TASK ACCOMPLISHED

To the tuning list,

I had promised you that the progression abstract would be ready in about two days and the purpose was achieved. I sent to tuning enough information on this subject a few hours ago.

I would thank you if you could tell me if the information is clear since it required many simple mathematical reasoning.

Mario

I don't think you posted it here - I only got your messages in my inbox.

Would you like me to upload them to the files section on the list so
everyone can see them?

Also, I feel like some information is missing - the progression of
cells goes from 104 to 417.

Also, do you know if your progression of cells tempers out any useful commas?

-Mike

On Fri, Mar 30, 2012 at 6:34 PM, Mario Pizarro <piagui@...> wrote:
> To the tuning list,
>
> I had promised you that the progression abstract would be ready in about two
> days and the purpose was achieved. I sent to tuning enough information on
> this subject a few hours ago.
>
> I would thank you if you could tell me if the information is clear since it
> required many simple mathematical reasoning.
>
> Mario

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Also, do you know if your progression of cells tempers out any useful commas?

I analyzed a previous version some time back, but Mario didn't buy it. It seemed to me that there was a basis change for the 5-limit lurking in the background.

Gene,

I am using the progression as a source of consonant tones, similar actions, you can find there an alternate 12 EDO, it served too in the K and P semtone calculation to mathematically get the three Piagui scales. Useful commas to sharpen the values of consonant tones are J/M and other applications. Should you dig in its features you get interesting properties like I found in conection with the ability of each cell to have "family" in the progression provided it is multiplied by (3/2) or (4/3) since in all cases the results correspond to other cells with exactness.
Another detail is that as soon you take one cell to start an investigation, automatically, a red of cells appear linked to your project, that is what it seems to me.

About Mike question, since M, J, U, (J/M = 1.00000221821), and other commas work within the M range along the whole progression there is a profuse number of additional cells which stay potentially in hundreds of M links just in one cycle of 624 cells. The following subcommas I was talking about:

III. 4 NEW COMMAS

The J and U commas were deduced in Chapter II.

J = [(33'554,432) 21/4 / 39'858,075] = 1.00113137110297

U = [(102,400) 31/2 / 177,147] = 1.00121369650659

The above commas, termed Piagui commas, can also be detected by ear, since they are slightly greater than M.

If we multiply any cell by M or J or U, the products are still consonant magnitudes whether or not the results are progression cells. For instance, if Cell No. 484 is multiplied by U we get 31/2 =1.732050807.

The square root of 3 is also another consonant frequency since it is obtained by multiplying a cell by the consonant comma U, its value 1.7320508094 lying between cells Nos. 485 and 486. This seems to show that other consonant frequencies work within the range of the basic comma M. If so, they might be functions of M, J and U.

In fact, Cell No. 484 = M298 J168 U18, therefore:

(M298 J168 U18) (U) = (M298 J168 U19) = [ (M299 J168 U18) (U/M) ] =

(Cell No. 485) (U/M) = 31/2 = 1.7320508094.

The above result indicates that a relative U/M factor works within the range of the M comma linking cells Nos. 485 and 486 and can be split by ratios J/M and U/J. M1/2 is another consonant frequency, and together with J/M and U/J establishes a first group of frequencies that lie in the mentioned range, as shown in the following pages.

As (51/2 / 2) = 1.11803398875, it might work between cells Nos. 98 and 99. Let us calculate the ratio between 51/2/2 and cell No. 98. Since cell No. 98 is equal to 1.11740330854, we have:

(51/2 / 2) / (Cell No. 98) = 1.00056441591 = M1/2, so

(51/2 / 2) = (Cell No. 98) M1/2

Therefore, 51/2 is a consonant frequency with respect to note C.

Similar calculations show that 61/2/2 falls between Cells Nos. 179 and 180. So, 61/2 is another consonant value.

The possibility that 71/2/2 might be a consonant figure between Cells Nos. 247 and 248 was studied. However, no relation with M, J or U was found.

Figures 81/2, 91/2, 101/2, 121/2... are also consonant values with respect to note C since 81/2 = (2 x 21/2), 91/2 = (1.5 x 2) and so forth. Consequently, 7, 11, 13, 14, 17, 19... as well as 71/2, 111/2, 131/2, 141/2, 171/2... are excluded from the theoretical infinite set of consonant frequencies, all of them being non-musical figures.

The square root of 3 can be settled in terms of the Zarlino commas, notes of the Pythagorean and Just Intonation scales, as well as the Piagui comma U. Let us see:

ZC = Zarlino comma = (81/80) = 1.0125

ZS = Zarlino semitone = (16/15) = 1.0666666...

D = Pythagorean and Just Intonation note D = (9/8) = 1.125 EAZ EAZ = Note E of the Aristoxenus-Zarlino scale = (5/4) = 1.25

U = The Piagui comma

Consequently, the square root of 3 can be given in terms of these musical terms: 31/2 = (ZC)2 (ZS) D2 EAZ U = 1.7320508094

The above identity is also given by:

31/2 = (Cell No. 485) (U/M) = (M299 J168 U18) (U/M) = (M298 J168 U19)

Electrical variables, particularly, are involved with frequency notes and the Piagui comma U.

If a balanced three-phase voltage with amplitude Vm is fed to a balanced three-phase resistive load, the current amplitude of each phase is Im. Since electrical power is equal to 31/2 (Vm Im / 2), then, it can be given in terms of musical parameters including the U comma:

Electrical Power = (ZC)2 (ZS) D2 EAZ U (VmI m / 2) watts

By oscilloscope inspection, we see that variations over time of instantaneous voltage, current and power draw periodic and aesthetic waves, provided that the three-phase voltage and the three-phase resistive load are balanced. Commas M, J and U are involved with the periodic shapes of sinusoids and power displays. As soon as distortion of the three-phase voltage source appears, the wave shapes of v(t), i(t), w(t) become irregular and stop being the exclusive functions of the commas and Vm , Im , since the aesthetic displays have gone.

The square root of 3 does not appear in the progression. An analysis is required of the empty space between cells Nos. 485 and 486 controlled by M in order to find not only the relative frequencies that might work within both cells, but also those comprised in the remaining M commas throughout the progression. The result of the search reveals that commas M, J and U take part of this apparently empty space.

It is not surprising that 'M, J and U's accuracy in revealing the set of 624 cells, a profuse set that provides us with knowledge of music's accurate links involved within the octave, but they also have the ability to detect the relative frequencies comprised by M. Cell No. 485C is the symmetry center of cells Nos. 485 and 486, as shown by the following table.

CELL MICRO-INTERVAL RELATIVE FREQUENCY

? ??

485 1 1.73190454693

485A J/M = 1.00000221822 J/M 1.73190838865

485B U/J = 1.00008223237 U/M (3)1/2 = 1.73205080757

485C (M3/2/U) = 1.00047992462 M1/2 1.73288206142

486 M1/2 = 1.00056441591 M 1.73386012761

CELL No. 485 A = (CELL No. 485) (J/M)

CELL No. 485 B = (CELL No. 485A) (U/J)

CELL No. 485 C = (CELL No. 485B) (M3/2/U)

CELL No. 486 = (CELL No. 485C) (M1/2)

? With respect to cell No. 485 ?? With respect to C = 1

J/M and U/J are much lower than M, so their consonance ratios cannot be distinguished by ear, and the product (J/M) (U/J) gives (U/M) = 1.0000844576. If we multiply this value by cell No. 485, the square root of 3 is obtained again. Likewise, the same group of micro-intervals works within any M comma in the progression.

There are two sorts of numbers; the first one is given by the non-musical figures 7, 11, 13, 14, 17, 19, 21, 23, 28, 29, 31... and 71/2, 111/2, 131/2, 141/2... The second one, by 1, 2, 3, 4, 5, 6, 8, 9... and 21/2, 31/2, 41/2, 51/2, 61/2, 81/2, 91/2... The latter two groups of figures are exclusive functions of M, J and U as explained in the following sentences and consequently, they are involved with music.

2 = Cell No. 612 = M376 J212 U24

3 = 2 x 1.5 = M596 J336 U38

4 = (M376 J212 U24)2

5 = 2 2 x 1.25 = M873 J492 U56

6 = M972 J548 U62

8 = M1128 J636 U72 and so on.

Let us take the square roots:

21/2 = M188 J106 U12

31/2 = M298 J168 U19

41/2 = M376 J212 U24 = 2

51/2 = M436.5 J246 U28

61/2 = M486 J274 U31

81/2 = M564 J318 U36 and so on.

The 3rd, 5th, 7th, 11th... overtones of two consonant tones decrease the consonance quality but, on the other hand, give the tone timbre. It is no just a coincidence that no cell, when multiplied by 2n, will result in one of the non-musical numbers 7, 11, 13, 14, 17 and so forh.

Values 31/2 and 51/2 were given in terms of M, J and U, with interesting results. Now after the detection of N = fi (M, J, U) and N1/2 = f 'i (M, J, U), where N is any of the series of numbers except non-musical ones, we realize that there are clear links between the number series, their square roots and music.

Analogously, if N1 = (Cell No. 98) = [(26 x 21/2) / 34] = 1.11740330855, then Cell No. 306 of the third segment is equal to
(26 x 21/2 / 34) (9/8)2 = 21/2, i.e. note F# of the tempered intonation, which might also be F# of the new musical octave.

Another peculiar result is that values 21/4, 21/2, 23/4, which are the tempered frequencies of notes Eb, F# and A, are progression cells whose values are accurately defined by the three Piagui commas.

Due to the features of the Natural Progression of Musical Cells, it can be seen that it is not a common set of simple figures. Its origins are based on unquestionable scientific parameters that generate jointed relative frequencies for establishing a new dodecatonic musical scale, in order to escape the discords that audiences have endured since 1722.

Zarlino settled three commas: (81/80) = 1.0125 = Cell No. 11.

(128 / 125) = 1.024 = Cell No. 21.

The third Zarlino Comma that is equal to (648 / 625) = 1.0368 is not a progression cell. It must be given only in M, J, U terms.

According to the foregoing table, U/J and (U/J)2 are consonant micro-intervals. Therefore, [(Cell No. 32) / (U/J)2] = (M20 J12) = (648/625) = 1.0368 = Zarlino comma is also consonant with respect to note C.

We could establish a group of very small intervals and relative frequencies comprised by M, which rule those contained in any of the progression's remaining M commas.

