ 600 = Toctave
P
701.955 49 358 G 1.5 701.955 . - 600 = C# = 101.955
P
701.955 49 407 Ab 1.58560948667 798.045 . - 600 = D = 198.045
K
701.955 52 459 A 1.68179283051 900 . - 600 = Eb = 300
K
701.955 52 511 Bb 1.78381067250 1001.955 . - 600 = E = 401.955
K
701.955 52 563 B 1.89201693432 1103.91 . - 600 = F = 503.91
K
701.955 52 615 & 2.00678700656 1205.865 . - 600 = F# = 605.865
Maj. 3d. K Toctave
401.955 52 667 &C# 2.1285190511 1307.82
P
407.820 49 716 &D 2.25 1403.91
K K =1.06066017178 =
401.955 52 768 &Eb 2.38648538649 1505.865
K (9/8)^(!/2)
396.09 52 820 &E 2.53125 1607.82
K
396.09 52 872 &F 2.68479605981 1709.775
K
396.090 52 924 &F# 2.84765625 1811.730
P P = 1.05707299111 =
401.955 49 973 &G 3.01018050983 1907.82
P (8/9)*2^(!/4)
407.82 49 1022 &Ab 3.18198051533 2003.91
K
407.82 52 1074 &A 3.375 2105.865
K
401.955 52 1126 &Bb 3.57972807974 2207.82
K
401.955 52 1178 &B 3.796875 2309.775
K
401.955 52 1230 &^2 4.02719408970 2411.73

K
52 1282 &^2 4.271484375 2513.685
P
49 1331 &^2 4.515270765 2609.775
K
52 1383 &^2 4.789167865 2711.73
K
52 1435 &^2 5.07967961 2813.685
K
52 1487 &^2 5.38781384809 2915.64
K
52 1539 &^2 5.714639562 3017.595
P
49 1588 &^2 6.040791135 3113.685
P
49 1637 &^2 6.385557153 3209.775
K
52 1689 &^2 6.772906147 3311.73
K
52 1741 &^2 7.183751797 3413.685
K
52 1793 &^2 7.619519416 3515.64
K
52 1845 &^3 8.081720772 3617.595

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Monday, August 08, 2011 11:24 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

Mario,

Would I be correct in stating your position?

Right?

-Mike

On Mon, Aug 8, 2011 at 8:48 PM, Mario Pizarro <piagui@...> wrote:
>
> Mike,
>
> As soon as I read that some members of the list disapprove the terms "true > octave" that I had been using, I changed to "toctave", I needed to use a > name related with octaves and at the same time gives the idea that itï¿½s > not the 2/1 octave. This change was done about 8 days ago.
>
> As respect to the response I sent to Gene Ward, I admit that part of it > contains inapropriated words that probably came out for he uses to write > short and polite scoffs on the toctave. Since he will read this message, I > avail these lines to say that I am sure that this kind of response he > wonï¿½t receive from me again. Some times he makes me remember a playful > friend.
>
> Regarding the toctave and since you said that I didnï¿½t respond your > questions around the following:
>
> "Why Cell # 615 should be the stretched octave the humans apparently want > to hear." , I hope you understand the following:
>
> Recently I informed you that I have done experiments on the guitar by a > slight frequency raise of the 6th, 4th and 1st open strings,
> The result was a clear harmony improvement. The microphone/electronic > counter (a very precise Gl counter) measured an average frequency raise of > 1.00437 times respect to the 2 octave (Average ratio for the three > strings). So 2*1.00437 = 2.00874 assumes the unavoidable error of harmony > appreciation and not of the instrument since its exactness is far better > fhan 1/50 of the frequency intervals showed by cells # 612 / # 613 / # 614 > / # 615.
>
> Whereas Cell # 612 = 2 and Cell # 615 = 2.006787....we see that Cell # 615 > is slightly lower than the measured 2.00874; since none of the Cells # 616 > and # 617 is the third comma either in group MMJ or JMM and also their > frequencies are much higher than 2.006787, I conclude that Cell # 615 is a > good choice for a stretched octave.
>
> There is a great number of cases that are shown in my book where the third > J comma of group
> MMJ and the third M comma of JMM share the same row of well known > consonances like 3/2, 4/3, 5/4, 81/80, 256/243,
> 25/24, 27/25, 135/128, 16/15, 9/8, (9/8)^(n/2),.....etc or a triad > frequencies llike 27/16 (E), 45/32, ....ETC
>
> I caused disgusts in tuning, from now and on I will only send messages > provided they contain useful information. Most of the list are prepared to > choice the stretched value for the octave.

