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22 EDO tone consonances

🔗Mario Pizarro <piagui@...>

2/6/2012 6:03:43 AM

To tuning,

Cell (A) A/B B/A (B) A/B
# PROGRESSION 22 EDO CENTS CENTS .....CONCLUSIONS
CELLS (22 EDO)
1.000000000 1 1 1.000000000 0.00 0 Any cell is consonant since
27 1.031133538 1.00084833 1.032008280 54.55 -1.468035 consonant, then the 22 EDO
56 1.065463598 1.00039671 1.065041084 109.09 0.686664 preceding cell by one of the
83 1.098632812 1.00045366 1.099131223 163.64 -0.785220 three consonant intervals
111 1.133927268 1.00033975 1.134312522 218.18 -0.588090 M, J, U.
139 1.170553269 1.00005693 1.170619915 272.73 -0.098565
167 1.208158227 1.00005693 1.208089444 327.27 0.098565 The ratios shown in A/B and
194 1.245775230 1.00078913 1.246758309 381.82 -1.365630 B/A are not necessarily
223 1.287245756 1.00045144 1.286664898 436.36 0.781380 consonant, then the 22 EDO
250 1.327322271 1.00039671 1.327848828 490.91 -0.686655 tone frequencies (B) are also
278 1.369963558 1.00028280 1.370350985 545.45 -0.489526 not necessarily consonant.
306 1.414213562 1 1.414213562 600.00 0
334 1.459646301 1.00011387 1.459480106 654.55 0.197130
362 1.506793071 1.00039671 1.506195553 709.09 0.686655
390 1.555455786 1.00067518 1.554406282 763.64 1.168500
417 1.603615321 1.00033975 1.604160153 818.18 -0.588090
445 1.655412309 1.00005693 1.655506560 872.73 -0.098565
473 1.708593750 1.00005693 1.708496477 927.27 0.098565
501 1.763777642 1.00033753 1.763182510 981.82 0.584250
529 1.820440406 1.00045144 1.819618949 1036.36 0.781380
556 1.877117157 1.00039671 1.877861821 1090.91 -0.686655
584 1.937421043 1.00028280 1.937968948 1145.45 -0.489526
612 2.000000000 1 2.000000000 1200.00 0

. Mario

February 06

🔗Charles Lucy <lucy@...>

2/6/2012 6:54:39 AM

To avoid re-inventing the wheels.

A more complete analysis of 22edo and 88edo can be found here:

http://www.lucytune.com/downloads/2288LT.pdf

The scale positions and note names from C are included, from which the harmonic significance and scales can be ascertained.

The scalecoding info. can be found here:

http://www.lucytune.com/scales/

This is without regard to the pres/absence of the "irrelevant" integer frequency ratios, which for the purposes of musical harmony, seem to be "red herrings".

On 6 Feb 2012, at 14:03, Mario Pizarro wrote:

>
> To tuning,
>
> Cell (A) A/B B/A (B) A/B
> # PROGRESSION 22 EDO CENTS CENTS ………..CONCLUSIONS
> CELLS (22 EDO)
> 1.000000000 1 1 1.000000000 0.00 0 Any cell is consonant since
> 27 1.031133538 1.00084833 1.032008280 54.55 -1.468035 consonant, then the 22 EDO
> 56 1.065463598 1.00039671 1.065041084 109.09 0.686664 preceding cell by one of the
> 83 1.098632812 1.00045366 1.099131223 163.64 -0.785220 three consonant intervals
> 111 1.133927268 1.00033975 1.134312522 218.18 -0.588090 M, J, U.
> 139 1.170553269 1.00005693 1.170619915 272.73 -0.098565
> 167 1.208158227 1.00005693 1.208089444 327.27 0.098565 The ratios shown in A/B and
> 194 1.245775230 1.00078913 1.246758309 381.82 -1.365630 B/A are not necessarily
> 223 1.287245756 1.00045144 1.286664898 436.36 0.781380 consonant, then the 22 EDO
> 250 1.327322271 1.00039671 1.327848828 490.91 -0.686655 tone frequencies (B) are also
> 278 1.369963558 1.00028280 1.370350985 545.45 -0.489526 not necessarily consonant.
> 306 1.414213562 1 1.414213562 600.00 0
> 334 1.459646301 1.00011387 1.459480106 654.55 0.197130
> 362 1.506793071 1.00039671 1.506195553 709.09 0.686655
> 390 1.555455786 1.00067518 1.554406282 763.64 1.168500
> 417 1.603615321 1.00033975 1.604160153 818.18 -0.588090
> 445 1.655412309 1.00005693 1.655506560 872.73 -0.098565
> 473 1.708593750 1.00005693 1.708496477 927.27 0.098565
> 501 1.763777642 1.00033753 1.763182510 981.82 0.584250
> 529 1.820440406 1.00045144 1.819618949 1036.36 0.781380
> 556 1.877117157 1.00039671 1.877861821 1090.91 -0.686655
> 584 1.937421043 1.00028280 1.937968948 1145.45 -0.489526
> 612 2.000000000 1 2.000000000 1200.00 0
> . Mario
> February 06
>
>