TABLE IX A - INTERVALS COMPRISED BY THE M COMMA

CELL COMMA R E L A T I V E F R E Q U E N C Y

No. RELATIONS -------------- ? -------------- 485 1 1.73190454693

485A (J/M)1/2 (J/M)1/2 = 1.0000011091 1.73190646779

485B (J/M)1/2 (J/M) = 1.00000221821 1.73190838865

485C (U/J)1/2 (J1/2U2/M) = 1.00004333364 1.73197959666

485D (U/J)1/2 (U/M) = 1.00008445076 1.73205080757

485E (M1/2U1/2/J) (U3/2/M1/2J) = 1.00012446033 1.73212010034

485F (M1/2U1/2/J) (U2/J2) = 1.00016447149 1.73218939583

485G (M1/4J/U) (M1/4U/J) = 1.00036442371 1.73253569401

485H (M1/4J/U) (M)1/2 = 1.00056441591 1.73288206146

485J (M1/4J/U) (M3/4J/U) = 1.00076444808 1.73322849804

485K (M1/4J/U) (MJ2/U2) = 1.00096452026 1.73357500393

485L (M1/2U1/2/J) (M3/2J/U3/2) = 1.00100456505 1.73364435771

485M (M1/2U1/2/J) (M2/U) = 1.00104461144 1.73371371416

485N (U/J)1/2 (M2/J1/2U1/2)= 1.0010857697 1.73378499641

485P (U/J)1/2 (M2/J) = 1.00112692969 1.73385628154

485Q (J/M)1/2 (M3/2J1/2) = 1.00112804004 1.7338582046

486 (J/M)1/2 M = 1.00112915039 1.73386012761

? With respect to cell number 485

The reader will notice that relative frequency 1.00096452026 with respect to cell number 485 also leads to the third Zarlino comma (1.0368) if it is multiplied by Cell number 31.

One of the powers of progression is based on cell symmetry centers SC1, SC2, SC3, etc. such as [(9/8) (9/8)2]1/2. By applying this power to the M comma that links Cells Nos. 485 and 486, and using mathematical reasoning, we obtain the values given in Table IX-A. This table does not invalidate the foregoing values of 485A, 485B and 485C. As stated, there are a great many consonant routes that may be defined by M, J, and U commas. However, among these innumerable routes, the Natural Progression of Musical Cells is the only one that will determine the true octave of an eminently good musical scale.

We have detailed some of the powers of the Natural Progression of Musical Cells. However, its crucial power emerges when it is taken as a whole set, from which a small group of consecutive cells is used as auxiliary information to solve two equations with four unknowns, as explained in the following chapter. Elementary mathematics states that solving this set of equations requires two additional equations or some other associated and valid source of information like the Natural Progression. This remarkable power leads to the object of this work.

In fact, two semitone factors K and P, which will replace the T Tempered factor, are deduced in the following chapter. The unobjectionable mathematical reasoning was essential to attain their proper values and further on the perfecting of harmony.

PLEASE SEE BELOW

<<<<<<<<<<<<<<<<<<<<<<

----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Friday, March 30, 2012 11:18 PM
Subject: [tuning] Re: TASK ACCOMPLISHED

>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>> Also, do you know if your progression of cells tempers out any useful >> commas?
>
> I analyzed a previous version some time back, but Mario didn't buy it. It > seemed to me that there was a basis change for the 5-limit lurking in the > background.
>
MIKE, GENE. THE TRUTH IS THAT THE LAST TIME I USED A SPREADSHEET WAS IN 1957. I DON�T GET "5-LIMIT LURKING IN THE BACKGROUND"

BY BY

MARIO

MARCH, 31

>
>
> ------------------------------------
>
> 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, I am very confused. Is what you posted below the "abstract", or is it something different?

Keenan

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Gene,
>
> I am using the progression as a source of consonant tones, similar actions,
> you can find there an alternate 12 EDO, it served too in the K and P semtone
> calculation to mathematically get the three Piagui scales. Useful commas to
> sharpen the values of consonant tones are J/M and other applications. Should
> you dig in its features you get interesting properties like I found in
> conection with the ability of each cell to have "family" in the progression
> provided it is multiplied by (3/2) or (4/3) since in all cases the results
> correspond to other cells with exactness.
> Another detail is that as soon you take one cell to start an investigation,
> automatically, a red of cells appear linked to your project, that is what it
> seems to me.
>
> About Mike question, since M, J, U, (J/M = 1.00000221821), and other commas
> work within the M range along the whole progression there is a profuse
> number of additional cells which stay potentially in hundreds of M links
> just in one cycle of 624 cells. The following subcommas I was talking about:
>
> III. 4 NEW COMMAS
>
> The J and U commas were deduced in Chapter II.
>
> J = [(33'554,432) 21/4 / 39'858,075] = 1.00113137110297
>
> U = [(102,400) 31/2 / 177,147] = 1.00121369650659
>
> The above commas, termed Piagui commas, can also be detected by ear, since
> they are slightly greater than M.
>
> If we multiply any cell by M or J or U, the products are still consonant
> magnitudes whether or not the results are progression cells. For instance,
> if Cell No. 484 is multiplied by U we get 31/2 =1.732050807.
>
> The square root of 3 is also another consonant frequency since it is
> obtained by multiplying a cell by the consonant comma U, its value
> 1.7320508094 lying between cells Nos. 485 and 486. This seems to show that
> other consonant frequencies work within the range of the basic comma M. If
> so, they might be functions of M, J and U.
>
> In fact, Cell No. 484 = M298 J168 U18, therefore:
>
> (M298 J168 U18) (U) = (M298 J168 U19) = [ (M299 J168 U18) (U/M) ] =
>
> (Cell No. 485) (U/M) = 31/2 = 1.7320508094.
>
> The above result indicates that a relative U/M factor works within the range
> of the M comma linking cells Nos. 485 and 486 and can be split by ratios J/M
> and U/J. M1/2 is another consonant frequency, and together with J/M and U/J
> establishes a first group of frequencies that lie in the mentioned range, as
> shown in the following pages.
>
> As (51/2 / 2) = 1.11803398875, it might work between cells Nos. 98 and 99.
> Let us calculate the ratio between 51/2/2 and cell No. 98. Since cell No.
> 98 is equal to 1.11740330854, we have:
>
> (51/2 / 2) / (Cell No. 98) = 1.00056441591 = M1/2, so
>
> (51/2 / 2) = (Cell No. 98) M1/2
>
> Therefore, 51/2 is a consonant frequency with respect to note C.
>
> Similar calculations show that 61/2/2 falls between Cells Nos. 179 and 180.
> So, 61/2 is another consonant value.
>
> The possibility that 71/2/2 might be a consonant figure between Cells Nos.
> 247 and 248 was studied. However, no relation with M, J or U was found.
>
> Figures 81/2, 91/2, 101/2, 121/2... are also consonant values with respect
> to note C since 81/2 = (2 x 21/2), 91/2 = (1.5 x 2) and so forth.
> Consequently, 7, 11, 13, 14, 17, 19... as well as 71/2, 111/2, 131/2, 141/2,
> 171/2... are excluded from the theoretical infinite set of consonant
> frequencies, all of them being non-musical figures.
>
> The square root of 3 can be settled in terms of the Zarlino commas, notes of
> the Pythagorean and Just Intonation scales, as well as the Piagui comma U.
> Let us see:
>
> ZC = Zarlino comma = (81/80) = 1.0125
>
> ZS = Zarlino semitone = (16/15) = 1.0666666...
>
> D = Pythagorean and Just Intonation note D = (9/8) = 1.125 EAZ EAZ
> = Note E of the Aristoxenus-Zarlino scale = (5/4) = 1.25
>
> U = The Piagui comma
>
> Consequently, the square root of 3 can be given in terms of these musical
> terms: 31/2 = (ZC)2 (ZS) D2 EAZ U = 1.7320508094
>
> The above identity is also given by:
>
> 31/2 = (Cell No. 485) (U/M) = (M299 J168 U18) (U/M) = (M298 J168 U19)
>
> Electrical variables, particularly, are involved with frequency notes and
> the Piagui comma U.
>
> If a balanced three-phase voltage with amplitude Vm is fed to a balanced
> three-phase resistive load, the current amplitude of each phase is Im.
> Since electrical power is equal to 31/2 (Vm Im / 2), then, it can be given
> in terms of musical parameters including the U comma:
>
> Electrical Power = (ZC)2 (ZS) D2 EAZ U (VmI m / 2) watts
>
> By oscilloscope inspection, we see that variations over time of
> instantaneous voltage, current and power draw periodic and aesthetic waves,
> provided that the three-phase voltage and the three-phase resistive load are
> balanced. Commas M, J and U are involved with the periodic shapes of
> sinusoids and power displays. As soon as distortion of the three-phase
> voltage source appears, the wave shapes of v(t), i(t), w(t) become irregular
> and stop being the exclusive functions of the commas and Vm , Im , since the
> aesthetic displays have gone.
>
> The square root of 3 does not appear in the progression. An analysis is
> required of the empty space between cells Nos. 485 and 486 controlled by M
> in order to find not only the relative frequencies that might work within
> both cells, but also those comprised in the remaining M commas throughout
> the progression. The result of the search reveals that commas M, J and U
> take part of this apparently empty space.
>
> It is not surprising that 'M, J and U's accuracy in revealing the set of 624
> cells, a profuse set that provides us with knowledge of music's accurate
> links involved within the octave, but they also have the ability to detect
> the relative frequencies comprised by M. Cell No. 485C is the symmetry
> center of cells Nos. 485 and 486, as shown by the following table.
>
> CELL MICRO-INTERVAL RELATIVE FREQUENCY
>
> ?
> ??
>
> 485 1
> 1.73190454693
>
> 485A J/M = 1.00000221822 J/M
> 1.73190838865
>
> 485B U/J = 1.00008223237 U/M (3)1/2 = 1.73205080757
>
> 485C (M3/2/U) = 1.00047992462 M1/2
> 1.73288206142
>
> 486 M1/2 = 1.00056441591 M
> 1.73386012761
>
> CELL No. 485 A = (CELL No. 485) (J/M)
>
> CELL No. 485 B = (CELL No. 485A) (U/J)
>
> CELL No. 485 C = (CELL No. 485B) (M3/2/U)
>
> CELL No. 486 = (CELL No. 485C) (M1/2)
>
> ? With respect to cell No. 485 ?? With respect to C = 1
>
>
>
> J/M and U/J are much lower than M, so their consonance ratios cannot be
> distinguished by ear, and the product (J/M) (U/J) gives (U/M) =
> 1.0000844576. If we multiply this value by cell No. 485, the square root of
> 3 is obtained again. Likewise, the same group of micro-intervals works
> within any M comma in the progression.
>
> There are two sorts of numbers; the first one is given by the non-musical
> figures 7, 11, 13, 14, 17, 19, 21, 23, 28, 29, 31... and 71/2, 111/2, 131/2,
> 141/2... The second one, by 1, 2, 3, 4, 5, 6, 8, 9... and 21/2, 31/2, 41/2,
> 51/2, 61/2, 81/2, 91/2... The latter two groups of figures are exclusive
> functions of M, J and U as explained in the following sentences and
> consequently, they are involved with music.
>
>
>
> 2 = Cell No. 612 = M376 J212 U24
>
> 3 = 2 x 1.5 = M596 J336 U38
>
> 4 = (M376 J212 U24)2
>
> 5 = 2 2 x 1.25 = M873 J492 U56
>
> 6 = M972 J548 U62
>
> 8 = M1128 J636 U72 and so on.
>
> Let us take the square roots:
>
> 21/2 = M188 J106 U12
>
> 31/2 = M298 J168 U19
>
> 41/2 = M376 J212 U24 = 2
>
> 51/2 = M436.5 J246 U28
>
> 61/2 = M486 J274 U31
>
> 81/2 = M564 J318 U36 and so on.
>
>
>
> The 3rd, 5th, 7th, 11th... overtones of two consonant tones decrease the
> consonance quality but, on the other hand, give the tone timbre. It is no
> just a coincidence that no cell, when multiplied by 2n, will result in one
> of the non-musical numbers 7, 11, 13, 14, 17 and so forh.
>
> Values 31/2 and 51/2 were given in terms of M, J and U, with interesting
> results. Now after the detection of N = fi (M, J, U) and N1/2 = f 'i (M,
> J, U), where N is any of the series of numbers except non-musical ones, we
> realize that there are clear links between the number series, their square
> roots and music.
>
> Analogously, if N1 = (Cell No. 98) = [(26 x 21/2) / 34] = 1.11740330855,
> then Cell No. 306 of the third segment is equal to
> (26 x 21/2 / 34) (9/8)2 = 21/2, i.e. note F# of the tempered intonation,
> which might also be F# of the new musical octave.
>
> Another peculiar result is that values 21/4, 21/2, 23/4, which are the
> tempered frequencies of notes Eb, F# and A, are progression cells whose
> values are accurately defined by the three Piagui commas.
>
> Due to the features of the Natural Progression of Musical Cells, it can be
> seen that it is not a common set of simple figures. Its origins are based
> on unquestionable scientific parameters that generate jointed relative
> frequencies for establishing a new dodecatonic musical scale, in order to
> escape the discords that audiences have endured since 1722.
>
> Zarlino settled three commas: (81/80) = 1.0125 = Cell No. 11.
>
> (128 / 125) = 1.024 = Cell No.
> 21.
>
> The third Zarlino Comma that is equal to (648 / 625) = 1.0368 is not a
> progression cell. It must be given only in M, J, U terms.
>
> According to the foregoing table, U/J and (U/J)2 are consonant
> micro-intervals. Therefore, [(Cell No. 32) / (U/J)2] = (M20 J12) =
> (648/625) = 1.0368 = Zarlino comma is also consonant with respect to note C.
>
> We could establish a group of very small intervals and relative frequencies
> comprised by M, which rule those contained in any of the progression's
> remaining M commas.
>
> TABLE IX A - INTERVALS COMPRISED BY THE M COMMA
>
> CELL COMMA R E L A T I V E F R E Q U E N C Y
>
> No. RELATIONS -------------- ? --------------
>
> 485
> 1 1.73190454693
>
> 485A (J/M)1/2 (J/M)1/2 = 1.0000011091 1.73190646779
>
> 485B (J/M)1/2 (J/M) = 1.00000221821 1.73190838865
>
> 485C (U/J)1/2 (J1/2U2/M) = 1.00004333364 1.73197959666
>
> 485D (U/J)1/2 (U/M) = 1.00008445076 1.73205080757
>
> 485E (M1/2U1/2/J) (U3/2/M1/2J) = 1.00012446033 1.73212010034
>
> 485F (M1/2U1/2/J) (U2/J2) = 1.00016447149 1.73218939583
>
> 485G (M1/4J/U) (M1/4U/J) = 1.00036442371 1.73253569401
>
> 485H (M1/4J/U) (M)1/2 = 1.00056441591 1.73288206146
>
> 485J (M1/4J/U) (M3/4J/U) = 1.00076444808 1.73322849804
>
> 485K (M1/4J/U) (MJ2/U2) = 1.00096452026 1.73357500393
>
> 485L (M1/2U1/2/J) (M3/2J/U3/2) = 1.00100456505 1.73364435771
>
> 485M (M1/2U1/2/J) (M2/U) = 1.00104461144 1.73371371416
>
> 485N (U/J)1/2 (M2/J1/2U1/2)= 1.0010857697 1.73378499641
>
> 485P (U/J)1/2 (M2/J) = 1.00112692969 1.73385628154
>
> 485Q (J/M)1/2 (M3/2J1/2) = 1.00112804004 1.7338582046
>
> 486 (J/M)1/2 M = 1.00112915039
> 1.73386012761
>
>
>
> ? With respect to cell number 485
>
> The reader will notice that relative frequency 1.00096452026 with
> respect to cell number 485 also leads to the third Zarlino comma (1.0368) if
> it is multiplied by Cell number 31.
>
> One of the powers of progression is based on cell symmetry centers SC1, SC2,
> SC3, etc. such as [(9/8) (9/8)2]1/2. By applying this power to the M comma
> that links Cells Nos. 485 and 486, and using mathematical reasoning, we
> obtain the values given in Table IX-A. This table does not invalidate the
> foregoing values of 485A, 485B and 485C. As stated, there are a great many
> consonant routes that may be defined by M, J, and U commas. However, among
> these innumerable routes, the Natural Progression of Musical Cells is the
> only one that will determine the true octave of an eminently good musical
> scale.
>
> We have detailed some of the powers of the Natural Progression of
> Musical Cells. However, its crucial power emerges when it is taken as a
> whole set, from which a small group of consecutive cells is used as
> auxiliary information to solve two equations with four unknowns, as
> explained in the following chapter. Elementary mathematics states that
> solving this set of equations requires two additional equations or some
> other associated and valid source of information like the Natural
> Progression. This remarkable power leads to the object of this work.
>
> In fact, two semitone factors K and P, which will replace the T Tempered
> factor, are deduced in the following chapter. The unobjectionable
> mathematical reasoning was essential to attain their proper values and
> further on the perfecting of harmony.
>
> PLEASE SEE BELOW
>
> <<<<<<<<<<<<<<<<<<<<<<
>
> ----- Original Message -----
> From: "genewardsmith" <genewardsmith@...>
> To: <tuning@yahoogroups.com>
> Sent: Friday, March 30, 2012 11:18 PM
> Subject: [tuning] Re: TASK ACCOMPLISHED
>
>
> >
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> >> Also, do you know if your progression of cells tempers out any useful
> >> commas?
> >
> > I analyzed a previous version some time back, but Mario didn't buy it. It
> > seemed to me that there was a basis change for the 5-limit lurking in the
> > background.
> >
> MIKE, GENE. THE TRUTH IS THAT THE LAST TIME I USED A SPREADSHEET WAS IN
> 1957. I DON´T GET "5-LIMIT LURKING IN THE BACKGROUND"
>
> BY BY
>
> MARIO
>
> MARCH, 31
>
>
>
> >
> >
> > ------------------------------------
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> >
> >
> >
> >
>