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

🔗Mario Pizarro <piagui@...>

Mike,

Just to clarify point (5) given below, it is necessary to add ("xxx") just after the word "three".

<5) You think that the cells are important because the third cell of
<each group of three(xxxxxxx) tends to be some just ratio like 3/2, 4/3, 5/4,
<6/5, etc
----------------------------------------------------
<5) You think that the cells are important because the third cell of
<each group of three, "either MMJ or JMM which form MMJJMM", tends to be some just ratio like 3/2, 4/3, 5/4,
<6/5, etc

Mario

August, 09

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- > From: "Mike Battaglia" <battaglia01@...>
> To: <tuning@yahoogroups.com>
> Sent: Monday, August 08, 2011 11:24 PM
> Subject: Re: [tuning] Re: A new equal tempered scale?

Right?

-Mike

>
> Mario,
>
> Would I be correct in stating your position?
>
> 1) The "octave" harmonic for most strings is slightly sharp because of
> string inharmonicity
> 2) People have been shown to prefer octaves sharp of 2/1
> 3) You did some personal experiments on a guitar and found you
> preferred an octave of ~1207.5 cents
> 4) The closest match to this is Cell 615
> 5) You think that the cells are important because the third cell of
> each group of three tends to be some just ratio like 3/2, 4/3, 5/4,
> 6/5, etc
>
> Right?
>
> -Mike
>
> On Mon, Aug 8, 2011 at 8:48 PM, Mario Pizarro <piagui@...> wrote:
>>
>> Mike,
>>
>> As soon as I read that some members of the list disapprove the terms >> "true
>> octave" that I had been using, I changed to "toctave", I needed to use a
>> name related with octaves and at the same time gives the idea that itï¿½s
>> not the 2/1 octave. This change was done about 8 days ago.
>>
>> As respect to the response I sent to Gene Ward, I admit that part of it
>> contains inapropriated words that probably came out for he uses to write
>> short and polite scoffs on the toctave. Since he will read this message, >> I
>> avail these lines to say that I am sure that this kind of response he
>> wonï¿½t receive from me again. Some times he makes me remember a playful
>> friend.
>>
>> Regarding the toctave and since you said that I didnï¿½t respond your
>> questions around the following:
>>
>> "Why Cell # 615 should be the stretched octave the humans apparently want
>> to hear." , I hope you understand the following:
>>
>> Recently I informed you that I have done experiments on the guitar by a
>> slight frequency raise of the 6th, 4th and 1st open strings,
>> The result was a clear harmony improvement. The microphone/electronic
>> counter (a very precise Gl counter) measured an average frequency raise >> of
>> 1.00437 times respect to the 2 octave (Average ratio for the three
>> strings). So 2*1.00437 = 2.00874 assumes the unavoidable error of harmony
>> appreciation and not of the instrument since its exactness is far better
>> fhan 1/50 of the frequency intervals showed by cells # 612 / # 613 / # >> 614
>> / # 615.
>>
>> Whereas Cell # 612 = 2 and Cell # 615 = 2.006787....we see that Cell # >> 615
>> is slightly lower than the measured 2.00874; since none of the Cells # >> 616
>> and # 617 is the third comma either in group MMJ or JMM and also their
>> frequencies are much higher than 2.006787, I conclude that Cell # 615 is >> a
>> good choice for a stretched octave.
>>
>> There is a great number of cases that are shown in my book where the >> third
>> J comma of group
>> MMJ and the third M comma of JMM share the same row of well known
>> consonances like 3/2, 4/3, 5/4, 81/80, 256/243,
>> 25/24, 27/25, 135/128, 16/15, 9/8, (9/8)^(n/2),.....etc or a triad
>> frequencies llike 27/16 (E), 45/32, ....ETC
>>
>> I caused disgusts in tuning, from now and on I will only send messages
>> provided they contain useful information. Most of the list are prepared >> to
>> choice the stretched value for the octave.
>
>
> ------------------------------------
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>

🔗Mario Pizarro <piagui@...>

Gene,

I really donï¿½t understand why I dared to use the impertinent words written in my message. I have never did it, I am saying the truth; the worst part of it was that you do not deserve to be treated with those improper words. I hope you and I forget this incident.
Let me offer you my friendship.

