Absolute errors of small EDOs: Difference between revisions
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{| class="wikitable" | {| class="wikitable" | ||
! | ! Funda-<br>mental | ||
! | ! colspan="2"| 3rd harmonic | ||
! | ! colspan="2"| 5th harmonic | ||
! | ! colspan="2"| 7th harmonic | ||
! | ! colspan="2"| 9th harmonic | ||
! | ! colspan="2"| 11th harmonic | ||
! | ! colspan="2"| 13th harmonic | ||
! | ! colspan="2"| 15th harmonic | ||
! | ! colspan="2"| 17th harmonic | ||
! | ! colspan="2"| 19th harmonic | ||
! | ! colspan="2"| 21st harmonic | ||
! | ! colspan="2"| 23rd harmonic | ||
|- | |- | ||
! Note | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
|- | |- | ||
| C | | C-0||style="background:#99c140;" | G-1 || 1.96||style="background:#e7b416;" | E-2 || -13.69||style="background:#db7b2b;" | Bb-2 || -31.17||style="background:#99c140;" | D-3 || 3.91||style="background:#cc3232;" | F#-3 || -48.68||style="background:#cc3232;" | G#-3 || 40.53||style="background:#99c140;" | B-3 || -11.73||style="background:#99c140;" | C#-4 || 4.96||style="background:#99c140;" | Eb-4 || -2.49||style="background:#db7b2b;" | F-4 || -29.22||style="background:#db7b2b;" | F#-4 || 28.27 | ||
|- | |- | ||
| | | C#-0||style="background:#99c140;" | G#-1 || 1.96||style="background:#e7b416;" | F-2 || -13.69||style="background:#db7b2b;" | B-2 || -31.17||style="background:#99c140;" | Eb-3 || 3.91||style="background:#cc3232;" | G-3 || -48.68||style="background:#cc3232;" | A-3 || 40.53||style="background:#99c140;" | C-4 || -11.73||style="background:#99c140;" | D-4 || 4.96||style="background:#99c140;" | E-4 || -2.49||style="background:#db7b2b;" | F#-4 || -29.22||style="background:#db7b2b;" | G-4 || 28.27 | ||
|- | |- | ||
| | | D-0||style="background:#99c140;" | A-1 || 1.96||style="background:#e7b416;" | F#-2 || -13.69||style="background:#db7b2b;" | C-3 || -31.17||style="background:#99c140;" | E-3 || 3.91||style="background:#cc3232;" | G#-3 || -48.68||style="background:#cc3232;" | Bb-3 || 40.53||style="background:#99c140;" | C#-4 || -11.73||style="background:#99c140;" | Eb-4 || 4.96||style="background:#99c140;" | F-4 || -2.49||style="background:#db7b2b;" | G-4 || -29.22||style="background:#db7b2b;" | G#-4 || 28.27 | ||
|- | |- | ||
| | | Eb-0||style="background:#99c140;" | Bb-1 || 1.96||style="background:#e7b416;" | G-2 || -13.69||style="background:#db7b2b;" | C#-3 || -31.17||style="background:#99c140;" | F-3 || 3.91||style="background:#cc3232;" | A-3 || -48.68||style="background:#cc3232;" | B-3 || 40.53||style="background:#99c140;" | D-4 || -11.73||style="background:#99c140;" | E-4 || 4.96||style="background:#99c140;" | F#-4 || -2.49||style="background:#db7b2b;" | G#-4 || -29.22||style="background:#db7b2b;" | A-4 || 28.27 | ||
|- | |- | ||
| | | E-0||style="background:#99c140;" | B-1 || 1.96||style="background:#e7b416;" | G#-2 || -13.69||style="background:#db7b2b;" | D-3 || -31.17||style="background:#99c140;" | F#-3 || 3.91||style="background:#cc3232;" | Bb-3 || -48.68||style="background:#cc3232;" | C-4 || 40.53||style="background:#99c140;" | Eb-4 || -11.73||style="background:#99c140;" | F-4 || 4.96||style="background:#99c140;" | G-4 || -2.49||style="background:#db7b2b;" | A-4 || -29.22||style="background:#db7b2b;" | Bb-4 || 28.27 | ||