On Sat, Mar 31, 2012 at 12:18 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Also, do you know if your progression of cells tempers out any useful
> > commas?
>
> I analyzed a previous version some time back, but Mario didn't buy it. It
> seemed to me that there was a basis change for the 5-limit lurking in the
> background.

I thought it might be a basis shift, but he has his "J" and "U" commas
set to the square roots of other JI commas. Maybe it's a basis change
for some contorted form of JI.

-Mike

On Sat, Mar 31, 2012 at 10:31 AM, Mario Pizarro <piagui@...> wrote:
>
> About Mike question, since M, J, U, (J/M = 1.00000221821), and other commas
> work within the M range along the whole progression there is a profuse
> number of additional cells which stay potentially in hundreds of M links
> just in one cycle of 624 cells. The following subcommas I was talking about:

Mario, do you know if your progression of cells rounds any JI
intervals off as being "approximately" equal to one another (i.e. in
the same cell)?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I thought it might be a basis shift, but he has his "J" and "U" commas
> set to the square roots of other JI commas. Maybe it's a basis change
> for some contorted form of JI.

That's why I said it was in the background--he uses fractional monzos, but I thought you could get rid of them.

Keenan

It is not the "abstract". Four pages containing explanations on how I derived the M, J, U "comma-factors" that generate all the cells plus three pages of the progression make the abstract. The abstract was already sent to Mike to whom I've asked that the four mentioned pages be filed to serve as general information and a complete set of the progression given in 7 pages will be sent this week for beeing filed.

When I was writing my answer to you I got confused for I thought I were writing to Mike who had said that:

> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> >> Also, do you know if your progression of cells tempers out any useful
> >> commas?
> >
<<<<<<<<<<<<<<<<<<<<<<<<

Since my response to his question, not so clear to me, required to go back to my zero y prefered to copy a part of my book where consonance is discussed so he could probably find there the needed response.

Mario
March 31

----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 11:28 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

Mario, I am very confused. Is what you posted below the "abstract", or is it something different?