Regards
Mario

August, 09
-----------------------------------------------------------
----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Monday, August 08, 2011 3:51 PM
Subject: [tuning] Re: A new equal tempered scale?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Granted, there's no convincing purely mathematical basis I have seen...but > if it really is true most listeners prefer a 6-cent-ish raised > octave...the general idea sounds OK to me.

Back when I was using TOP tunings involving much smaller octave stretching, I got some bitter complaints and was a little dubious about the extra shimmer myself, so I'm far from convinced most people want octaves stretched and less so than that they'd prefer it by so large an amount. The results on sine waves are not very meaningful unless you propose to use only sine waves for your music, which changes a lot more things than just octaves.

There are also three questions here: do people like octaves stretched, if so by how much, and do they like them stretched for 12edo? These are not the same, since stretching 12edo actually, on average, makes the consonance worse, not better.

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

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Aug 8, 2011 at 4:51 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> > Granted, there's no convincing purely mathematical basis I have seen...but if it really is true most listeners prefer a 6-cent-ish raised octave...the general idea sounds OK to me.
>
> Back when I was using TOP tunings involving much smaller octave stretching, I got some bitter complaints and was a little dubious about the extra shimmer myself, so I'm far from convinced most people want octaves stretched and less so than that they'd prefer it by so large an amount. The results on sine waves are not very meaningful unless you propose to use only sine waves for your music, which changes a lot more things than just octaves.

Unless you're using a timbre with stretched partials. If people like
octaves stretched with sine waves, it probably reflects that they like
their timbres stretched. That's not something I've ever heard tested
formally, but seems to be true for me. I dunno what the ideal stretch
would be, but I also notice I prefer fifths a little sharp (like in
17-equal) and major thirds a little sharp, etc. Then again, flat
intervals can be very relaxing.

> There are also three questions here: do people like octaves stretched, if so by how much, and do they like them stretched for 12edo? These are not the same, since stretching 12edo actually, on average, makes the consonance worse, not better.

It makes the consonance worse if we're assuming that the maximum
consonance point is exactly at 2/1, 3/2, 4/3, etc. If some property of
the auditory system causes everyone to like things a little bit sharp
of this, as they do with the octave, then we could always incorporate
a stretching factor into the equation.

Keep in mind that I'm taking this discussion a little bit more
low-level; I would not assume that you can just throw stretched JI
over a perfectly harmonic timbre, for instance, and have everything
instantly be better, because whatever harmonic property we seem to
prefer in stretched octaves would be overtaken by the additional
roughness we've just added. I'm more suggesting that the evolutionary
response in humans to millenia repeated exposure with harmonic timbres
could have been, for whatever reason, the perfect concordance point
being slightly sharp. No, there's no need to throw JI away, and I
doubt the difference would be too great to really matter, but no need
to rule it out, especially when we're seeing weird preferences for
stretched octaves in the literature.

For the record, I actually did like Mario's stretched-octave tuning a
lot. It made the chroma of each note somehow sound "brighter." As
always, not sure how my experience translates to anyone else's.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Graham Breed <gbreed@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Aug 10, 2011 at 5:09 AM, Graham Breed <gbreed@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Unless you're using a timbre with stretched partials. If
> > people like octaves stretched with sine waves, it
> > probably reflects that they like their timbres stretched.
> <snip>
>
> No, it means they hear bright timbres as having a higher
> pitch than sine waves, relative to the mathematically
> correct virtual pitch. Adding partials above the root
> does, subjectively, raise the pitch. The lower a note, the
> more noticeable the upper partials, and so the more a rich
> timbre makes it sound sharper. It's natural that our
> hearing's optimized for harmonic timbres of middling
> complexity, and so pure sine waves give stretched scales
> relative to them.

When you say "brightness," you mean literally brightness, as in the EQ
is set so that the highs are boosted? If so, I'm not understanding
your last point, because it seems like it should work in reverse. If
you're citing the Fletcher-Munson curve to claim that higher partials
will seem louder for identical timbres at lower pitches, and also
claiming that a timbre with loud upper partials leads to a subjective
raise in pitch, then that would imply that we hear octaves for complex
timbres as being flat, because the lower note will be sharper. So then
if that's the case, why should we prefer sharp octaves with sine
waves? It seems like we'd want them to be flat, or that we'd want to
sharpen the lower note to compensate for the lack of virtual
sharpening caused by the presence of upper partials.