|- | |- | ||
| F | | F-0||style="background:#99c140;" | C-2 || 1.96||style="background:#e7b416;" | A-2 || -13.69||style="background:#db7b2b;" | Eb-3 || -31.17||style="background:#99c140;" | G-3 || 3.91||style="background:#cc3232;" | B-3 || -48.68||style="background:#cc3232;" | C#-4 || 40.53||style="background:#99c140;" | E-4 || -11.73||style="background:#99c140;" | F#-4 || 4.96||style="background:#99c140;" | G#-4 || -2.49||style="background:#db7b2b;" | Bb-4 || -29.22||style="background:#db7b2b;" | B-4 || 28.27 | ||
|- | |- | ||
| | | F#-0||style="background:#99c140;" | C#-2 || 1.96||style="background:#e7b416;" | Bb-2 || -13.69||style="background:#db7b2b;" | E-3 || -31.17||style="background:#99c140;" | G#-3 || 3.91||style="background:#cc3232;" | C-4 || -48.68||style="background:#cc3232;" | D-4 || 40.53||style="background:#99c140;" | F-4 || -11.73||style="background:#99c140;" | G-4 || 4.96||style="background:#99c140;" | A-4 || -2.49||style="background:#db7b2b;" | B-4 || -29.22||style="background:#db7b2b;" | C-5 || 28.27 | ||
|- | |- | ||
| G | | G-0||style="background:#99c140;" | D-2 || 1.96||style="background:#e7b416;" | B-2 || -13.69||style="background:#db7b2b;" | F-3 || -31.17||style="background:#99c140;" | A-3 || 3.91||style="background:#cc3232;" | C#-4 || -48.68||style="background:#cc3232;" | Eb-4 || 40.53||style="background:#99c140;" | F#-4 || -11.73||style="background:#99c140;" | G#-4 || 4.96||style="background:#99c140;" | Bb-4 || -2.49||style="background:#db7b2b;" | C-5 || -29.22||style="background:#db7b2b;" | C#-5 || 28.27 | ||
|- | |- | ||
| | | G#-0||style="background:#99c140;" | Eb-2 || 1.96||style="background:#e7b416;" | C-3 || -13.69||style="background:#db7b2b;" | F#-3 || -31.17||style="background:#99c140;" | Bb-3 || 3.91||style="background:#cc3232;" | D-4 || -48.68||style="background:#cc3232;" | E-4 || 40.53||style="background:#99c140;" | G-4 || -11.73||style="background:#99c140;" | A-4 || 4.96||style="background:#99c140;" | B-4 || -2.49||style="background:#db7b2b;" | C#-5 || -29.22||style="background:#db7b2b;" | D-5 || 28.27 | ||
|- | |- | ||
| | | A-0||style="background:#99c140;" | E-2 || 1.96||style="background:#e7b416;" | C#-3 || -13.69||style="background:#db7b2b;" | G-3 || -31.17||style="background:#99c140;" | B-3 || 3.91||style="background:#cc3232;" | Eb-4 || -48.68||style="background:#cc3232;" | F-4 || 40.53||style="background:#99c140;" | G#-4 || -11.73||style="background:#99c140;" | Bb-4 || 4.96||style="background:#99c140;" | C-5 || -2.49||style="background:#db7b2b;" | D-5 || -29.22||style="background:#db7b2b;" | Eb-5 || 28.27 | ||
|- | |- | ||
| B-0||style="background:#99c140;" | F#-2 || 1.96||style="background:#e7b416;" | Eb-3 || -13.69||style="background:#db7b2b;" | A-3 || -31.17||style="background:#99c140;" | C#-4 || 3.91||style="background:#cc3232;" | F-4 || -48.68||style="background:#cc3232;" | G-4 || 40.53||style="background:#99c140;" | Bb-4 || -11.73||style="background:#99c140;" | C-5 || 4.96||style="background:#99c140;" | D-5 || -2.49||style="background:#db7b2b;" | E-5 || -29.22 | | Bb-0||style="background:#99c140;" | F-2 || 1.96||style="background:#e7b416;" | D-3 || -13.69||style="background:#db7b2b;" | G#-3 || -31.17||style="background:#99c140;" | C-4 || 3.91||style="background:#cc3232;" | E-4 || -48.68||style="background:#cc3232;" | F#-4 || 40.53||style="background:#99c140;" | A-4 || -11.73||style="background:#99c140;" | B-4 || 4.96||style="background:#99c140;" | C#-5 || -2.49||style="background:#db7b2b;" | Eb-5 || -29.22||style="background:#db7b2b;" | E-5 || 28.27 | ||