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can found at:

http://www.lullabies.co.uk

🔗Mario Pizarro <piagui@...>

2/6/2012 9:36:59 AM

JOHN, I don´t have the Charles Lucy address. Please, if necessary, send him a copy of this message. Thanks, Mario.

Mr. Lucy,

Thanks for your informations, I will examine them.

The first paragraph of my message was printed wrongly, below you have the corrected version.

Since you know well this matter I won´t insist on my conclusion. However I would like to know why A/B, B/A as being non consonant ratios I guess, lets the consonance between the progression cells and 22 EDO tones. Finally, ¿are they consonant?.

"Any cell is consonant since
they are obtained by the product
of the former cell by one of the
three consonant intervals
M, J, U.

The ratios shown in A/B and
B/A are not necessarily
consonant, then the 22 EDO
tone frequencies (B) are also
not necessarily consonant."

Thanks

Mario

February 06

----- Original Message -----
From: Charles Lucy
To: tuning@yahoogroups.com
Sent: Monday, February 06, 2012 9:54 AM
Subject: Re: [tuning] 22 EDO tone consonances

To avoid re-inventing the wheels.

A more complete analysis of 22edo and 88edo can be found here:

http://www.lucytune.com/downloads/2288LT.pdf

The scale positions and note names from C are included, from which the harmonic significance and scales can be ascertained.

The scalecoding info. can be found here:

http://www.lucytune.com/scales/

This is without regard to the pres/absence of the "irrelevant" integer frequency ratios, which for the purposes of musical harmony, seem to be "red herrings".

On 6 Feb 2012, at 14:03, Mario Pizarro wrote:

To tuning,

Cell (A) A/B B/A (B) A/B
# PROGRESSION 22 EDO CENTS CENTS ………..CONCLUSIONS
CELLS (22 EDO)
1.000000000 1 1 1.000000000 0.00 0 Any cell is consonant since
27 1.031133538 1.00084833 1.032008280 54.55 -1.468035 consonant, then the 22 EDO
56 1.065463598 1.00039671 1.065041084 109.09 0.686664 preceding cell by one of the
83 1.098632812 1.00045366 1.099131223 163.64 -0.785220 three consonant intervals
111 1.133927268 1.00033975 1.134312522 218.18 -0.588090 M, J, U.
139 1.170553269 1.00005693 1.170619915 272.73 -0.098565
167 1.208158227 1.00005693 1.208089444 327.27 0.098565 The ratios shown in A/B and
194 1.245775230 1.00078913 1.246758309 381.82 -1.365630 B/A are not necessarily
223 1.287245756 1.00045144 1.286664898 436.36 0.781380 consonant, then the 22 EDO
250 1.327322271 1.00039671 1.327848828 490.91 -0.686655 tone frequencies (B) are also
278 1.369963558 1.00028280 1.370350985 545.45 -0.489526 not necessarily consonant.
306 1.414213562 1 1.414213562 600.00 0
334 1.459646301 1.00011387 1.459480106 654.55 0.197130
362 1.506793071 1.00039671 1.506195553 709.09 0.686655
390 1.555455786 1.00067518 1.554406282 763.64 1.168500
417 1.603615321 1.00033975 1.604160153 818.18 -0.588090
445 1.655412309 1.00005693 1.655506560 872.73 -0.098565
473 1.708593750 1.00005693 1.708496477 927.27 0.098565
501 1.763777642 1.00033753 1.763182510 981.82 0.584250
529 1.820440406 1.00045144 1.819618949 1036.36 0.781380
556 1.877117157 1.00039671 1.877861821 1090.91 -0.686655
584 1.937421043 1.00028280 1.937968948 1145.45 -0.489526
612 2.000000000 1 2.000000000 1200.00 0

. Mario

February 06

Charles Lucy
lucy@...

-- Promoting global harmony through LucyTuning --

For more information on LucyTuning go to:

http://www.lucytune.com

LucyTuned Lullabies (from around the world) can found at:

http://www.lullabies.co.uk