> What timbre gives a perfect octave seems to depend on the
> individual. There is evidence for a tendency to stretch
> octaves in orchestral music, so maybe orchestral timbres
> tend to be on the pure side. You can also explain that by
> saying that we tend to like the melody to be a little sharp
> and the bass to be a little flat.

Could be, I haven't done much work on it. I've notice that I like
sharp octaves myself, and I've also noticed that whatever it is I tend
to like about sharp octaves I also tend to like with other sharp
dyads. I haven't done any real work to quantify the phenomenon or
really figure out what's going on beyond that. I notice that other
people on here have stated that they like sharp fifths as well, namely
Margo Schulter (and I believe George Secor) who like the fifth of
17-equal. Then again, I've come to also enjoy flat intervals as well
lately, like the 3/2 and 5/4 in 16-equal, so who knows.

-Mike

🔗Graham Breed <gbreed@...>

Mike Battaglia <battaglia01@...> wrote:

> When you say "brightness," you mean literally brightness,
> as in the EQ is set so that the highs are boosted? If so,
> I'm not understanding your last point, because it seems
> like it should work in reverse. If you're citing the
> Fletcher-Munson curve to claim that higher partials will
> seem louder for identical timbres at lower pitches, and
> also claiming that a timbre with loud upper partials
> leads to a subjective raise in pitch, then that would
> imply that we hear octaves for complex timbres as being
> flat, because the lower note will be sharper. So then if
> that's the case, why should we prefer sharp octaves with
> sine waves? It seems like we'd want them to be flat, or
> that we'd want to sharpen the lower note to compensate
> for the lack of virtual sharpening caused by the presence
> of upper partials.

By "brightness" I mean the total spectral content.

I didn't say anything about Fletcher-Munson curves. In
fact, I got the pitch shift effect wrong -- complex timbres
are heard as lower in pitch. Here's Terhardt's page on it:

http://www.mmk.ei.tum.de/persons/ter/top/pshifts.html

Graham

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> I have a few questions:

I have a spreadsheet with the complete sequence of 624 commas, but I am conscious that Mario has mentioned copyright so I can't post it.

> 1) Does the third entry in each cell sync up EXACTLY with a just
> ratio, or just close to a just ratio?
A: (there is only one entry per cell; I think you mean the entry in the last cell of a MMJ or a JMM sequence) it is exact when it is Just; however to my mind there are many of them that are not Just; and there are at least some Just ratios that are not in those particular cells. This is a point that I have intended to take up with Mario. Of course, it may be that the sequence I have is incorrect, but I am sure I got it from Mario.

> 2) Is the sequence just MMJ JMM MMJ JMM etc, forever, alternating?
A: No; remember that there is a third comma, U, and remember that I already revealed (tut) that the minimal repeating sequence is of 104 cells (not a multiple of 3).

> What is the sequence generating the cells?
Mario may tell you this!

> I wonder how to analyze what Mario's doing as a linear temperament,
> and if his progression of cells is MOS.
It can't be MOS, as there are three different intervals (or is there some extended definition of MOS I don't know)? Other than that, I don't really know how to analyse it - perhaps Gene could, if he had the sequence.

Mario, if you want to send the sequence to Mike, can I suggest you make use of my spreadsheet. The point is that, as far as I am aware, you have done all your work using decimals, which is OK but suffers from rounding error. My spreadsheet converts the letters M, J, U to powers of 2, 3 and 5, and then progressing through the cells can be done without rounding error - cell 612 is literally calculated as 2^1 * 3^0 * 5^0.

Steve M.

🔗Mario Pizarro <piagui@...>

Mike,

These years I trayed to find by myself the meaning of MOS. It seems to be a progression.