Keenan

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Gene,
>
> I am using the progression as a source of consonant tones, similar > actions,
> you can find there an alternate 12 EDO, it served too in the K and P > semtone
> calculation to mathematically get the three Piagui scales. Useful commas > to
> sharpen the values of consonant tones are J/M and other applications. > Should
> you dig in its features you get interesting properties like I found in
> conection with the ability of each cell to have "family" in the > progression
> provided it is multiplied by (3/2) or (4/3) since in all cases the results
> correspond to other cells with exactness.
> Another detail is that as soon you take one cell to start an > investigation,
> automatically, a red of cells appear linked to your project, that is what > it
> seems to me.
>
> About Mike question, since M, J, U, (J/M = 1.00000221821), and other > commas
> work within the M range along the whole progression there is a profuse
> number of additional cells which stay potentially in hundreds of M links
> just in one cycle of 624 cells. The following subcommas I was talking > about:
>
> III. 4 NEW COMMAS
>
> The J and U commas were deduced in Chapter II.
>
> J = [(33'554,432) 21/4 / 39'858,075] = 1.00113137110297
>
> U = [(102,400) 31/2 / 177,147] = 1.00121369650659
>
> The above commas, termed Piagui commas, can also be detected by ear, since
> they are slightly greater than M.
>
> If we multiply any cell by M or J or U, the products are still consonant
> magnitudes whether or not the results are progression cells. For instance,
> if Cell No. 484 is multiplied by U we get 31/2 =1.732050807.
>
> The square root of 3 is also another consonant frequency since it is
> obtained by multiplying a cell by the consonant comma U, its value
> 1.7320508094 lying between cells Nos. 485 and 486. This seems to show > that
> other consonant frequencies work within the range of the basic comma M. > If
> so, they might be functions of M, J and U.
>
> In fact, Cell No. 484 = M298 J168 U18, therefore:
>
> (M298 J168 U18) (U) = (M298 J168 U19) = [ (M299 J168 U18) (U/M) ] =
>
> (Cell No. 485) (U/M) = 31/2 = 1.7320508094.
>
> The above result indicates that a relative U/M factor works within the > range
> of the M comma linking cells Nos. 485 and 486 and can be split by ratios > J/M
> and U/J. M1/2 is another consonant frequency, and together with J/M and > U/J
> establishes a first group of frequencies that lie in the mentioned range, > as
> shown in the following pages.
>
> As (51/2 / 2) = 1.11803398875, it might work between cells Nos. 98 and 99.
> Let us calculate the ratio between 51/2/2 and cell No. 98. Since cell No.
> 98 is equal to 1.11740330854, we have:
>
> (51/2 / 2) / (Cell No. 98) = 1.00056441591 = M1/2, so
>
> (51/2 / 2) = (Cell No. 98) M1/2
>
> Therefore, 51/2 is a consonant frequency with respect to note C.
>
> Similar calculations show that 61/2/2 falls between Cells Nos. 179 and > 180.
> So, 61/2 is another consonant value.
>
> The possibility that 71/2/2 might be a consonant figure between Cells Nos.
> 247 and 248 was studied. However, no relation with M, J or U was found.
>
> Figures 81/2, 91/2, 101/2, 121/2... are also consonant values with respect
> to note C since 81/2 = (2 x 21/2), 91/2 = (1.5 x 2) and so forth.
> Consequently, 7, 11, 13, 14, 17, 19... as well as 71/2, 111/2, 131/2, > 141/2,
> 171/2... are excluded from the theoretical infinite set of consonant
> frequencies, all of them being non-musical figures.
>
> The square root of 3 can be settled in terms of the Zarlino commas, notes > of
> the Pythagorean and Just Intonation scales, as well as the Piagui comma U.
> Let us see:
>
> ZC = Zarlino comma = (81/80) = 1.0125
>
> ZS = Zarlino semitone = (16/15) = 1.0666666...
>
> D = Pythagorean and Just Intonation note D = (9/8) = 1.125 EAZ > EAZ
> = Note E of the Aristoxenus-Zarlino scale = (5/4) = 1.25
>
> U = The Piagui comma
>
> Consequently, the square root of 3 can be given in terms of these musical
> terms: 31/2 = (ZC)2 (ZS) D2 EAZ U = 1.7320508094
>
> The above identity is also given by:
>
> 31/2 = (Cell No. 485) (U/M) = (M299 J168 U18) (U/M) = (M298 J168 U19)
>
> Electrical variables, particularly, are involved with frequency notes and
> the Piagui comma U.
>
> If a balanced three-phase voltage with amplitude Vm is fed to a balanced
> three-phase resistive load, the current amplitude of each phase is Im.
> Since electrical power is equal to 31/2 (Vm Im / 2), then, it can be given
> in terms of musical parameters including the U comma:
>
> Electrical Power = (ZC)2 (ZS) D2 EAZ U (VmI m / 2) watts
>
> By oscilloscope inspection, we see that variations over time of
> instantaneous voltage, current and power draw periodic and aesthetic > waves,
> provided that the three-phase voltage and the three-phase resistive load > are
> balanced. Commas M, J and U are involved with the periodic shapes of
> sinusoids and power displays. As soon as distortion of the three-phase
> voltage source appears, the wave shapes of v(t), i(t), w(t) become > irregular
> and stop being the exclusive functions of the commas and Vm , Im , since > the
> aesthetic displays have gone.
>
> The square root of 3 does not appear in the progression. An analysis is
> required of the empty space between cells Nos. 485 and 486 controlled by M
> in order to find not only the relative frequencies that might work within
> both cells, but also those comprised in the remaining M commas throughout
> the progression. The result of the search reveals that commas M, J and U
> take part of this apparently empty space.
>
> It is not surprising that 'M, J and U's accuracy in revealing the set of > 624
> cells, a profuse set that provides us with knowledge of music's accurate
> links involved within the octave, but they also have the ability to detect
> the relative frequencies comprised by M. Cell No. 485C is the symmetry
> center of cells Nos. 485 and 486, as shown by the following table.
>
> CELL MICRO-INTERVAL RELATIVE FREQUENCY
>
> ?
> ??
>
> 485 1
> 1.73190454693
>
> 485A J/M = 1.00000221822 J/M
> 1.73190838865
>
> 485B U/J = 1.00008223237 U/M (3)1/2 = > 1.73205080757
>
> 485C (M3/2/U) = 1.00047992462 M1/2
> 1.73288206142
>
> 486 M1/2 = 1.00056441591 M
> 1.73386012761
>
> CELL No. 485 A = (CELL No. 485) (J/M)
>
> CELL No. 485 B = (CELL No. 485A) (U/J)
>
> CELL No. 485 C = (CELL No. 485B) (M3/2/U)
>
> CELL No. 486 = (CELL No. 485C) (M1/2)
>
> ? With respect to cell No. 485 ?? With respect to C = 1
>
>
>
> J/M and U/J are much lower than M, so their consonance ratios cannot be
> distinguished by ear, and the product (J/M) (U/J) gives (U/M) =
> 1.0000844576. If we multiply this value by cell No. 485, the square root > of
> 3 is obtained again. Likewise, the same group of micro-intervals works
> within any M comma in the progression.
>
> There are two sorts of numbers; the first one is given by the non-musical
> figures 7, 11, 13, 14, 17, 19, 21, 23, 28, 29, 31... and 71/2, 111/2, > 131/2,
> 141/2... The second one, by 1, 2, 3, 4, 5, 6, 8, 9... and 21/2, 31/2, > 41/2,
> 51/2, 61/2, 81/2, 91/2... The latter two groups of figures are exclusive
> functions of M, J and U as explained in the following sentences and
> consequently, they are involved with music.
>
>
>
> 2 = Cell No. 612 = M376 J212 U24
>
> 3 = 2 x 1.5 = M596 J336 U38
>
> 4 = (M376 J212 U24)2
>
> 5 = 2 2 x 1.25 = M873 J492 U56
>
> 6 = M972 J548 U62
>
> 8 = M1128 J636 U72 and so on.
>
> Let us take the square roots:
>
> 21/2 = M188 J106 U12
>
> 31/2 = M298 J168 U19
>
> 41/2 = M376 J212 U24 = 2
>
> 51/2 = M436.5 J246 U28
>
> 61/2 = M486 J274 U31
>
> 81/2 = M564 J318 U36 and so on.
>
>
>
> The 3rd, 5th, 7th, 11th... overtones of two consonant tones decrease the
> consonance quality but, on the other hand, give the tone timbre. It is no
> just a coincidence that no cell, when multiplied by 2n, will result in one
> of the non-musical numbers 7, 11, 13, 14, 17 and so forh.
>
> Values 31/2 and 51/2 were given in terms of M, J and U, with interesting
> results. Now after the detection of N = fi (M, J, U) and N1/2 = f 'i (M,
> J, U), where N is any of the series of numbers except non-musical ones, we
> realize that there are clear links between the number series, their square
> roots and music.
>
> Analogously, if N1 = (Cell No. 98) = [(26 x 21/2) / 34] = 1.11740330855,
> then Cell No. 306 of the third segment is equal to
> (26 x 21/2 / 34) (9/8)2 = 21/2, i.e. note F# of the tempered intonation,
> which might also be F# of the new musical octave.
>
> Another peculiar result is that values 21/4, 21/2, 23/4, which are the
> tempered frequencies of notes Eb, F# and A, are progression cells whose
> values are accurately defined by the three Piagui commas.
>
> Due to the features of the Natural Progression of Musical Cells, it can be
> seen that it is not a common set of simple figures. Its origins are based
> on unquestionable scientific parameters that generate jointed relative
> frequencies for establishing a new dodecatonic musical scale, in order to
> escape the discords that audiences have endured since 1722.
>
> Zarlino settled three commas: (81/80) = 1.0125 = Cell No. 11.
>
> (128 / 125) = 1.024 = Cell > No.
> 21.
>
> The third Zarlino Comma that is equal to (648 / 625) = 1.0368 is not a
> progression cell. It must be given only in M, J, U terms.
>
> According to the foregoing table, U/J and (U/J)2 are consonant
> micro-intervals. Therefore, [(Cell No. 32) / (U/J)2] = (M20 J12) =
> (648/625) = 1.0368 = Zarlino comma is also consonant with respect to note > C.
>
> We could establish a group of very small intervals and relative > frequencies
> comprised by M, which rule those contained in any of the progression's
> remaining M commas.
>
> TABLE IX A - INTERVALS COMPRISED BY THE M COMMA
>
> CELL COMMA R E L A T I V E F R E Q U E N C Y
>
> No. RELATIONS -------------- ? -------------- >
> 485
> 1 1.73190454693
>
> 485A (J/M)1/2 (J/M)1/2 = 1.0000011091 1.73190646779
>
> 485B (J/M)1/2 (J/M) = 1.00000221821 1.73190838865
>
> 485C (U/J)1/2 (J1/2U2/M) = 1.00004333364 1.73197959666
>
> 485D (U/J)1/2 (U/M) = 1.00008445076 1.73205080757
>
> 485E (M1/2U1/2/J) (U3/2/M1/2J) = 1.00012446033 1.73212010034
>
> 485F (M1/2U1/2/J) (U2/J2) = 1.00016447149 > 1.73218939583
>
> 485G (M1/4J/U) (M1/4U/J) = 1.00036442371 1.73253569401
>
> 485H (M1/4J/U) (M)1/2 = 1.00056441591 1.73288206146
>
> 485J (M1/4J/U) (M3/4J/U) = 1.00076444808 1.73322849804
>
> 485K (M1/4J/U) (MJ2/U2) = 1.00096452026 1.73357500393
>
> 485L (M1/2U1/2/J) (M3/2J/U3/2) = 1.00100456505 1.73364435771
>
> 485M (M1/2U1/2/J) (M2/U) = 1.00104461144 1.73371371416
>
> 485N (U/J)1/2 (M2/J1/2U1/2)= 1.0010857697 > 1.73378499641
>
> 485P (U/J)1/2 (M2/J) = 1.00112692969 1.73385628154
>
> 485Q (J/M)1/2 (M3/2J1/2) = 1.00112804004 1.7338582046
>
> 486 (J/M)1/2 M = 1.00112915039
> 1.73386012761
>
>
>
> ? With respect to cell number 485
>
> The reader will notice that relative frequency 1.00096452026 with
> respect to cell number 485 also leads to the third Zarlino comma (1.0368) > if
> it is multiplied by Cell number 31.
>
> One of the powers of progression is based on cell symmetry centers SC1, > SC2,
> SC3, etc. such as [(9/8) (9/8)2]1/2. By applying this power to the M > comma
> that links Cells Nos. 485 and 486, and using mathematical reasoning, we
> obtain the values given in Table IX-A. This table does not invalidate the
> foregoing values of 485A, 485B and 485C. As stated, there are a great > many
> consonant routes that may be defined by M, J, and U commas. However, > among
> these innumerable routes, the Natural Progression of Musical Cells is the
> only one that will determine the true octave of an eminently good musical
> scale.
>
> We have detailed some of the powers of the Natural Progression of
> Musical Cells. However, its crucial power emerges when it is taken as a
> whole set, from which a small group of consecutive cells is used as
> auxiliary information to solve two equations with four unknowns, as
> explained in the following chapter. Elementary mathematics states that
> solving this set of equations requires two additional equations or some
> other associated and valid source of information like the Natural
> Progression. This remarkable power leads to the object of this work.
>
> In fact, two semitone factors K and P, which will replace the T Tempered
> factor, are deduced in the following chapter. The unobjectionable
> mathematical reasoning was essential to attain their proper values and
> further on the perfecting of harmony.
>
> PLEASE SEE BELOW
>
> <<<<<<<<<<<<<<<<<<<<<<
>
> ----- Original Message ----- > From: "genewardsmith" <genewardsmith@...>
> To: <tuning@yahoogroups.com>
> Sent: Friday, March 30, 2012 11:18 PM
> Subject: [tuning] Re: TASK ACCOMPLISHED
>
>
> >
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> >> Also, do you know if your progression of cells tempers out any useful
> >> commas?
> >
> > I analyzed a previous version some time back, but Mario didn't buy it. > > It
> > seemed to me that there was a basis change for the 5-limit lurking in > > the
> > background.
> >
> MIKE, GENE. THE TRUTH IS THAT THE LAST TIME I USED A SPREADSHEET WAS IN
> 1957. I DON�T GET "5-LIMIT LURKING IN THE BACKGROUND"
>
> BY BY
>
> MARIO
>
> MARCH, 31
>
>
>
> >
> >
> > ------------------------------------
> >
> > You can configure your subscription by sending an empty email to one
> > of these addresses (from the address at which you receive the list):
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - leave the group.
> > tuning-nomail@yahoogroups.com - turn off mail from the group.
> > tuning-digest@yahoogroups.com - set group to send daily digests.
> > tuning-normal@yahoogroups.com - set group to send individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> >
> >
> >
> >
>

