Yahoo Tuning Groups Ultimate Backup tuning Information

I concluded that Piagui I Major D is not a good referential triad because its chord wave peaks response shows additional peaks when it comes from D + F# + A. Since the inversion F# + A + 2D produced an aesthetic response I wrongly thought that it is an harmonious chord despite that this response doesn't show marks periodicity. It is a good new to know that chord wave peak graphs detect low degree of discordance.

Since (K^8)*(P^4) = 2 is valid, [K = (9/8)^(1/2)], [P = (8/9)*2^(1/4)], I extended the research and finally got an interesting set whose values are ordained as follows:
1
R
RS
(R^2)*S

(R^3)*S
(R^3)*(S^2)
(R^4)*(S^2)

(R^5)*(S^2)
(R^5)*(S^3)
(R^6)*(S^3)

(R^7)*(S^3)
(R^7)*(S^4)
(R^8)*(S^4)

Ratios (Eb/C) = (E/C#) = (F/D) = (F#/Eb) = (G/E) =...... 2^(1/4).
Ratios C#/C, Eb/D, E/Eb, F#/F, G/F#, A/Ab, Bb/A, 2C/B are constant.
Ratios D/C#, F/E, Ab/G, B/Bb are constant.

I checked the first 8 chord wave peak graph responses, they look fine. The remaining 16 responses will be checked in the following days; they will be fine too I think.I know that most of you do not rely on K and P consonant factors, time will decide.

R and S are functions of K and P.

Thanks

Mario Pizarro

Lima, November 04

Mike,

Weeks ago I informed to tuning that the progression of cells is an useful tool to determine if a ratio whether it is a common fraction
or decimal figure is or it is not consonant and sent the following mesage to tuning saying that 1.75 is not consonant. This report was wrong due to the following reasons.

1) I didn´t avail a table I wrote in my book concerning to the existance of 16 additional consonant cells which work within the interval of two contiguous cells distanced by the M factor. For instance, between cells # 143 and 144 (see below) work 16 complementary cells. See table IX A.

SEE THE INFORMATION PLACED BELOW THE FOLLOWING MESSAGE.
---------------------------------------------------------------------------------------------------------------------------------------------
--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> To the members of the tuning list.
>
> .......CELL #
>
>....... J - 142 .......1.17452815104 = 36529/31101
>.......M - 143.......1.17585436996 = 6847/5823
>.......M - 144.......1.17718208638 = 3601/3059
>
>.......M - 493.......1.74791410141 = 12779/7311
> ......M - 494.......1.74988775930 = 42874/24501
>....... J - 495....... 1.75186753174 = 14071/8032
>
> 1.75 and 1.175 are not cells so they are not consonant.

Haha, well there you go Mike, that's your answer.

Keenan
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

THIS IS THE TABLE THAT I COPIED FROM MY BOOK :

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

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 regarding note C and regarding the remaining cells.

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

No................... -------------- ** --------------

485 ................................................................... 1.73190454693....1.74988775930 = (Cell # 494)

485A ................(J/M)1/2 =........ 1.0000011091...... 1.73190646779....1.7498897001

485B ................(J/M) = ..........1.00000221821..... 1.73190838865....1.74989164092

485C.................(J1/2U2/M) = ....1.00004333364.... 1.73197959666....1.74996358831

485D ................(U/M) = ......1.00008445076....(3^0.5) = 1.73205080757....1.75003553865 =appr. to 1.75

485E.................(U3/2/M1/2J) =...1.00012446033.....1.73212010034....(Cell # 494)*(Cell # 485E)

485F .................(U2/J2) = ........1.00016447149......1.73218939583....(Cell # 494)*(Cell # 485F)

485G.......... ......(M1/4U/J) = .....1.00036442371......1.73253569401....(Cell # 494)*(Cell # 485G)

485H.................(M)1/2 = .........1.00056441591......1.73288206146....(Cell # 494)*(Cell # 485H)

485J................. (M3/4J/U) =......1.00076444808......1.73322849804....(Cell # 494)*(Cell # 485 J)

485K................. (MJ2/U2) =......1.00096452026......1.73357500393.....(Cell # 494)*(Cell # 485 K)

485L .................(M3/2J/U3/2)=...1.00100456505......1.73364435771.....(Cell # 494)*(Cell # 485 L)

485M.................(M2/U) = ........1.00104461144......1.73371371416.....(Cell # 494)*(Cell # 485 M)

485N ................(M2/J1/2U1/2)=...1.0010857697.......1.73378499641.....(Cell # 494)*(Cell # 485 N)

485P.................(M2/J) =...........1.00112692969......1.73385628154.....(Cell # 494)*(Cell # 485 P)

485Q.................(M3/2J1/2) =......1.00112804004.......1.7338582046.... 1.75186170276

486................... M = ................1.00112915039.......1.73386012761....1.75186364575 = Cell # 495

** With respect to cell number 485. <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

THE THIRD COLUMN IS APPLIED TO ANY PAIR OF CELLS WHOSE INTERVAL IS M.

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

FROM THE PROGRESSION OF CELLS :

# 494 = 1.74988775930

# 494*M = Next Cell = (1.74988775930 * M) = 1.75186364575 = Cell # 495

(1.00008445076 * 1.74988775930) = 1.7500355 . THE ERROR OF +0.0000355 IS NEGLECTABLE SO 1.75 RATIO IS CONSONANT.

DO YOU WANT ME TO CHECK IF 1.175 is CONSONANT ?

BTW: THE TABLE INDICATES THAT (3)^(1/2) IS ALSO CONSONANT.

Mario

Information

🔗Mario Pizarro <piagui@...>

🔗Mario Pizarro <piagui@...>

🔗Mike Battaglia <battaglia01@...>