19/10: Difference between revisions
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In [[19-limit]] [[just intonation]], '''19/10''' is the '''undevicesimal diminished octave''', measuring about 1111.2¢. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished octave'', obtained by adding [[81/80]] and [[513/512]] to the [[4096/2187|Pythagorean diminished octave]], but it may be called the '''Eratosthenes' major seventh''' as it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''. | In [[19-limit]] [[just intonation]], '''19/10''' is the '''undevicesimal diminished octave''', measuring about 1111.2¢. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished octave'', obtained by adding [[81/80]] and [[513/512]] to the [[4096/2187|Pythagorean diminished octave]], but it may be called the '''Eratosthenes' major seventh''' as it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''. | ||
== Approximation == | |||
{{Interval edo approximation|19/10}} | |||
[[Category:Octave]] | [[Category:Octave]] | ||
Latest revision as of 13:04, 3 November 2025
| Interval information |
Eratosthenes' major seventh
[sound info]
In 19-limit just intonation, 19/10 is the undevicesimal diminished octave, measuring about 1111.2¢. In the Functional Just System and Helmholtz-Ellis notation, it is a diminished octave, obtained by adding 81/80 and 513/512 to the Pythagorean diminished octave, but it may be called the Eratosthenes' major seventh as it is sharp of the Pythagorean major seventh (243/128) by 1216/1215, the password aka Eratosthenes' comma.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 13 | 12\13 | 1107.69 | -3.51 | -3.80 |
| 14 | 13\14 | 1114.29 | +3.09 | +3.60 |
| 26 | 24\26 | 1107.69 | -3.51 | -7.60 |
| 27 | 25\27 | 1111.11 | -0.09 | -0.20 |
| 28 | 26\28 | 1114.29 | +3.09 | +7.20 |
| 40 | 37\40 | 1110.00 | -1.20 | -4.00 |
| 41 | 38\41 | 1112.20 | +1.00 | +3.40 |
| 53 | 49\53 | 1109.43 | -1.77 | -7.80 |
| 54 | 50\54 | 1111.11 | -0.09 | -0.40 |
| 55 | 51\55 | 1112.73 | +1.53 | +7.00 |
| 67 | 62\67 | 1110.45 | -0.75 | -4.20 |
| 68 | 63\68 | 1111.76 | +0.57 | +3.20 |
| 80 | 74\80 | 1110.00 | -1.20 | -8.00 |