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

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.
Yahoo! Groups Links

MIKE: SEE BELOW.-- MARIO
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 11:53 AM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Sat, Mar 31, 2012 at 12:18 AM, genewardsmith
> <genewardsmith@...> wrote:
>>
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> > Also, do you know if your progression of cells tempers out any useful
>> > commas?
>>
>> I analyzed a previous version some time back, but Mario didn't buy it. It
>> seemed to me that there was a basis change for the 5-limit lurking in the
>> background.
>
> I thought it might be a basis shift, but he has his "J" and "U" commas
> set to the square roots of other JI commas. Maybe it's a basis change
> for some contorted form of JI.
>
> -Mike
------------------------------------
MIKE,

There was no any basis change (I don�t know what "5-limit lurking in the
background) means. About 2.5 years ago I gave some copies of the progression to two or three members of the list and one of them were you Mike if I am not wrong. Any how, the book printed on July 2004, can demonstrate that all the 624 cells did not change. The Q, R, R� cell groups containing 104 cells each one were replaced by SSSVSRSSS.

There is no any connection with JI commas. �Which are the JI commas?.
�How can I imagine the sense of "contorted form of JI" is?

Mario
March 31

>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

On Sat, Mar 31, 2012 at 3:31 PM, Mario Pizarro <piagui@...> wrote:
>
> MIKE: SEE BELOW.-- MARIO

OK, I'll rephrase the question: are all rational intervals in your
system represented exactly? Or are some only represented
approximately?

-Mike

MIKE,

All the cells given in the progression whether rational or irrational are the exact representations of the values found.
What is happening? . Not one cell was represented approximatelly.

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 2:37 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Sat, Mar 31, 2012 at 3:31 PM, Mario Pizarro <piagui@...> wrote:
>>
>> MIKE: SEE BELOW.-- MARIO
>
> OK, I'll rephrase the question: are all rational intervals in your
> system represented exactly? Or are some only represented
> approximately?
>
> -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
>
>
>
>

What's the point of the irrational cells in your system? Why is
everything not just rational?

-Mike

On Sat, Mar 31, 2012 at 4:32 PM, Mario Pizarro <piagui@...> wrote:
>
> MIKE,
>
> All the cells given in the progression whether rational or irrational are
> the exact representations of the values found.
> What is happening? . Not one cell was represented approximatelly.

MIKE,

I understand you Mike. This evening and tomorrow I am dedicated to analize the problem. What I got from you is that a good progression should show a reasonable number of rational numbers instead of the great number of 5-limit we have now. Right now it is 10:30 pm, I made some progress, I think I took the right way, but I should go to bed, I got tired. I will continue early in the morning.

Mario

March 31
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: "Mario Pizarro" <piagui@...>
Sent: Saturday, March 31, 2012 6:10 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

Is the goal of your progression to contain lots of 5-limit rational numbers?

-Mike

On Sat, Mar 31, 2012 at 6:30 PM, Mario Pizarro <piagui@...> wrote:
>
> I already wrote that all the cells are represented exactly and in no case > I
> registered an approximated value, why I would spoil its correct value. > COME
> ON MIKE, YOU KNOW THAT I AM YOUR FRIEND, TELL ME WHAT HAS HAPPENED.
> YOUR QUESTIONS SOUND AS SOMETHING BAD HAS OCURRED.
> MARIO

No, it's not that at all. I'm just trying to figure out why you have
things like 1/4 of a pythagorean comma in there. If you got rid of all
things which were some equal division of a rational number, what would
remain?

-Mike

On Sat, Mar 31, 2012 at 11:39 PM, Mario Pizarro <piagui@...> wrote:
>
> MIKE,
>
> I understand you Mike. This evening and tomorrow I am dedicated to analize
> the problem. What I got from you is that a good progression should show a
> reasonable number of rational numbers instead of the great number of
> 5-limit
> we have now. Right now it is 10:30 pm, I made some progress, I think I
> took
> the right way, but I should go to bed, I got tired. I will continue early
> in
> the morning.
>
> Mario
>
> March 31

Mike,

News----- Finally I found the distribution pattern of rational cells in the progression. I will extend the number of them. According to the pattern there are about 30 or more rational cells (provisional information).

Mario

April, 01

------------------------------------------------
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 11:11 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> No, it's not that at all. I'm just trying to figure out why you have
> things like 1/4 of a pythagorean comma in there. If you got rid of all
> things which were some equal division of a rational number, what would
> remain?
>
> -Mike
>
> On Sat, Mar 31, 2012 at 11:39 PM, Mario Pizarro <piagui@...> wrote:
>>
>> MIKE,
>>
>> I understand you Mike. This evening and tomorrow I am dedicated to >> analize
>> the problem. What I got from you is that a good progression should show a
>> reasonable number of rational numbers instead of the great number of
>> 5-limit
>> we have now. Right now it is 10:30 pm, I made some progress, I think I
>> took
>> the right way, but I should go to bed, I got tired. I will continue early
>> in
>> the morning.
>>
>> Mario
>>
>> March 31
>
>
> ------------------------------------
>
> 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
>
>
>
>

M .= Rational number = 1.00112915039
M M.= Rational number
MMMM .= Rational number

J .= Irational number = 1.0011313711
J J .= Irational number
U .= Irational number

Mike,
This is the first time I deal with cells and rational or irational so I am not sure about the

way how I am doing the steps.

Please disregard my latest message where I
wrote that the rational or irational types of the
cells are going to be completed and
distinguished in the progression pages.

In cases like cells N� 11, 22, 47, 68, 104 the
type is rational of course.
Taking N� 31 (1.03580094900. I we go to the
computer, click in format to expand the
number of digits to 15, we have
1.035800949001410. Then, it is rational because
if we increase de number of digits more zeros
will be added, there are no more digits.

M entered with its 11 digits and only they are
shown on the fx white line of the osciloscope.
But if we go again to format and change the
number from 11 digits to 15
1.00112915039 do not change despite the
complete value of this schisma is
1.00112915039

CONCLUSION: I shouldn�t go further because
you are probably thinking different. I need to
know your parameters Mike. I will stay
waiting your advise. Mario

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 11:11 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> No, it's not that at all. I'm just trying to figure out why you have
> things like 1/4 of a pythagorean comma in there. If you got rid of all
> things which were some equal division of a rational number, what would
> remain?
>
> -Mike
>
> On Sat, Mar 31, 2012 at 11:39 PM, Mario Pizarro <piagui@...> wrote:
>>
>> MIKE,
>>
>> I understand you Mike. This evening and tomorrow I am dedicated to >> analize
>> the problem. What I got from you is that a good progression should show a
>> reasonable number of rational numbers instead of the great number of
>> 5-limit
>> we have now. Right now it is 10:30 pm, I made some progress, I think I
>> took
>> the right way, but I should go to bed, I got tired. I will continue early
>> in
>> the morning.
>>
>> Mario
>>
>> March 31
>
>
> ------------------------------------
>
> 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
>
>
>
>

Is the goal of your progression of cells to contain lots of exact
rational numbers?

-Mike

On Sun, Apr 1, 2012 at 11:56 PM, Mario Pizarro <piagui@ec-red.com> wrote:
>         M .= Rational number = 1.00112915039
>       M M.= Rational number
>     MMMM .= Rational number
>
>          J .= Irational number = 1.0011313711
>        J J .= Irational number
>          U .= Irational number
>
>
>     Mike,
>     This is the first time I deal with cells and rational or irational so I
> am not sure about the
>
>       way how I am doing the steps.
>
>       Please disregard my latest message where I
>       wrote that the rational or irational types of the
>       cells are going to be completed and
>       distinguished in the progression pages.
>
>       In cases like cells Nº 11, 22, 47, 68, 104 the
>       type is rational of course.
>       Taking Nº 31 (1.03580094900. I we go to the
>       computer, click in format to expand the
>       number of digits to 15, we have
>       1.035800949001410. Then, it is rational because
>       if we increase de number of digits more zeros
>       will be added, there are no more digits.
>
>       M entered with its 11 digits and only they are
>       shown on the fx white line of the osciloscope.
>       But if we go again to format and change the
>       number from 11 digits to 15
>       1.00112915039 do not change despite the
>       complete value of this schisma is
>       1.00112915039
>
>       CONCLUSION: I shouldn´t go further because
>       you are probably thinking different. I need to
>       know your parameters Mike. I will stay
>       waiting your advise. Mario
>
>
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
>
> ----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, March 31, 2012 11:11 PM
>
> Subject: Re: [tuning] Re: TASK ACCOMPLISHED
>
>
>> No, it's not that at all. I'm just trying to figure out why you have
>> things like 1/4 of a pythagorean comma in there. If you got rid of all
>> things which were some equal division of a rational number, what would
>> remain?
>>
>> -Mike
>>
>> On Sat, Mar 31, 2012 at 11:39 PM, Mario Pizarro <piagui@...> wrote:
>>>
>>>
>>> MIKE,
>>>
>>> I understand you Mike. This evening and tomorrow I am dedicated to
>>> analize
>>> the problem. What I got from you is that a good progression should show a
>>> reasonable number of rational numbers instead of the great number of
>>> 5-limit
>>> we have now. Right now it is 10:30 pm, I made some progress, I think I
>>> took
>>> the right way, but I should go to bed, I got tired. I will continue early
>>> in
>>> the morning.
>>>
>>> Mario
>>>
>>> March 31
>>
>>
>>
>> ------------------------------------
>>
>>
>> You can configure your subscription by sending an empty email to one
>> of these addresses (from the address at which you receive the list):
>>  tuning-subscribe@yahoogroups.com - join the tuning group.
>>  tuning-unsubscribe@yahoogroups.com - leave the group.
>>  tuning-nomail@yahoogroups.com - turn off mail from the group.
>>  tuning-digest@yahoogroups.com - set group to send daily digests.
>>  tuning-normal@yahoogroups.com - set group to send individual emails.
>>  tuning-help@yahoogroups.com - receive general help information.
>> Yahoo! Groups Links
>>
>>
>>
>>
>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> M .= Rational number = 1.00112915039
> M M.= Rational number
> MMMM .= Rational number

You shouldn't write these as decimal expansions. M = 32805/32768

> J .= Irational number = 1.0011313711
> J J .= Irational number
> U .= Irational number

J = ???, U = ???. You don't define things, so no one knows what you are saying.

