7/4, 11/8

Mike Battaglia

OK. The only point to define is the acceptable difference between the ratio
(1.75 = 7/4) whose condition of consonant or disonant is to be known and the
decimal value of the cell. The difference should be less than a reference.
The lowest difference is 0.000112 that is less than the established
reference of 0.0005. So, based on a reference of 0.0005, 7/4 is consonant.

Similarly, 11/8 = 1.375 is also consonant.
M 279 1.37151045250
M 280 1.37305909407
J 281 1.37461253344
J 282 1.37616773034
U 283 1.37783798031
U 284 1.37951025746

I suggest you to contact Mike Battaglia and propose this plan or a better
one, it is your idea.
.............Cell frequency
M- 493- 1.74791410141
M- 494- 1.74988775930
J- 495- 1.75186753174
J- 496- 1.75384954404
M- 497- 1.75582990393
M- 498- 1.7578125
..........................................
493 ---1.75 - 1.747914 = 0.002086
494 ---1.75 - 1.749887 = 0.000112 --- If it is settled 0.000500 as the reference.
495 ---1.75 - 1.751867 = 0.001867
496 --- > .......................................
497 --- >> .....................................
498 --- >>> ...................................

Mario

January, 7

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "John H. Chalmers" <jhchalmers@...>
To: "Mario Pizarro" <piagui@...m>
Sent: Saturday, January 07, 2012 3:04 PM
Subject: Re: A useful tool to recognize consonance.

> Mario: J 281 and J 282 are so close to 1.375 that I doubt in music
> performance, one could hear the difference between either of them and
> 11/8. Likewise, M493, M494 and J495 are so close to 7/4, that the
> difference wouldn't matter.
>
> As I said in my previous post, consonance is a very complex phenomenon
> that depends upon context, timbre, register, loudness, style and prior
> experience. Close approximations to consonant intervals are perceived as
> consonant also--for thirds, some people actually prefer slightly mistuned
> intervals, perhaps because of their experience with 12-tone equal
> temperament or because they like the richer and dynamic sound of the
> tempered intervals. If these perceptual findings weren't true, meantone
> and equal temperament would never have been adopted in Western music.
>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

OK. The only point to define is the acceptable difference between the ratio
(1.75 = 7/4) whose condition of consonant or disonant is to be known and the
decimal value of the cell. The difference should be less than a reference.
The lowest difference is 0.000112 that is less than the established
reference of 0.0005. So, based on a reference of 0.0005, 7/4 is consonant.

Similarly, 11/8 = 1.375 is also consonant.
M 279 1.37151045250
M 280 1.37305909407
J 281 1.37461253344
J 282 1.37616773034
U 283 1.37783798031
U 284 1.37951025746

I suggest you to contact Mike Battaglia and propose this plan or a better
one, it is your idea.
.............Cell frequency
M- 493- 1.74791410141
M- 494- 1.74988775930
J- 495- 1.75186753174
J- 496- 1.75384954404
M- 497- 1.75582990393
M- 498- 1.7578125
..........................................
493 ---1.75 - 1.747914 = 0.002086
494 ---1.75 - 1.749887 = 0.000112 --- If it is settled 0.000500 as the reference.
495 ---1.75 - 1.751867 = 0.001867
496 --- > .......................................
497 --- >> .....................................
498 --- >>> ...................................

Mario

January, 7

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "John H. Chalmers" <jhchalmers@...>
To: "Mario Pizarro" <piagui@...>
Sent: Saturday, January 07, 2012 3:04 PM
Subject: Re: A useful tool to recognize consonance.

> Mario: J 281 and J 282 are so close to 1.375 that I doubt in music
> performance, one could hear the difference between either of them and
> 11/8. Likewise, M493, M494 and J495 are so close to 7/4, that the
> difference wouldn't matter.
>
> As I said in my previous post, consonance is a very complex phenomenon
> that depends upon context, timbre, register, loudness, style and prior
> experience. Close approximations to consonant intervals are perceived as
> consonant also--for thirds, some people actually prefer slightly mistuned
> intervals, perhaps because of their experience with 12-tone equal
> temperament or because they like the richer and dynamic sound of the
> tempered intervals. If these perceptual findings weren't true, meantone
> and equal temperament would never have been adopted in Western music.