17/9
| Interval information |
[sound info]
In 17-limit just intonation, 17/9 is the septendecimal diminished octave or the septendecimal major seventh, depending on how one views it. It measures about 1101¢. It is the mediant between 15/8 and 2/1. Its inversion is 18/17, the "small septendecimal semitone".
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 17/9 should be a major seventh or a diminished octave. The diminished octave view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 4096/2187, the Pythagorean diminished octave. The major seventh view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 243/128, the Pythagorean major seventh.
In practice, the interval category may, arguably, vary by context. One solution for the JI user who uses expanded circle-of-fifths notation is to prepare a Pythagorean comma accidental so that the interval can be notated in either category.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 11 | 10\11 | 1090.91 | -10.14 | -9.29 |
| 12 | 11\12 | 1100.00 | -1.05 | -1.05 |
| 13 | 12\13 | 1107.69 | +6.65 | +7.20 |
| 24 | 22\24 | 1100.00 | -1.05 | -2.09 |
| 25 | 23\25 | 1104.00 | +2.95 | +6.16 |
| 36 | 33\36 | 1100.00 | -1.05 | -3.14 |
| 37 | 34\37 | 1102.70 | +1.66 | +5.11 |
| 48 | 44\48 | 1100.00 | -1.05 | -4.18 |
| 49 | 45\49 | 1102.04 | +1.00 | +4.06 |
| 60 | 55\60 | 1100.00 | -1.05 | -5.23 |
| 61 | 56\61 | 1101.64 | +0.59 | +3.02 |
| 72 | 66\72 | 1100.00 | -1.05 | -6.27 |
| 73 | 67\73 | 1101.37 | +0.32 | +1.97 |