Mike,

The situation is normal now. The problem of having "hidden" rational cells caused confusion. The 11 digits of the calculator were adding extra digits and many rational cells were not detected. i.e.: for instance cell # 498 with 1.7578125 had been printed 1,75781250143 and passed custom house without being detected.

A map of the positions of rational cells was made, this makes easy to find rational elements.

The number series decided that both, rational an irational numbers make possible the work of the system.

Mario

April 02

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, March 31, 2012 3:34 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> What's the point of the irrational cells in your system? Why is
> everything not just rational?
>
> -Mike
>
>
> On Sat, Mar 31, 2012 at 4:32 PM, Mario Pizarro <piagui@...> wrote:
>>
>> MIKE,
>>
>> All the cells given in the progression whether rational or irrational are
>> the exact representations of the values found.
>> What is happening? . Not one cell was represented approximatelly.
>
>
> ------------------------------------
>
> 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
>
>
>
>

GENE,

Those writings are not going to be printed that way. Don�t worry my friend.

Regards

Mario

April, 02

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Monday, April 02, 2012 12:25 PM
Subject: [tuning] Re: TASK ACCOMPLISHED

>
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> M .= Rational number = 1.00112915039
>> M M.= Rational number
>> MMMM .= Rational number
>
> You shouldn't write these as decimal expansions. M = 32805/32768
>
>> J .= Irational number = 1.0011313711
>> J J .= Irational number
>> U .= Irational number
>
> J = ???, U = ???. You don't define things, so no one knows what you are > saying.
>
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

I'm so confused. So you're saying that there ARE some numbers that are
only represented approximately, right? That at least increases the
changes of it being a regular temperament.

-Mike

On Mon, Apr 2, 2012 at 3:56 PM, Mario Pizarro <piagui@...> wrote:
>
> GENE,
>
> Those writings are not going to be printed that way. Don´t worry my friend.
>
> Regards
>
> Mario

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> GENE,
>
> Those writings are not going to be printed that way. Don´t worry my friend.

You were the one who complained of being ignored. What else can you expect?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'm so confused. So you're saying that there ARE some numbers that are
> only represented approximately, right? That at least increases the
> changes of it being a regular temperament.

Last time I checked all of his numbers could be expressed as rational numbers or nth roots of same, and hence as fractional monzos. I doubt that has changed, but since he insists on doing things the wrong way, who knows?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Is the goal of your progression of cells to contain lots of exact
> rational numbers?

Let me ask Mario a more open-ended question.

Mario, what is the goal of your progression of cells?

Are some combinations of them supposed to sound a particular way? If so, which combinations?

Just tell me what the purpose is! I don't think anyone else here knows the purpose. Maybe I'll find out when I read your book...

Keenan

Keenan,

When I derived the progression of cells , years ago, I didn�thave idea about its application, however I was satisfied of its properties; for instance if you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a higher one is obtained, All historical frequencies are contained in the set. Regarding your rational numbers question my answer is no.

About : > Mario, what is the goal of your progression of cells?

One application is explained in the book and also you will find there some other particularities of the progression. Right now I can not define an specific goal, we�d better don�t mind, it may come.

> Are some combinations of them supposed to sound a particular way? If so, > which combinations?

The wide spectrum of sound is totally known, nevertheless if we talk about sound combinations the road to be walk is more than inmense, perhaps the progression helps to know and apply new expressions.

Have a good time

----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, April 03, 2012 11:20 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> Is the goal of your progression of cells to contain lots of exact
>> rational numbers?
>
> Let me ask Mario a more open-ended question.
>
> Mario, what is the goal of your progression of cells?
>
> Are some combinations of them supposed to sound a particular way? If so, > which combinations?
>
> Just tell me what the purpose is! I don't think anyone else here knows the > purpose. Maybe I'll find out when I read your book...
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> for instance if
> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
> higher one is obtained

This cannot possibly be correct (unless the cells were infinitely dense) because of the Fundamental Theorem of Arithmetic.

For any finite list of cells you provide, I can find one such that either the exact 3/2 above it or the exact 4/3 above it is missing from the list.

> All historical frequencies are contained in the set.

This is also patently false.

Keenan

Keenan,

It seems that I didn�t explain clear that if you take for instance cell # 3, its perfect fourth coincides with cell # 257. The same
occurs with any cell of the progression when we take their perfect fifths..
PERFECT FOURTHS AND PERFECT FIFTHS OF ANY CELL PRODUCE HIGHER VALUE CELLS WITH EXACTNESS
(M M J) = (Pythagorean comma)^0.25
CELL N� CELL FREQUENCY CELL FREQ. COINCIDENT CELL CELL CELL FREQ. COINCIDENT
0 1 = Note C x 1.333333333 N� CELL N� FREQUENCY x 1.333333333 N� CELL
M 1 1.00112915039 1.334838867 255 1.334838867 M 53 1.06185781663 1.415810422 307 1.415810422
M 2 1.00225957576 1.336346101 256 1.336346101 M 54 1.06305681380 1.417409085 308 1.417409085
S J 3 1.00339350328 1.337858004 257 1.337858004 J 55 1.06425952555 1.419012701 309 1.419012701
J 4 1.00452871369 1.339371618 258 1.339371618 J 56 1.06546359803 1.420618131 310 1.420618131
M 5 1.00566297768 1.340883970 259 1.340883970 M 57 1.06666666666 1.422222222 311 1.422222222
M 6 1.00679852243 1.342398030 260 1.342398030 M 58 1.06787109375 1.423828125 312 1.423828125
M 7 1.00793534937 1.343913799 261 1.343913799 M 59 1.06907688081 1.425435841 313 1.425435841
M 8 1.00907345997 1.345431280 262 1.345431280 M 60 1.07028402939 1.427045373 314 1.427045373
S J 9 1.01021509652 1.346953462 263 1.346953462 J 61 1.07149491781 1.428659890 315 1.428659890
J 10 1.01135802469 1.348477366 264 1.348477366 J 62 1.07270717620 1.430276235 316 1.430276235
M 11 1.01250000000 1.35 265 1.35 M 63 1.07391842393 1.431891232 317 1.431891232
M 12 1.01364326477 1.351524353 266 1.351524353 M 64 1.07513103933 1.433508052 318 1.433508052
M 13 1.01478782046 1.353050427 267 1.353050427 M 65 1.07634502396 1.435126699 319 1.435126699
M 14 1.01593366853 1.354578225 268 1.354578225 M 66 1.07756037937 1.436747172 320 1.436747172
S J 15 1.01708306652 1.356110755 269 1.356110755 J 67 1.07877950004 1.438372667 321 1.438372667
J 16 1.01823376491 1.357645020 270 1.357645020 J 68 1.08 1.44 322 1.44
M 17 1.01938350395 1.359178005 271 1.359178005 M 69 1.08121948241 1.441625977 323 1.441625977
M 18 1.02053454123 1.360712722 272 1.360712722 M 70 1.08244034181 1.443253789 324 1.443253789
M 19 1.02168687821 1.362249171 273 1.362249171 M 71 1.08366257974 1.444883440 325 1.444883440
M 20 1.02284051635 1.363787355 274 1.363787355 M 72 1.08488619777 1.446514930 326 1.446514930
V J 21 1.02399772855 1.365330305 275 1.365330305 J 73 1.08611360666 1.448151476 327 1.448151476
J 22 1.02515625 1.366875 276 1.366875 J 74 1.08734240420 1.449789872 328 1.449789872
U 23 1.02640047856 1.368533971 277 1.368533971 U 75 1.08866210789 1.451549477 329 1.451549477
U 24 1.02764621724 1.370194956 278 1.370194956 U 76 1.08998341329 1.453311218 330 1.453311218
M 25 1.02880658437 1.371742112 279 1.371742112 M 77 1.09121416848 1.454952225 331 1.454952225
M 26 1.02996826172 1.373291016 280 1.373291016 M 78 1.09244631339 1.456595085 332 1.456595084
S J 27 1.03113353805 1.374844717 281 1.374844717 J 79 1.09368227557 1.458243034 333 1.458243034
J 28 1.03230013273 1.376400177 282 1.376400177 J 80 1.09491963609 1.459892848 334 1.459892848
M 29 1.03346575483 1.377954340 283 1.377954340 M 81 1.09615596503 1.461541287 335 1.461541287
M 30 1.03463269309 1.379510257 284 1.379510257 M 82 1.09739368996 1.463191587 336 1.463191587
M 31 1.03580094900 1.381067932 285 1.381067932 M 83 1.09863281248 1.464843750 337 1.464843750
R M 32 1.03697052405 1.382627365 286 1.382627365 M 84 1.09987333414 1.466497779 338 1.466497779
J 33 1.03814372253 1.384191630 287 1.384191630 J 85 1.10111769905 1.468156932 339 1.468156932
J 34 1.03931824833 1.385757664 288 1.385757664 J 86 1.10236347179 1.469817962 340 1.469817962
M 35 1.04049179494 1.387322393 289 1.387322393 M 87 1.10360820593 1.471477608 341 1.471477608
M 36 1.04166666666 1.388888888 290 1.388888888 M 88 1.10485434557 1.473139127 342 1.473139127
S J 37 1.04284517822 1.390460238 291 1.390460238 J 89 1.10610434585 1.474802523 343 1.474802523
J 38 1.04402502312 1.392033364 292 1.392033364 J 90 1.10735576034 1.476467797 344 1.476467797
M 39 1.04520388438 1.393605179 293 1.393605179 M 91 1.10860613153 1.478138230 345 1.478138230
M 40 1.04638407675 1.395178769 294 1.395178769 M 92 1.10985791457 1.479810553 346 1.479810553
M 41 1.04756560173 1.396754136 295 1.396754136 M 93 1.11111111111 1.481481481 347 1.481481481
M 42 1.04874846085 1.398331281 296 1.398331281 M 94 1.11236572266 1.483154297 348 1.483154297
S J 43 1.04993498455 1.399913313 297 1.399913313 J 95 1.11362422109 1.484832295 349 1.484832295
J 44 1.05112285065 1.401497134 298 1.401497134 J 96 1.11488414335 1.486512191 350 1.486512191
M 45 1.05230972642 1.403079635 299 1.403079635 M 97 1.11614301522 1.488190687 351 1.488190687
M 46 1.05349794236 1.404663923 300 1.404663923 M 98 1.11740330854 1.489871078 352 1.489871078
M 47 1.0546875 1.40625 301 1.40625 M 99 1.11866502492 1.491553367 353 1.491553367
M 48 1.05587840080 1.407837868 302 1.407837868 M 100 1.11992816597 1.493237555 354 1.493237555
S J 49 1.05707299111 1.409430655 303 1.409430655 J 101 1.12119522034 1.494926960 355 1.494926960
J 50 1.05826893295 1.411025244 304 1.411025244 J 102 1.12246370821 1.496618278 356 1.496618278
M 51 1.05946387773 1.412618504 305 1.412618504 M 103 1.12373113855 1.498308185 357 1.498308185
M 52 1.06066017178 1.414213562 306 1.414213562 M 104 1.125 1.5 358 1.5
.= (9/8)^(1/2) .= (9/8)
M .= 1.00112915039 J = 1.00113137110 U .= 1.00121369651
P/T 1.000000739 P/T 1.000001479