Mario

August, 10

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, August 09, 2011 11:10 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

>I have a few questions:
> 1) Does the third entry in each cell sync up EXACTLY with a just
> ratio, or just close to a just ratio?
> 2) Is the sequence just MMJ JMM MMJ JMM etc, forever, alternating?
> What is the sequence generating the cells?
>
> I wonder how to analyze what Mario's doing as a linear temperament,
> and if his progression of cells is MOS.
>
> -Mike
>
>
>
> On Tue, Aug 9, 2011 at 3:52 PM, Mario Pizarro <piagui@...> wrote:
>> Mike,
>>
>> Right!!! Right!!!!
>>
>> I just completed 1 and a half pages of a table containing three coupled
>> toctaves. If I place this table on this page you will received it >> garbled,
>> so I will also send it to your personal email.
>>
>> Thanks
>>
>> Mario
>>
>> August, 09
>
>
> ------------------------------------
>
> 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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>
>
>
>

🔗Mario Pizarro <piagui@...>

Mike,

--- (1) question is not clear to me. Iï¿½d better explain something around your question:

a) 52 is a cyclical set of cells that comprise 7 "S" identical groups of cells: S = MMJJMM = (6 Cells generators)

b) Each set of 52 cells presents the sequence S S S V S R S S S where you see the 7 "S" identical groups.

c) Three types of commas (M, J, U) generate 624 cells (the great set), the final cell # 624 equals (9/8)^6. Therefore the great set is constructed by the successive products of:

"[(cell m*comma a) = cell p], [(cell p*comma a ) = cell q], [(cell q*comma b) = cell r], [(cell r*comma b) = cell s]......

NOTICE THAT THE GENERATOR COMMAS a, b, work by pairs a, a, b, b, c, c, --- Letï¿½s see the first six cells produced by generators MMJJMM:

Cell # 0 ---------- 1

Cell # 1 ---------- (1 * M) = M = 1.00112915039 = (32805 / 32768) = (The preceding 1)*M
Cell # 2 ---------- ( M * M) = M^2 = 1.00225957576 = (18186 / 8145) = (The preceding M)*M
Cell # 3 ---------- (M^2)* J = MMJ = 1.00339350328 = (49083 / 40917)

Cell # 4 ---------- (MMJ)*J = MMJJ = 1.00452871369 = (36821 / 36655)

Cell # 5 ----------(MMJJ)*M = MMJJM = 1.00566297768 = (26993 / 26841)

Cell # 6 ----------(MMJJM)*M = MMJJMM = 1.00679852243 = (107662 / 106935)

The great set of 624 cells is formed by:

(SSSVSRSSS)(SSSVSRSSS)(SSSVSRSSS)(SSSVSRSSS)(SSSVSRSSS)(SSSVSRSSS)(SSSVSRSSS)......=
To the product of 12 sets (See item "b" above)

So the great set contains 52*12 = 624 cells. The products of the first 12 cells and the last 12 give the pythagorean comma.

Cell # 52 = (9/8)^(1/2) = 1.0606017178 = SSSVRSSS =

(MMJJMM)(MMJJMM)(MMJJMM) (MMJJUU) (MMJJ) (MMJJMM) (MMJJMM)(MMJJMM)(MMJJMM)= # 52
-----S---- -----S------ -----S----- -----V---- ---R---- -----S ---- ------S---- -----S----- -----S------
V = MMJJUU
R = MMJJ

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, August 09, 2011 11:10 PM
Subject: Re: [tuning] Re: A new equal tempered scale?

🔗Mario Pizarro <piagui@...>

Steve,

PLEASE FORGET ABOUT COPYRIGHT. I AUTHORIZE YOU AND ALSO AUTHORIZE TO ALL THE MEMBERS OF TUNING TO POST ANY INFORMATION AVAILABLE IN THE PROGRESSION. UNDER YOUR CRITERIA YOU MAY MENTION MY NAME (C. MARIO PIZARRO)
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 10, 2011 9:00 AM
Subject: [tuning] Re: A new equal tempered scale?

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> I have a few questions:
>
> I have a spreadsheet with the complete sequence of 624 commas, but I am > conscious that Mario has mentioned copyright so I can't post it.
>
>> 1) Does the third entry in each cell sync up EXACTLY with a just
>> ratio, or just close to a just ratio?
> A: (there is only one entry per cell; I think you mean the entry in the > last cell of a MMJ or a JMM sequence) it is exact when it is Just; however > to my mind there are many of them that are not Just; and there are at > least some Just ratios that are not in those particular cells. This is a > point that I have intended to take up with Mario. Of course, it may be > that the sequence I have is incorrect, but I am sure I got it from Mario.
>
>> 2) Is the sequence just MMJ JMM MMJ JMM etc, forever, alternating?
> A: No; remember that there is a third comma, U, and remember that I > already revealed (tut) that the minimal repeating sequence is of 104 cells > (not a multiple of 3).
>
>> What is the sequence generating the cells?
> Mario may tell you this!
>
>> I wonder how to analyze what Mario's doing as a linear temperament,
>> and if his progression of cells is MOS.
> It can't be MOS, as there are three different intervals (or is there some > extended definition of MOS I don't know)? Other than that, I don't really > know how to analyse it - perhaps Gene could, if he had the sequence.
>
> Mario, if you want to send the sequence to Mike, can I suggest you make > use of my spreadsheet. The point is that, as far as I am aware, you have > done all your work using decimals, which is OK but suffers from rounding > error. My spreadsheet converts the letters M, J, U to powers of 2, 3 and > 5, and then progressing through the cells can be done without rounding > error - cell 612 is literally calculated as 2^1 * 3^0 * 5^0.
>
> Steve M.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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🔗Mario Pizarro <piagui@...>