|- | |||
| B-0||style="background:#99c140;" | F#-2 || 1.96||style="background:#e7b416;" | Eb-3 || -13.69||style="background:#db7b2b;" | A-3 || -31.17||style="background:#99c140;" | C#-4 || 3.91||style="background:#cc3232;" | F-4 || -48.68||style="background:#cc3232;" | G-4 || 40.53||style="background:#99c140;" | Bb-4 || -11.73||style="background:#99c140;" | C-5 || 4.96||style="background:#99c140;" | D-5 || -2.49||style="background:#db7b2b;" | E-5 || -29.22||style="background:#db7b2b;" | F-5 || 28.27 | |||
|} | |} | ||
| Line 54: | Line 69: | ||
{| class="wikitable" | {| class="wikitable" | ||
! | ! Funda-<br>mental | ||
! | ! colspan="2"| 3rd harmonic | ||
! | ! colspan="2"| 5th harmonic | ||
! | ! colspan="2"| 7th harmonic | ||
! | ! colspan="2"| 9th harmonic | ||
! | ! colspan="2"| 11th harmonic | ||
! | ! colspan="2"| 13th harmonic | ||
! | ! colspan="2"| 15th harmonic | ||
! | ! colspan="2"| 17th harmonic | ||
! | ! colspan="2"| 19th harmonic | ||
! | ! colspan="2"| 21st harmonic | ||
! | ! colspan="2"| 23rd harmonic | ||
|- | |- | ||
! Note | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
! Note | |||
! Err(¢) | |||
|- | |- | ||
| C | | C-0||style="background:#e7b416;" | G-1 || 5.18||style="background:#99c140;" | E-2 || -0.78||style="background:#99c140;" | vBb-2 || 1.08||style="background:#db7b2b;" | D-3 || 10.36||style="background:#e7b416;" | ^F-3 || 9.38||style="background:#db7b2b;" | vA-3 || -11.09||style="background:#99c140;" | B-3 || 4.4||style="background:#db7b2b;" | ^C#-4 || -11.17||style="background:#db7b2b;" | Eb-4 || -12.16||style="background:#e7b416;" | vF-4 || 6.26||style="background:#e7b416;" | ^F#-4 || 8.92 | ||
|- | |- | ||
| C | | ^C-0||style="background:#e7b416;" | ^G-1 || 5.18||style="background:#99c140;" | ^E-2 || -0.78||style="background:#99c140;" | Bb-2 || 1.08||style="background:#db7b2b;" | ^D-3 || 10.36||style="background:#e7b416;" | F#-3 || 9.38||style="background:#db7b2b;" | A-3 || -11.09||style="background:#99c140;" | ^B-3 || 4.4||style="background:#db7b2b;" | vD-4 || -11.17||style="background:#db7b2b;" | vE-4 || -12.16||style="background:#e7b416;" | F-4 || 6.26||style="background:#e7b416;" | vG-4 || 8.92 | ||
|- | |- | ||
| | | C#-0||style="background:#e7b416;" | G#-1 || 5.18||style="background:#99c140;" | vF-2 || -0.78||style="background:#99c140;" | vB-2 || 1.08||style="background:#db7b2b;" | D#-3 || 10.36||style="background:#e7b416;" | ^F#-3 || 9.38||style="background:#db7b2b;" | ^A-3 || -11.09||style="background:#99c140;" | vC-3 || 4.4||style="background:#db7b2b;" | D-4 || -11.17||style="background:#db7b2b;" | E-4 || -12.16||style="background:#e7b416;" | ^F-4 || 6.26||style="background:#e7b416;" | G-4 || 8.92 | ||
|- | |- | ||