2

CELL CELL CELL FREQ. COINCIDENT CELL CELL CELL FREQ. COINCIDENT
N� FREQUENCY x 1.333333333 N� CELL N� FREQUENCY x 1.333333333 N� CELL
M 105 1.12627029419 1.501693726 359 1.501693726 M 157 1.19459004371 1.592786725 411 1.592786725
M 106 1.12754202273 1.503389364 360 1.503389364 M 158 1.19593891552 1.594585221 412 1.594585221

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

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> for instance if
>> you multiply any cell frequency by 1.5 or 4/3, the exact frequency of a
>> higher one is obtained
>
> This cannot possibly be correct (unless the cells were infinitely dense) > because of the Fundamental Theorem of Arithmetic.
>
> For any finite list of cells you provide, I can find one such that either > the exact 3/2 above it or the exact 4/3 above it is missing from the list. > < THE TABULATION ABOVE SHOWS WHAT I WROTE
>
>> All historical frequencies are contained in the set.
>
> This is also patently false.< I AM LOOKING AT THEM IN THE PROGRESSION, > WHAT IS WRONG?
>
> Keenan
> I THINK THAT I SHOULD GIVE YOU THE COMPLETE PROGRESION BY MAIL BECAUSE > THERE ARE PRINTING ERRORS IN THE BOOK BUT I HAVE A PROBLEM: YOU ASKED NOT > TO EMAIL TO YOUR PERSONAL ADDRESS. AS YOU KNOW, ATTACHEMENTS ARE NOT > ACCEPTED BY TUNING.

MARIO
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> > I THINK THAT I SHOULD GIVE YOU THE COMPLETE PROGRESION BY MAIL BECAUSE
> > THERE ARE PRINTING ERRORS IN THE BOOK BUT I HAVE A PROBLEM: YOU ASKED NOT
> > TO EMAIL TO YOUR PERSONAL ADDRESS. AS YOU KNOW, ATTACHEMENTS ARE NOT
> > ACCEPTED BY TUNING.

Please email me the whole progression; you have my permission.

I would really prefer *exact* representations of the values. For example, 1.333333333 is *not* an exact representation of 4/3 because it represents the rational number 1333333333/1000000000 which is a different rational number from 4/3.

However, since you seem to prefer decimals, decimals will suffice to demonstrate what I want to demonstrate as long as they are all accurate to *at least* 8 significant figures (7 digits after the decimal point).

Keenan

Keenan:
The whole progression proves that perfect fifth and perfect thirds of cells gives these results. Please....

PERFECT FOURTHS AND PERFECT FIFTHS OF ANY CELL PRODUCE HIGHER VALUE CELLS WITH EXACTNESS

(M M J) = (Pythagorean comma)^ 0.25

CELL
N�
CELL FREQUENCY
CELL FREQ.

COINCIDENT

CELL
CELL

0
1 = Note C
x 1.333333333
N�
CELL

N�
FREQUENCY
x 1.333333333

M
1
1.00112915039
1.334838867
255
1.334838867

M
53
1.06185781663
1.415810422

M
2
1.00225957576
1.336346101
256
1.336346101

M
54
1.06305681380
1.417409085

S
J
3
1.00339350328
1.337858004
257
1.337858004

J
55
1.06425952555
1.419012701

J
4
1.00452871369
1.339371618
258
1.339371618

J
56
1.06546359803
1.420618131

M
5
1.00566297768
1.340883970
259
1.340883970

M
57
1.06666666666
1.422222222

M
6
1.00679852243
1.342398030
260
1.342398030

M
58
1.06787109375
1.423828125

M
7
1.00793534937
1.343913799
261
1.343913799

M
59
1.06907688081
1.425435841

M
8
1.00907345997
1.345431280
262
1.345431280

M
60
1.07028402939
1.427045373

S
J
9
1.01021509652
1.346953462
263
1.346953462

J
61
1.07149491781
1.428659890

J
10
1.01135802469
1.348477366
264
1.348477366

J
62
1.07270717620
1.430276235

M
11
1.01250000000
1.35
265
1.35

M
63
1.07391842393
1.431891232

M
12
1.01364326477
1.351524353
266
1.351524353

M
64
1.07513103933
1.433508052

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

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

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:

> (M M J) = (Pythagorean comma)^0.25

Since M = 32805/32768, this means that J^4 = |101 -52 -8>, so J = |101/4 -13 -2>. In 612et, J is 1 step. Compared to a step of 612edo, M is 0.9964 and J is 0.9984. What are U and V?

Keenan:

I will send you the progression to your personal email.

* About the 1.33333......, 1.66666........,... etc representations, there is a low number of this type of values. Besides this type of representations gives a more clear representation of its magnitude; in Europe, they prefer this way and your name "Keenan" was born there (�?). I am using 11 and 9 decimal digits after the decimal point.

EXTRA EXTRA. I am detecting more rational cells thanks to another progression property.

Mario

April, 04

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 11:59 AM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> > I THINK THAT I SHOULD GIVE YOU THE COMPLETE PROGRESION BY MAIL BECAUSE
>> > THERE ARE PRINTING ERRORS IN THE BOOK BUT I HAVE A PROBLEM: YOU ASKED >> > NOT
>> > TO EMAIL TO YOUR PERSONAL ADDRESS. AS YOU KNOW, ATTACHEMENTS ARE NOT
>> > ACCEPTED BY TUNING.
>
> Please email me the whole progression; you have my permission.
>
> I would really prefer *exact* representations of the values. For example, > 1.333333333 is *not* an exact representation of 4/3 because it represents > the rational number 1333333333/1000000000 which is a different rational > number from 4/3.
>
> However, since you seem to prefer decimals, decimals will suffice to > demonstrate what I want to demonstrate as long as they are all accurate to > *at least* 8 significant figures (7 digits after the decimal point).
>
> Keenan
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@> wrote:
>
> > (M M J) = (Pythagorean comma)^0.25
>
> Since M = 32805/32768, this means that J^4 = |101 -52 -8>, so J = |101/4 -13 -2>. In 612et, J is 1 step. Compared to a step of 612edo, M is 0.9964 and J is 0.9984. What are U and V?
>

By the way, (J/M)^4 = |161 -84 -12>, the Kirnberger atom.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> By the way, (J/M)^4 = |161 -84 -12>, the Kirnberger atom.

For more details about that very tiny interval see the refernce
http://arxiv.org/abs/0907.5249

Gene, here you have the values:

M = (32805 / 32768) = 1.001129150390625 = Rational schisma

J = [(335544*2^1/4) / 39858075] = 1.00113137110297 = Irational

U = [(102400*3^1/2 ) /177147 = 1.0012136965059] = Irational

WHAT YOU MEAN BY THIS : "|101/4 -13 -2>. "------ "M is 0.9964 and J is 0.9984." ---INNECESARY CHANGES.
DO YOU EXPECT THAT ALL OF US FOLLOW YOUR CHANGES?- THERE IS NO A REASON TO DO IT.

MARIO

APRIL 04

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 12:53 PM
Subject: [tuning] Re: TASK ACCOMPLISHED

>
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
>> (M M J) = (Pythagorean comma)^0.25
>
> Since M = 32805/32768, this means that J^4 = |101 -52 -8>, so J = > |101/4 -13 -2>. In 612et, J is 1 step. Compared to a step of 612edo, M is > 0.9964 and J is 0.9984. What are U and V?
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>
>

On Wed, Apr 4, 2012 at 2:02 PM, Mario Pizarro <piagui@...> wrote:
>
> Keenan:
>
> I will send you the progression to your personal email.

Would you mind sending me the entire progression as well?

Actually, I have a request. Can you send it to me as a simple string
of letters, like JMMJMJMMMJMJUUMMJMJM..., with no other formatting?
That would make it easy for me to perform calculations on the cells.

Thanks
-Mike

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan:
>
> I will send you the progression to your personal email.
>
> * About the 1.33333......, 1.66666........,... etc representations, there is
> a low number of this type of values. Besides this type of representations
> gives a more clear representation of its magnitude; in Europe, they prefer
> this way and your name "Keenan" was born there (¿?). I am using 11 and 9
> decimal digits after the decimal point.

No, mathematicians in Europe also prefer to represent exact rational numbers as fractions (and exact algebraic irrationals as radical expressions or fractional powers). It has nothing to do with which continent you're on, it has to do with mathematics.

The reason for this is that 1.33333, if it represents any rational number exactly, represents 133333/100000. This is a distinct rational number from 4/3.

The origin of my first name is especially irrelevant.

> EXTRA EXTRA. I am detecting more rational cells thanks to another
> progression property.

If you had exact expressions for these numbers, it would be easy to determine which were rational and which were irrational...

Keenan

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:

> U = [(102400*3^1/2 ) /177147 = 1.0012136965059] = Irational

U = |12 -21/2 2>, 1.0701 steps of 612edo.

> DO YOU EXPECT THAT ALL OF US FOLLOW YOUR CHANGES?- THERE IS NO A REASON TO
> DO IT.

I didn't put it like that for you, but so that other people would find it easier to follow.

As for my previous comment about a coordinate change "lurking", if you take M (the schisma), J^4 and U^2, then they define a unimodular matrix, and so every 5-limit interval can be expressed in terms of M, J^4 and U^2, call them M, J4 and U2. This is the conclusion I reached before. If v376 is the 376edo patent val, v53 the 53edo val, and v12 the 12edo val, then for any 5-limit interval q we have

q = M^v376(q) J4^v53(q) U2^v12(q)

On Wed, Apr 4, 2012 at 4:52 PM, genewardsmith <genewardsmith@...>
wrote:
>
> As for my previous comment about a coordinate change "lurking", if you
> take M (the schisma), J^4 and U^2, then they define a unimodular matrix, and
> so every 5-limit interval can be expressed in terms of M, J^4 and U^2, call
> them M, J4 and U2. This is the conclusion I reached before. If v376 is the
> 376edo patent val, v53 the 53edo val, and v12 the 12edo val, then for any
> 5-limit interval q we have
>
> q = M^v376(q) J4^v53(q) U2^v12(q)

Right, so I reached the same conclusion, except the fact that there
are fractional monzos in there throws me off. What's the point of
them? Why not just toss them?