Steve,

YOU WROTE:

Steve M.

Steve,

You are correct. I guess you have the progression; if you donï¿½t have it, I can send it to you. Please inform.
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 10, 2011 9:00 AM
Subject: [tuning] Re: A new equal tempered scale?

🔗martinsj013 <martinsj@...>

🔗Mario Pizarro <piagui@...>

Steve,

I donï¿½t know what is going on with the progression. The first and second version of the progression contain the same information. The same M, J, U commas, the same cells. I have never practiced with spreadsheets; I just saw the converted progression with data appearing in different columns. Understanding = 0

You wrote that only 13 cells out of every 104 are different and none of these are just intervals. I had concluded that since J contains the 2^(1/4) factor; each four Jï¿½s the irrationality ends. Regarding U, since it contains 3^(1/2), its irrationality ends as soon as the two contiguous (UU) work. When developed the progression many years ago I didnï¿½t pay attention to these particularities otherwise I would have replaced MMJJMM*MMJJMM by MMMM*(JJJJ)*MMMM in order to eliminate the irrational comma J whereas schisma M is an exact decimal number.

Note that JJJJ = [(33554432)*2^1/4)/39858075] ^4 gives an exact decimal number. I cannot imagine the results of these replacements; tomorrow I will do that and see the results. I am very curious. Do you realize that these replacements might produce positive changes?. What do you think about.

Mario

August, 11
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, August 11, 2011 4:02 PM
Subject: [tuning] Re: A new equal tempered scale?

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> PLEASE FORGET ABOUT COPYRIGHT. I AUTHORIZE YOU AND ALSO AUTHORIZE TO ALL >> THE
>> MEMBERS OF TUNING TO POST ANY INFORMATION AVAILABLE IN THE PROGRESSION.
>
> 1) Mario has sent me the sequence; it has indeed changed since I first had > it. Here is my spreadsheet with the (new) sequence:
> /tuning/files/SteveMartin/Pizarro2.xls
>
> 2) I found my source for the (old) sequence; see:
> /tuning/topicId_88730.html#88952
>
> 3) only 13 cells out of every 104 are different; none of these are "just" > intervals as far as I can see.
>
> S.
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

🔗Mario <piagui@...>

Steve,

I didn´t read your message given below where you made a serious analysis of the progression. As regards point "2) Mario says that the system is derived using mathematical principles, but I am not sure what they are.",I suggest you to read a few pages of Chapter II of my book which I can send them to you. There you can see a detailed explanation of the comma J derivation since M interval is the skisma. I can prepare a file containing the mathematically derivations of J and U commas. Just give me your OK and I will send them.