| | | ^C#-0||style="background:#e7b416;" | ^G#-1 || 5.18||style="background:#99c140;" | F-2 || -0.78||style="background:#99c140;" | B-2 || 1.08||style="background:#db7b2b;" | Eb-3 || 10.36||style="background:#e7b416;" | vG-3 || 9.38||style="background:#db7b2b;" | vBb-3 || -11.09||style="background:#99c140;" | C-4 || 4.4||style="background:#db7b2b;" | ^D-4 || -11.17||style="background:#db7b2b;" | ^E-4 || -12.16||style="background:#e7b416;" | F#-4 || 6.26||style="background:#e7b416;" | ^G-4 || 8.92 | ||
|- | |- | ||
| | | vD-0||style="background:#e7b416;" | vA-1 || 5.18||style="background:#99c140;" | ^F-2 || -0.78||style="background:#99c140;" | ^B-2 || 1.08||style="background:#db7b2b;" | vE-3 || 10.36||style="background:#e7b416;" | G-3 || 9.38||style="background:#db7b2b;" | Bb-3 || -11.09||style="background:#99c140;" | ^C-4 || 4.4||style="background:#db7b2b;" | D#-4 || -11.17||style="background:#db7b2b;" | vF-4 || -12.16||style="background:#e7b416;" | ^F#-4 || 6.26||style="background:#e7b416;" | G#-4 || 8.92 | ||
|- | |- | ||
| | | D-0||style="background:#e7b416;" | A-1 || 5.18||style="background:#99c140;" | F#-2 || -0.78||style="background:#99c140;" | vC-2 || 1.08||style="background:#db7b2b;" | E-3 || 10.36||style="background:#e7b416;" | ^G-3 || 9.38||style="background:#db7b2b;" | vB-3 || -11.09||style="background:#99c140;" | C#-4 || 4.4||style="background:#db7b2b;" | Eb-4 || -11.17||style="background:#db7b2b;" | F-4 || -12.16||style="background:#e7b416;" | vG-4 || 6.26||style="background:#e7b416;" | ^G#-4 || 8.92 | ||
|- | |- | ||
| D | | ^D-0||style="background:#e7b416;" | ^A-1 || 5.18||style="background:#99c140;" | ^F#-2 || -0.78||style="background:#99c140;" | C-3 || 1.08||style="background:#db7b2b;" | ^E-3 || 10.36||style="background:#e7b416;" | G#-3 || 9.38||style="background:#db7b2b;" | B-3 || -11.09||style="background:#99c140;" | ^C#-4 || 4.4||style="background:#db7b2b;" | vE-4 || -11.17||style="background:#db7b2b;" | ^F-4 || -12.16||style="background:#e7b416;" | G-4 || 6.26||style="background:#e7b416;" | vA-4 || 8.92 | ||
|- | |- | ||
| | | D#-0||style="background:#e7b416;" | vBb-1 || 5.18||style="background:#99c140;" | vG-2 || -0.78||style="background:#99c140;" | ^C-3 || 1.08||style="background:#db7b2b;" | vF-3 || 10.36||style="background:#e7b416;" | ^G#-3 || 9.38||style="background:#db7b2b;" | ^B-3 || -11.09||style="background:#99c140;" | vD-4 || 4.4||style="background:#db7b2b;" | E-4 || -11.17||style="background:#db7b2b;" | F#-4 || -12.16||style="background:#e7b416;" | ^G-4 || 6.26||style="background:#e7b416;" | A-4 || 8.92 | ||
|- | |- | ||
| | | Eb-0||style="background:#e7b416;" | Bb-1 || 5.18||style="background:#99c140;" | G-2 || -0.78||style="background:#99c140;" | C#-3 || 1.08||style="background:#db7b2b;" | F-3 || 10.36||style="background:#e7b416;" | vA-3 || 9.38||style="background:#db7b2b;" | vC-3 || -11.09||style="background:#99c140;" | D-4 || 4.4||style="background:#db7b2b;" | ^E-4 || -11.17||style="background:#db7b2b;" | ^F#-4 || -12.16||style="background:#e7b416;" | G#-4 || 6.26||style="background:#e7b416;" | ^A-4 || 8.92 | ||
|- | |- | ||
| | | vE-0||style="background:#e7b416;" | vB-1 || 5.18||style="background:#99c140;" | ^G-2 || -0.78||style="background:#99c140;" | ^C#-3 || 1.08||style="background:#db7b2b;" | ^F-3 || 10.36||style="background:#e7b416;" | A-3 || 9.38||style="background:#db7b2b;" | C-4 || -11.09||style="background:#99c140;" | ^D-4 || 4.4||style="background:#db7b2b;" | vF-4 || -11.17||style="background:#db7b2b;" | vG-4 || -12.16||style="background:#e7b416;" | ^G#-4 || 6.26||style="background:#e7b416;" | vBb-4 || 8.92 | ||