Also, he's now talking about there being a circle of 3/2's, which
makes me think that he's tempering something somewhere.

-Mike

Mike,

I am detecting more rational cells. Fortunately on each set of 104 cells,( there are 6 sets), the rational cells distributions are exactly the same. As a consequence its number is increasing every hour and at this rate in one or two days all members of the list shall receive the six schems which are similar to the scheme page I sent you recently.

The research was quite interesting and to discover the equal routes that follow the rational cells, I only had to apply the data and experience I got after years of working with the progression.

Geneward is planing to change the data to a matrix. In that case the presentation we have at the present should be given out first since the readers will understand with ease; it is being exposed didactically by adding in the near future information on how the cells were ordained to form the progression. If somebody wants to write an article on this matter I aprove it and give my written permission to comply with the copyright properly.

Mario

April 05

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 9:06 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Wed, Apr 4, 2012 at 4:52 PM, genewardsmith > <genewardsmith@...>
> wrote:
>>
>> As for my previous comment about a coordinate change "lurking", if you
>> take M (the schisma), J^4 and U^2, then they define a unimodular matrix, >> and
>> so every 5-limit interval can be expressed in terms of M, J^4 and U^2, >> call
>> them M, J4 and U2. This is the conclusion I reached before. If v376 is >> the
>> 376edo patent val, v53 the 53edo val, and v12 the 12edo val, then for any
>> 5-limit interval q we have
>>
>> q = M^v376(q) J4^v53(q) U2^v12(q)
>
> Right, so I reached the same conclusion, except the fact that there
> are fractional monzos in there throws me off. What's the point of
> them? Why not just toss them?
>
> Also, he's now talking about there being a circle of 3/2's, which
> makes me think that he's tempering something somewhere.
>
> -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
>
>
>
>

On Thu, Apr 5, 2012 at 1:31 AM, Mario Pizarro <piagui@...> wrote:
>
> Mike,
>
> I am detecting more rational cells. Fortunately on each set of 104 cells,(
> there are 6 sets), the rational cells distributions are exactly the same.
> As a consequence its number is increasing every hour and at this rate in
> one
> or two days all members of the list shall receive the six schems which are
> similar to the scheme page I sent you recently.

Can you just send me the full progression of cells please, even if
they're not labeled? I just want the progression as follows: MMJJMM...
all the way to the end.

-Mike

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, April 05, 2012 12:46 AM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Thu, Apr 5, 2012 at 1:31 AM, Mario Pizarro <piagui@...> wrote:
>>
>> Mike,
>>
>> I am detecting more rational cells. Fortunately on each set of 104 >> cells,(
>> there are 6 sets), the rational cells distributions are exactly the same.
>> As a consequence its number is increasing every hour and at this rate in
>> one
>> or two days all members of the list shall receive the six schems which >> are
>> similar to the scheme page I sent you recently.
>
> Can you just send me the full progression of cells please, even if
> they're not labeled? I just want the progression as follows: MMJJMM...
> all the way to the end.
> DO YOU MEAN THE FOUR PAGES CONTAINING THE GRADUAL INCREASING OF CELLS > STARTING
WITH A GROUP OF 47 ???????---MARIO-- April 05

> -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
>
>
>
>

MIKE, IT SEEMS THAT YOI ARE ASKING THE SIX PAGES OF THE PROGRESSION. I WILL SEND IT IN A FEW MINUTES. --- MARIO

---------------------
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, April 05, 2012 12:46 AM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Thu, Apr 5, 2012 at 1:31 AM, Mario Pizarro <piagui@...> wrote:
>>
>> Mike,
>>
>> I am detecting more rational cells. Fortunately on each set of 104 >> cells,(
>> there are 6 sets), the rational cells distributions are exactly the same.
>> As a consequence its number is increasing every hour and at this rate in
>> one
>> or two days all members of the list shall receive the six schems which >> are
>> similar to the scheme page I sent you recently.
>
> Can you just send me the full progression of cells please, even if
> they're not labeled? I just want the progression as follows: MMJJMM...
> all the way to the end.
>
> -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
>
>
>
>

MIKE,

I ASK YOUR CONSENT FOR SENDING THE 6 PAGES OF TABULATED PROGRESSION YOU REQUIRED TO YOUR PERSONAL EMAIL.--------

MARIO

APRIL 05

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 9:06 PM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Wed, Apr 4, 2012 at 4:52 PM, genewardsmith > <genewardsmith@...>
> wrote:
>>
>> As for my previous comment about a coordinate change "lurking", if you
>> take M (the schisma), J^4 and U^2, then they define a unimodular matrix, >> and
>> so every 5-limit interval can be expressed in terms of M, J^4 and U^2, >> call
>> them M, J4 and U2. This is the conclusion I reached before. If v376 is >> the
>> 376edo patent val, v53 the 53edo val, and v12 the 12edo val, then for any
>> 5-limit interval q we have
>>
>> q = M^v376(q) J4^v53(q) U2^v12(q)
>
> Right, so I reached the same conclusion, except the fact that there
> are fractional monzos in there throws me off. What's the point of
> them? Why not just toss them?
>
> Also, he's now talking about there being a circle of 3/2's, which
> makes me think that he's tempering something somewhere.
>
> -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
>
>
>
>

Am 05.04.2012 16:02, schrieb Mario Pizarro:
> MIKE,
>
> I ASK YOUR CONSENT FOR SENDING THE 6 PAGES OF TABULATED PROGRESSION YOU
> REQUIRED TO YOUR PERSONAL EMAIL.--------

CCCCC AAA PPPPPP SSSSS
CC C AAAAA PP PP SS
CC AA AA PPPPPP SSSSS
CC C AAAAAAA PP SS
CCCCC AA AA PP SSSSS

LL OOOOO CCCCC KK KK EEEEEEE DDDDD
LL OO OO CC C KK KK EE DD DD
LL OO OO CC KKKK EEEEE DD DD
LL OO OO CC C KK KK EE DD DD
LLLLLLL OOOO0 CCCCC KK KK EEEEEEE DDDDDD

???
?? ??
??
??
?? SCNR :-) Wolf

Mike, Attached you have the scheme that I am using for detecting rational cells.

How did you receive the 7 pages of the progression.

Mario
April 7
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, April 05, 2012 12:46 AM
Subject: Re: [tuning] Re: TASK ACCOMPLISHED

> On Thu, Apr 5, 2012 at 1:31 AM, Mario Pizarro <piagui@...> wrote:
>>
>> Mike,
>>
>> I am detecting more rational cells. Fortunately on each set of 104 >> cells,(
>> there are 6 sets), the rational cells distributions are exactly the same.
>> As a consequence its number is increasing every hour and at this rate in
>> one
>> or two days all members of the list shall receive the six schems which >> are
>> similar to the scheme page I sent you recently.
>
> Can you just send me the full progression of cells please, even if
> they're not labeled? I just want the progression as follows: MMJJMM...
> all the way to the end.
>
> -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
>
>
>
>

Gene,

Do I pretend all of you follow my changes?. I am not suggesting nothing to anybody and note that you are very sensible to a little mistake. The words written in that message were not addressed to you, consequently I don�t know why I am writing you. Well, let�s have better time from now on.

Regarding the U rationality or irrationality.

Cell # 24 = 1.02764621722 , formed by the product of (Cell # 23)*U.

Cell # 24 = (1.04049179492 / 1.0125), no doubt the denominator is rational and after testing the numerator by means of a special method I checked that it was rational too.

31
1.03580094900

32
1.03697052405

33
1.03814372253

34
1.03931824833

35
1.04049179494

The mistake happened at the moment I copied the number given at the bottom since the blue ones were rationals and the white box irrational but my secretary copied number 33 instead of 35 starting the confusion. Nobody is free of this confusion. By the way, quotient (1.04049179494 / 1.0125) = 1.02764621722 = Cell # 24.

Mario

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 3:52 PM
Subject: [tuning] Re: TASK ACCOMPLISHED

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
>> U = [(102400*3^1/2 ) /177147 = 1.0012136965059] = Irational
>
> U = |12 -21/2 2>, 1.0701 steps of 612edo.
>
>> DO YOU EXPECT THAT ALL OF US FOLLOW YOUR CHANGES?- THERE IS NO A REASON
>> TO
>> DO IT.
>
> I didn't put it like that for you, but so that other people would find it
> easier to follow.
>
> As for my previous comment about a coordinate change "lurking", if you
> take M (the schisma), J^4 and U^2, then they define a unimodular matrix,
> and so every 5-limit interval can be expressed in terms of M, J^4 and U^2,
> call them M, J4 and U2. This is the conclusion I reached before. If v376
> is the 376edo patent val, v53 the 53edo val, and v12 the 12edo val, then
> for any 5-limit interval q we have
>
> q = M^v376(q) J4^v53(q) U2^v12(q)
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

Keenan,

Attached you have the Progression of Musical Cells.

I improvised a method to determine whether a frequency number is rational or irrational.
It seems to work correctly and to be sure I would like to know if you could check it.

Thanks

Mario

April, 8

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, April 04, 2012 3:15 PM
Subject: [tuning] Re: TASK ACCOMPLISHED

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan:
>
> I will send you the progression to your personal email.
>
> * About the 1.33333......, 1.66666........,... etc representations, there > is
> a low number of this type of values. Besides this type of representations
> gives a more clear representation of its magnitude; in Europe, they prefer
> this way and your name "Keenan" was born there (�?). I am using 11 and 9
> decimal digits after the decimal point.

No, mathematicians in Europe also prefer to represent exact rational numbers as fractions (and exact algebraic irrationals as radical expressions or fractional powers). It has nothing to do with which continent you're on, it has to do with mathematics.

The reason for this is that 1.33333, if it represents any rational number exactly, represents 133333/100000. This is a distinct rational number from 4/3.

The origin of my first name is especially irrelevant.

> EXTRA EXTRA. I am detecting more rational cells thanks to another
> progression property.

If you had exact expressions for these numbers, it would be easy to determine which were rational and which were irrational...

Keenan

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

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.
Yahoo! Groups Links

On Sun, Apr 8, 2012 at 5:49 PM, Mario Pizarro <piagui@...> wrote:
>
> Keenan,
>
> Attached you have the Progression of Musical Cells.

Mario, I note that in this progression, some cells are in bold, some
are red, and some are purple. What do these different indicators mean?

-Mike

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan,
>
> Attached you have the Progression of Musical Cells.

What is cell #277? Is it 1.368533971 or is it 1.36841840744?

At position H28 in this Excel file it says that #277 is 1.368533971, whereas at position L144 it says that #277 is 1.36841840744.

Keenan

One of the following may help; the second one has a link to a spreadsheet (sorry, Gene, not an ascii file!).

/tuning/topicId_88730.html#88952
/tuning/topicId_101004.html#101156
/tuning/topicId_101004.html#101067

But there is some confusion about the definitive sequence of M, J and U. I also discussed offline with Mario the same point Keenan makes - that the statement about pure 4/3 or 3/2 ratios cannot be true.

Steve M.