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Absolute errors of small EDOs

Revision as of 09:52, 19 May 2024 by FloraC (talk | contribs) (FloraC moved page Equal Temperament Overtone Approximations to Absolute errors of small EDOs without leaving a redirect: Follow "relative errors of small EDOs")

This is a list of approximations for overtones in various equal temperaments. For space reasons octaves of already mentioned notes are not listed. For each base note the list shows the k-th harmonic up to a sufficiently large k and the frequency deviation in cents. Notes are highlighted with four different colors (green, yellow, orange, red) indicating distance to the maximum deviation (green = very good approximation)

12-TET

3 cents 5 cents 7 cents 9 cents 11 cents 13 cents 15 cents 17 cents 19 cents 21 cents
C-0 G-1 1.96 E-2 -13.69 Bb-2 -31.17 D-3 3.91 F#-3 -48.68 G#-3 40.53 B-3 -11.73 C#-4 4.96 Eb-4 -2.49 F-4 -29.22
C#-0 G#-1 1.96 F-2 -13.69 B-2 -31.17 Eb-3 3.91 G-3 -48.68 A-3 40.53 C-4 -11.73 D-4 4.96 E-4 -2.49 F#-4 -29.22
D-0 A-1 1.96 F#-2 -13.69 C-3 -31.17 E-3 3.91 G#-3 -48.68 Bb-3 40.53 C#-4 -11.73 Eb-4 4.96 F-4 -2.49 G-4 -29.22
Eb-0 Bb-1 1.96 G-2 -13.69 C#-3 -31.17 F-3 3.91 A-3 -48.68 B-3 40.53 D-4 -11.73 E-4 4.96 F#-4 -2.49 G#-4 -29.22
E-0 B-1 1.96 G#-2 -13.69 D-3 -31.17 F#-3 3.91 Bb-3 -48.68 C-4 40.53 Eb-4 -11.73 F-4 4.96 G-4 -2.49 A-4 -29.22
F-0 C-2 1.96 A-2 -13.69 Eb-3 -31.17 G-3 3.91 B-3 -48.68 C#-4 40.53 E-4 -11.73 F#-4 4.96 G#-4 -2.49 Bb-4 -29.22
F#-0 C#-2 1.96 Bb-2 -13.69 E-3 -31.17 G#-3 3.91 C-4 -48.68 D-4 40.53 F-4 -11.73 G-4 4.96 A-4 -2.49 B-4 -29.22
G-0 D-2 1.96 B-2 -13.69 F-3 -31.17 A-3 3.91 C#-4 -48.68 Eb-4 40.53 F#-4 -11.73 G#-4 4.96 Bb-4 -2.49 C-5 -29.22
G#-0 Eb-2 1.96 C-3 -13.69 F#-3 -31.17 Bb-3 3.91 D-4 -48.68 E-4 40.53 G-4 -11.73 A-4 4.96 B-4 -2.49 C#-5 -29.22
A-0 E-2 1.96 C#-3 -13.69 G-3 -31.17 B-3 3.91 Eb-4 -48.68 F-4 40.53 G#-4 -11.73 Bb-4 4.96 C-5 -2.49 D-5 -29.22
Bb-0 F-2 1.96 D-3 -13.69 G#-3 -31.17 C-4 3.91 E-4 -48.68 F#-4 40.53 A-4 -11.73 B-4 4.96 C#-5 -2.49 Eb-5 -29.22
B-0 F#-2 1.96 Eb-3 -13.69 A-3 -31.17 C#-4 3.91 F-4 -48.68 G-4 40.53 Bb-4 -11.73 C-5 4.96 D-5 -2.49 E-5 -29.22