|- | |- | ||
| | | E-0||style="background:#e7b416;" | B-1 || 5.18||style="background:#99c140;" | G#-2 || -0.78||style="background:#99c140;" | vD-3 || 1.08||style="background:#db7b2b;" | F#-3 || 10.36||style="background:#e7b416;" | ^A-3 || 9.38||style="background:#db7b2b;" | ^C-4 || -11.09||style="background:#99c140;" | D#-4 || 4.4||style="background:#db7b2b;" | F-4 || -11.17||style="background:#db7b2b;" | G-4 || -12.16||style="background:#e7b416;" | vA-4 || 6.26||style="background:#e7b416;" | Bb-4 || 8.92 | ||
|- | |- | ||
| | | ^E-0||style="background:#e7b416;" | ^B-1 || 5.18||style="background:#99c140;" | ^G#-2 || -0.78||style="background:#99c140;" | D-3 || 1.08||style="background:#db7b2b;" | ^F#-3 || 10.36||style="background:#e7b416;" | vBb-3 || 9.38||style="background:#db7b2b;" | C#-4 || -11.09||style="background:#99c140;" | Eb-4 || 4.4||style="background:#db7b2b;" | ^F-4 || -11.17||style="background:#db7b2b;" | ^G-4 || -12.16||style="background:#e7b416;" | A-4 || 6.26||style="background:#e7b416;" | vB-4 || 8.92 | ||
|- | |- | ||
| | | vF-0||style="background:#e7b416;" | vC-1 || 5.18||style="background:#99c140;" | vA-2 || -0.78||style="background:#99c140;" | ^D-3 || 1.08||style="background:#db7b2b;" | vG-3 || 10.36||style="background:#e7b416;" | Bb-3 || 9.38||style="background:#db7b2b;" | ^C#-4 || -11.09||style="background:#99c140;" | vE-4 || 4.4||style="background:#db7b2b;" | F#-4 || -11.17||style="background:#db7b2b;" | G#-4 || -12.16||style="background:#e7b416;" | ^A-4 || 6.26||style="background:#e7b416;" | B-4 || 8.92 | ||
|- | |- | ||
| | | F-0||style="background:#e7b416;" | C-2 || 5.18||style="background:#99c140;" | A-2 || -0.78||style="background:#99c140;" | D#-3 || 1.08||style="background:#db7b2b;" | G-3 || 10.36||style="background:#e7b416;" | vB-3 || 9.38||style="background:#db7b2b;" | vD-4 || -11.09||style="background:#99c140;" | E-4 || 4.4||style="background:#db7b2b;" | ^F#-4 || -11.17||style="background:#db7b2b;" | ^G#-4 || -12.16||style="background:#e7b416;" | vBb-4 || 6.26||style="background:#e7b416;" | ^B-4 || 8.92 | ||
|- | |- | ||
| F | | ^F-0||style="background:#e7b416;" | ^C-2 || 5.18||style="background:#99c140;" | ^A-2 || -0.78||style="background:#99c140;" | Eb-3 || 1.08||style="background:#db7b2b;" | ^G-3 || 10.36||style="background:#e7b416;" | B-3 || 9.38||style="background:#db7b2b;" | D-4 || -11.09||style="background:#99c140;" | ^E-4 || 4.4||style="background:#db7b2b;" | vG-4 || -11.17||style="background:#db7b2b;" | vA-4 || -12.16||style="background:#e7b416;" | Bb-4 || 6.26||style="background:#e7b416;" | vC-4 || 8.92 | ||
|- | |- | ||
| | | F#-0||style="background:#e7b416;" | C#-2 || 5.18||style="background:#99c140;" | vBb-2 || -0.78||style="background:#99c140;" | vE-3 || 1.08||style="background:#db7b2b;" | G#-3 || 10.36||style="background:#e7b416;" | ^B-3 || 9.38||style="background:#db7b2b;" | ^D-4 || -11.09||style="background:#99c140;" | vF-4 || 4.4||style="background:#db7b2b;" | G-4 || -11.17||style="background:#db7b2b;" | A-4 || -12.16||style="background:#e7b416;" | vB-4 || 6.26||style="background:#e7b416;" | C-5 || 8.92 | ||