Mario

September,06

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > ... What's MMJ JMM? What are the Cells? And wouldn't Cell 614 be flatter than an octave ...?
>
> As it's quiet here, I'll post my summary of what I've managed to glean about this (actually I wrote this about a year ago):
>
> --------------
> 1) In case it is not obvious, the 612 "cells" are simply 612 different notes, within the octave, relative to an origin or 1/1 note. To me, this is reminiscent of the Indian system, where 22 notes forming JI ratios with the origin are derived by the three different sruti sizes occurring in the right order. In Mario's case there are three much smaller "sruti" (M, J, U) and hence many more notes before the octave is reached. Note also that in the Indian system the sruti are formed of integer powers of 2, 3 and 5, but in Mario's system two of them contain fractional powers of 2 or 3.
>
> 2) Mario says that the system is derived using mathematical principles, but I am not sure what they are. However, we can see a number of features in the 612 note set. The 22 Indian notes are all there, and many more notes from the extended "5-limit JI lattice" formed by combining the 2:3 and the 4:5 interval in familiar ways. For example, the Pythagorean diatonic scale is found in cells: (0,) 104, 208, 254, 358, 462, 566, 612; and the JI syntonic scale in (0,) 104, 197, 254, 358, 451, 555, 612.
>
> 3) However, in between these "just" intervals there are other positions with fractional powers of 2 or 3. They "fill in" the gaps between the more "just" values. They include the cells 153, 306, 459, which together with 612 (=0) split the octave precisely into quarters, i.e. they form a diminished 7th chord in 12-tET. (NB the other cells that are multiples of 51 give very close approximations to 12-tET notes, but they are not exact.) This diminished chord is a feature in the first three Piagui scales.
>
> 4) The three sruti M, J, U are very similar in size, so overall this scheme is very similar to 612-EDO. However, whereas in 612-EDO the JI ratios are approximated, (e.g. 2^(197/612) approx 4:5; 2^(358/612) approx 2:3), in Mario's scheme they are exact (e.g cell 197 = 4:5; cell 358 = 2:3).
>
> 5) Because the division of the octave is unequal, this means that a constant number of sruti does not always equal the same interval - it depends where you start and end (just as in the Indian system). So we can say that often, but not always, 197sruti=4:5, 358sruti=2:3, 104sruti=8:9, 58sruti=2048:2187, 46sruti=243:256, 12sruti=Pythagorean comma, 11sruti=syntonic comma, 21sruti=diesis, 1sruti=schisma. More precisely, we can express any interval in terms of the number of M, J, U it contains, as a vector. For the intervals in this paragraph, the vectors are (121,68,8), (220,124,14), (64,36,4), (36,20,2), (28,16,2), (8,4,0), (7,4,0), (13,8,0), (1,0,0). This vector is precise for the interval, but may not be available at every point within the octave.
>
> 6) The smallest repeating pattern in the order of the srutis is that of the 8:9 interval, that consists of 104 srutis (64 M, 36 J, 4 U). The pattern is also symmetric. Therefore I suspect that Mario intends the pattern not to repeat after the octave (that is 612 sruti) but after 624 sruti, that is the interval (9/8)^6, a Pythagorean comma greater than one octave. This is supported by the fact that he says that he has a full set of 88 notes for a piano. OTOH it is slightly contradicted by the way he describes the sets of 12 notes in Piagui 1, 2, 3.
>
> --------------
>
> To answer your questions, MMJJMM is a sequence that occurs often within the full sequence; and cell 612 is the octave so 614 is still bigger. None of this means that I understand why 615 is special. In fact I'm still not sure exactly what Carrillo's result was - even if it is to do with harmonics themselves or with human perception ...
>
> Steve.
>

🔗Mario Pizarro <piagui@...>

Dear fellows,

Thank you Steve for using your spreadsheet and filing the converted progression in your folder.
Perhaps the following information is useful to you. The first one is the compacted progression of cells and the second shows how those terms are ordained along the first 52 cells. "PC" means "pythagorean comma".

1) ((U^24)*(81/80)^48)*(PC)^6)

2).......... 1

............. (81/80)

............. # 11 = 1.0125

............. (81/80)

............. # 22 = 1.02515625

............ U

........... U

........... (81/80)

...........# 35 = 1.04049179494

.......... (81/80)

.......... # 46 = (256/243)

.......... (PC)^(1/2) = (1.01364326477)^(1/2) = MMJJMM

......... # 52 = 1.06066017178 = (9/8)^(1/2)
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Each set of 52 cells comply with the following comma sequence generating the cells (Mike):

MMJJMM MMJJMM MMJJMM MMJJUU MMJJMM MMJJ MMJJMM MMJJMM MMJJMM

M = SCKISMA = (32805/32768) = 1.001129150390625

J = COMMA = ((33554432*2^(1/4) / 39858075) = 1.0011313711...

U = COMMA = ((102400*3^(1/2) / 177147) = 1.0012136965066...
-----------------------------

> It can't be MOS, as there are three different intervals (or is there some > extended definition of MOS I don't know)? Other than that, I don't really > know how to analyse it - perhaps Gene could, if he had the sequence.

Mario

September, 10

----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, August 10, 2011 9:00 AM
Subject: [tuning] Re: A new equal tempered scale?