31-TET

3 cents 5 cents 7 cents 9 cents 11 cents 13 cents 15 cents 17 cents 19 cents 21 cents 23 cents
C-0 G-1 5.18 E-2 -0.78 vBb-2 1.08 D-3 10.36 ^F-3 9.38 vA-3 -11.09 B-3 4.4 ^C#-4 -11.17 Eb-4 -12.16 vF-4 6.26 ^F#-4 8.92
C^-0 ^G-1 5.18 ^E-2 -0.78 Bb-2 1.08 ^D-3 10.36 F#-3 9.38 A-3 -11.09 ^B-3 4.4 vD-4 -11.17 vE-4 -12.16 F-4 6.26 vG-4 8.92
C#-0 G#-1 5.18 vF-2 -0.78 vB-2 1.08 D#-3 10.36 ^F#-3 9.38 ^A-3 -11.09 vC-3 4.4 D-4 -11.17 E-4 -12.16 ^F-4 6.26 G-4 8.92
^C#-0 ^G#-1 5.18 F-2 -0.78 B-2 1.08 Eb-3 10.36 vG-3 9.38 vBb-3 -11.09 C-4 4.4 ^D-4 -11.17 ^E-4 -12.16 F#-4 6.26 ^G-4 8.92
vD-0 vA-1 5.18 ^F-2 -0.78 ^B-2 1.08 vE-3 10.36 G-3 9.38 Bb-3 -11.09 C^-4 4.4 D#-4 -11.17 vF-4 -12.16 ^F#-4 6.26 G#-4 8.92
D-0 A-1 5.18 F#-2 -0.78 vC-2 1.08 E-3 10.36 ^G-3 9.38 vB-3 -11.09 C#-4 4.4 Eb-4 -11.17 F-4 -12.16 vG-4 6.26 ^G#-4 8.92
^D-0 ^A-1 5.18 ^F#-2 -0.78 C-3 1.08 ^E-3 10.36 G#-3 9.38 B-3 -11.09 ^C#-4 4.4 vE-4 -11.17 ^F-4 -12.16 G-4 6.26 vA-4 8.92
D#-0 vBb-1 5.18 vG-2 -0.78 C^-3 1.08 vF-3 10.36 ^G#-3 9.38 ^B-3 -11.09 vD-4 4.4 E-4 -11.17 F#-4 -12.16 ^G-4 6.26 A-4 8.92
Eb-0 Bb-1 5.18 G-2 -0.78 C#-3 1.08 F-3 10.36 vA-3 9.38 vC-3 -11.09 D-4 4.4 ^E-4 -11.17 ^F#-4 -12.16 G#-4 6.26 ^A-4 8.92
vE-0 vB-1 5.18 ^G-2 -0.78 ^C#-3 1.08 ^F-3 10.36 A-3 9.38 C-4 -11.09 ^D-4 4.4 vF-4 -11.17 vG-4 -12.16 ^G#-4 6.26 vBb-4 8.92
E-0 B-1 5.18 G#-2 -0.78 vD-3 1.08 F#-3 10.36 ^A-3 9.38 C^-4 -11.09 D#-4 4.4 F-4 -11.17 G-4 -12.16 vA-4 6.26 Bb-4 8.92
^E-0 ^B-1 5.18 ^G#-2 -0.78 D-3 1.08 ^F#-3 10.36 vBb-3 9.38 C#-4 -11.09 Eb-4 4.4 ^F-4 -11.17 ^G-4 -12.16 A-4 6.26 vB-4 8.92
vF-0 vC-1 5.18 vA-2 -0.78 ^D-3 1.08 vG-3 10.36 Bb-3 9.38 ^C#-4 -11.09 vE-4 4.4 F#-4 -11.17 G#-4 -12.16 ^A-4 6.26 B-4 8.92
F-0 C-2 5.18 A-2 -0.78 D#-3 1.08 G-3 10.36 vB-3 9.38 vD-4 -11.09 E-4 4.4 ^F#-4 -11.17 ^G#-4 -12.16 vBb-4 6.26 ^B-4 8.92
^F-0 C^-2 5.18 ^A-2 -0.78 Eb-3 1.08 ^G-3 10.36 B-3 9.38 D-4 -11.09 ^E-4 4.4 vG-4 -11.17 vA-4 -12.16 Bb-4 6.26 vC-4 8.92