|- | |- | ||
| | | ^F#-0||style="background:#e7b416;" | ^C#-2 || 5.18||style="background:#99c140;" | Bb-2 || -0.78||style="background:#99c140;" | E-3 || 1.08||style="background:#db7b2b;" | ^G#-3 || 10.36||style="background:#e7b416;" | vC-3 || 9.38||style="background:#db7b2b;" | D#-4 || -11.09||style="background:#99c140;" | F-4 || 4.4||style="background:#db7b2b;" | ^G-4 || -11.17||style="background:#db7b2b;" | ^A-4 || -12.16||style="background:#e7b416;" | B-4 || 6.26||style="background:#e7b416;" | ^C-5 || 8.92 | ||
|- | |- | ||
| | | vG-0||style="background:#e7b416;" | vD-2 || 5.18||style="background:#99c140;" | vB-2 || -0.78||style="background:#99c140;" | ^E-3 || 1.08||style="background:#db7b2b;" | vA-3 || 10.36||style="background:#e7b416;" | C-4 || 9.38||style="background:#db7b2b;" | Eb-4 || -11.09||style="background:#99c140;" | ^F-4 || 4.4||style="background:#db7b2b;" | G#-4 || -11.17||style="background:#db7b2b;" | vBb-4 || -12.16||style="background:#e7b416;" | ^B-4 || 6.26||style="background:#e7b416;" | C#-5 || 8.92 | ||
|- | |- | ||
| | | G-0||style="background:#e7b416;" | D-2 || 5.18||style="background:#99c140;" | B-2 || -0.78||style="background:#99c140;" | vF-3 || 1.08||style="background:#db7b2b;" | A-3 || 10.36||style="background:#e7b416;" | ^C-4 || 9.38||style="background:#db7b2b;" | vE-4 || -11.09||style="background:#99c140;" | F#-4 || 4.4||style="background:#db7b2b;" | ^G#-4 || -11.17||style="background:#db7b2b;" | Bb-4 || -12.16||style="background:#e7b416;" | vC-4 || 6.26||style="background:#e7b416;" | ^C#-5 || 8.92 | ||
|- | |- | ||
| G | | ^G-0||style="background:#e7b416;" | ^D-2 || 5.18||style="background:#99c140;" | ^B-2 || -0.78||style="background:#99c140;" | F-3 || 1.08||style="background:#db7b2b;" | ^A-3 || 10.36||style="background:#e7b416;" | C#-4 || 9.38||style="background:#db7b2b;" | E-4 || -11.09||style="background:#99c140;" | ^F#-4 || 4.4||style="background:#db7b2b;" | vA-4 || -11.17||style="background:#db7b2b;" | vB-4 || -12.16||style="background:#e7b416;" | C-5 || 6.26||style="background:#e7b416;" | vD-5 || 8.92 | ||
|- | |- | ||
| | | G#-0||style="background:#e7b416;" | D#-2 || 5.18||style="background:#99c140;" | vC-2 || -0.78||style="background:#99c140;" | ^F-3 || 1.08||style="background:#db7b2b;" | vBb-3 || 10.36||style="background:#e7b416;" | ^C#-4 || 9.38||style="background:#db7b2b;" | ^E-4 || -11.09||style="background:#99c140;" | vG-4 || 4.4||style="background:#db7b2b;" | A-4 || -11.17||style="background:#db7b2b;" | B-4 || -12.16||style="background:#e7b416;" | ^C-5 || 6.26||style="background:#e7b416;" | D-5 || 8.92 | ||
|- | |- | ||
| | | ^G#-0||style="background:#e7b416;" | Eb-2 || 5.18||style="background:#99c140;" | C-3 || -0.78||style="background:#99c140;" | F#-3 || 1.08||style="background:#db7b2b;" | Bb-3 || 10.36||style="background:#e7b416;" | vD-4 || 9.38||style="background:#db7b2b;" | vF-4 || -11.09||style="background:#99c140;" | G-4 || 4.4||style="background:#db7b2b;" | ^A-4 || -11.17||style="background:#db7b2b;" | ^B-4 || -12.16||style="background:#e7b416;" | C#-5 || 6.26||style="background:#e7b416;" | ^D-5 || 8.92 | ||
|- | |- | ||
| | | vA-0||style="background:#e7b416;" | vE-2 || 5.18||style="background:#99c140;" | ^C-3 || -0.78||style="background:#99c140;" | ^F#-3 || 1.08||style="background:#db7b2b;" | vB-3 || 10.36||style="background:#e7b416;" | D-4 || 9.38||style="background:#db7b2b;" | F-4 || -11.09||style="background:#99c140;" | ^G-4 || 4.4||style="background:#db7b2b;" | vBb-4 || -11.17||style="background:#db7b2b;" | vC-4 || -12.16||style="background:#e7b416;" | ^C#-5 || 6.26||style="background:#e7b416;" | D#-5 || 8.92 | ||
|- | |- | ||
| | | A-0||style="background:#e7b416;" | E-2 || 5.18||style="background:#99c140;" | C#-3 || -0.78||style="background:#99c140;" | vG-3 || 1.08||style="background:#db7b2b;" | B-3 || 10.36||style="background:#e7b416;" | ^D-4 || 9.38||style="background:#db7b2b;" | ^F-4 || -11.09||style="background:#99c140;" | G#-4 || 4.4||style="background:#db7b2b;" | Bb-4 || -11.17||style="background:#db7b2b;" | C-5 || -12.16||style="background:#e7b416;" | vD-5 || 6.26||style="background:#e7b416;" | Eb-5 || 8.92 | ||
|- | |- | ||
| | | ^A-0||style="background:#e7b416;" | ^E-2 || 5.18||style="background:#99c140;" | ^C#-3 || -0.78||style="background:#99c140;" | G-3 || 1.08||style="background:#db7b2b;" | ^B-3 || 10.36||style="background:#e7b416;" | D#-4 || 9.38||style="background:#db7b2b;" | F#-4 || -11.09||style="background:#99c140;" | ^G#-4 || 4.4||style="background:#db7b2b;" | vB-4 || -11.17||style="background:#db7b2b;" | ^C-5 || -12.16||style="background:#e7b416;" | D-5 || 6.26||style="background:#e7b416;" | vE-5 || 8.92 | ||
|- | |- | ||
| | | vBb-0||style="background:#e7b416;" | vF-2 || 5.18||style="background:#99c140;" | vD-3 || -0.78||style="background:#99c140;" | ^G-3 || 1.08||style="background:#db7b2b;" | vC-3 || 10.36||style="background:#e7b416;" | Eb-4 || 9.38||style="background:#db7b2b;" | ^F#-4 || -11.09||style="background:#99c140;" | vA-4 || 4.4||style="background:#db7b2b;" | B-4 || -11.17||style="background:#db7b2b;" | C#-5 || -12.16||style="background:#e7b416;" | ^D-5 || 6.26||style="background:#e7b416;" | E-5 || 8.92 | ||
|- | |- | ||
| | | Bb-0||style="background:#e7b416;" | F-2 || 5.18||style="background:#99c140;" | D-3 || -0.78||style="background:#99c140;" | G#-3 || 1.08||style="background:#db7b2b;" | C-4 || 10.36||style="background:#e7b416;" | vE-4 || 9.38||style="background:#db7b2b;" | vG-4 || -11.09||style="background:#99c140;" | A-4 || 4.4||style="background:#db7b2b;" | ^B-4 || -11.17||style="background:#db7b2b;" | ^C#-5 || -12.16||style="background:#e7b416;" | D#-5 || 6.26||style="background:#e7b416;" | ^E-5 || 8.92 | ||
|- | |- | ||
| | | vB-0||style="background:#e7b416;" | ^F-2 || 5.18||style="background:#99c140;" | ^D-3 || -0.78||style="background:#99c140;" | ^G#-3 || 1.08||style="background:#db7b2b;" | ^C-4 || 10.36||style="background:#e7b416;" | E-4 || 9.38||style="background:#db7b2b;" | G-4 || -11.09||style="background:#99c140;" | ^A-4 || 4.4||style="background:#db7b2b;" | vC-4 || -11.17||style="background:#db7b2b;" | vD-5 || -12.16||style="background:#e7b416;" | Eb-5 || 6.26||style="background:#e7b416;" | vF-5 || 8.92 | ||
|- | |- | ||