F#-0 C#-2 5.18 vBb-2 -0.78 vE-3 1.08 G#-3 10.36 ^B-3 9.38 ^D-4 -11.09 vF-4 4.4 G-4 -11.17 A-4 -12.16 vB-4 6.26 C-5 8.92
^F#-0 ^C#-2 5.18 Bb-2 -0.78 E-3 1.08 ^G#-3 10.36 vC-3 9.38 D#-4 -11.09 F-4 4.4 ^G-4 -11.17 ^A-4 -12.16 B-4 6.26 C^-5 8.92
vG-0 vD-2 5.18 vB-2 -0.78 ^E-3 1.08 vA-3 10.36 C-4 9.38 Eb-4 -11.09 ^F-4 4.4 G#-4 -11.17 vBb-4 -12.16 ^B-4 6.26 C#-5 8.92
G-0 D-2 5.18 B-2 -0.78 vF-3 1.08 A-3 10.36 C^-4 9.38 vE-4 -11.09 F#-4 4.4 ^G#-4 -11.17 Bb-4 -12.16 vC-4 6.26 ^C#-5 8.92
^G-0 ^D-2 5.18 ^B-2 -0.78 F-3 1.08 ^A-3 10.36 C#-4 9.38 E-4 -11.09 ^F#-4 4.4 vA-4 -11.17 vB-4 -12.16 C-5 6.26 vD-5 8.92
G#-0 D#-2 5.18 vC-2 -0.78 ^F-3 1.08 vBb-3 10.36 ^C#-4 9.38 ^E-4 -11.09 vG-4 4.4 A-4 -11.17 B-4 -12.16 C^-5 6.26 D-5 8.92
^G#-0 Eb-2 5.18 C-3 -0.78 F#-3 1.08 Bb-3 10.36 vD-4 9.38 vF-4 -11.09 G-4 4.4 ^A-4 -11.17 ^B-4 -12.16 C#-5 6.26 ^D-5 8.92
vA-0 vE-2 5.18 C^-3 -0.78 ^F#-3 1.08 vB-3 10.36 D-4 9.38 F-4 -11.09 ^G-4 4.4 vBb-4 -11.17 vC-4 -12.16 ^C#-5 6.26 D#-5 8.92
A-0 E-2 5.18 C#-3 -0.78 vG-3 1.08 B-3 10.36 ^D-4 9.38 ^F-4 -11.09 G#-4 4.4 Bb-4 -11.17 C-5 -12.16 vD-5 6.26 Eb-5 8.92
^A-0 ^E-2 5.18 ^C#-3 -0.78 G-3 1.08 ^B-3 10.36 D#-4 9.38 F#-4 -11.09 ^G#-4 4.4 vB-4 -11.17 C^-5 -12.16 D-5 6.26 vE-5 8.92
vBb-0 vF-2 5.18 vD-3 -0.78 ^G-3 1.08 vC-3 10.36 Eb-4 9.38 ^F#-4 -11.09 vA-4 4.4 B-4 -11.17 C#-5 -12.16 ^D-5 6.26 E-5 8.92
Bb-0 F-2 5.18 D-3 -0.78 G#-3 1.08 C-4 10.36 vE-4 9.38 vG-4 -11.09 A-4 4.4 ^B-4 -11.17 ^C#-5 -12.16 D#-5 6.26 ^E-5 8.92
vB-0 ^F-2 5.18 ^D-3 -0.78 ^G#-3 1.08 C^-4 10.36 E-4 9.38 G-4 -11.09 ^A-4 4.4 vC-4 -11.17 vD-5 -12.16 Eb-5 6.26 vF-5 8.92
B-0 F#-2 5.18 D#-3 -0.78 vA-3 1.08 C#-4 10.36 ^E-4 9.38 ^G-4 -11.09 vBb-4 4.4 C-5 -11.17 D-5 -12.16 vE-5 6.26 F-5 8.92
^B-0 ^F#-2 5.18 Eb-3 -0.78 A-3 1.08 ^C#-4 10.36 vF-4 9.38 G#-4 -11.09 Bb-4 4.4 C^-5 -11.17 ^D-5 -12.16 E-5 6.26 ^F-5 8.92
vC-0 vG-2 5.18 vE-3 -0.78 ^A-3 1.08 vD-4 10.36 F-4 9.38 ^G#-4 -11.09 vB-4 4.4 C#-5 -11.17 D#-5 -12.16 ^E-5 6.26 F#-5 8.92
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