| | | B-0||style="background:#e7b416;" | F#-2 || 5.18||style="background:#99c140;" | D#-3 || -0.78||style="background:#99c140;" | vA-3 || 1.08||style="background:#db7b2b;" | C#-4 || 10.36||style="background:#e7b416;" | ^E-4 || 9.38||style="background:#db7b2b;" | ^G-4 || -11.09||style="background:#99c140;" | vBb-4 || 4.4||style="background:#db7b2b;" | C-5 || -11.17||style="background:#db7b2b;" | D-5 || -12.16||style="background:#e7b416;" | vE-5 || 6.26||style="background:#e7b416;" | F-5 || 8.92 | ||
|- | |- | ||
| vC-0||style="background:#e7b416;" | vG-2 || 5.18||style="background:#99c140;" | vE-3 || -0.78||style="background:#99c140;" | ^A-3 || 1.08||style="background:# | | ^B-0||style="background:#e7b416;" | ^F#-2 || 5.18||style="background:#99c140;" | Eb-3 || -0.78||style="background:#99c140;" | A-3 || 1.08||style="background:#db7b2b;" | ^C#-4 || 10.36||style="background:#e7b416;" | vF-4 || 9.38||style="background:#db7b2b;" | G#-4 || -11.09||style="background:#99c140;" | Bb-4 || 4.4||style="background:#db7b2b;" | ^C-5 || -11.17||style="background:#db7b2b;" | ^D-5 || -12.16||style="background:#e7b416;" | E-5 || 6.26||style="background:#e7b416;" | ^F-5 || 8.92 | ||
|- | |||
| vC-0||style="background:#e7b416;" | vG-2 || 5.18||style="background:#99c140;" | vE-3 || -0.78||style="background:#99c140;" | ^A-3 || 1.08||style="background:#db7b2b;" | vD-4 || 10.36||style="background:#e7b416;" | F-4 || 9.38||style="background:#db7b2b;" | ^G#-4 || -11.09||style="background:#99c140;" | vB-4 || 4.4||style="background:#db7b2b;" | C#-5 || -11.17||style="background:#db7b2b;" | D#-5 || -12.16||style="background:#e7b416;" | ^E-5 || 6.26||style="background:#e7b416;" | F#-5 || 8.92 | |||
|} | |} | ||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Tables]] | [[Category:Tables]] | ||
{{Todo| rework }} | |||
Latest revision as of 10:08, 25 March 2025
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
| Funda- mental |
3rd harmonic | 5th harmonic | 7th harmonic | 9th harmonic | 11th harmonic | 13th harmonic | 15th harmonic | 17th harmonic | 19th harmonic | 21st harmonic | 23rd harmonic | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Note | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) |
| 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 | F#-4 | 28.27 |
| 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 | G-4 | 28.27 |
| 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 | G#-4 | 28.27 |
| 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 | A-4 | 28.27 |
| 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 | Bb-4 | 28.27 |
| 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 | B-4 | 28.27 |
| 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 | C-5 | 28.27 |
| 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 | C#-5 | 28.27 |
| 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 | D-5 | 28.27 |
| 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 | Eb-5 | 28.27 |
| 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 | E-5 | 28.27 |
| 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 | F-5 | 28.27 |
31-TET
| Funda- mental |
3rd harmonic | 5th harmonic | 7th harmonic | 9th harmonic | 11th harmonic | 13th harmonic | 15th harmonic | 17th harmonic | 19th harmonic | 21st harmonic | 23rd harmonic | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Note | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) | Note | Err(¢) |
| 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 |