32/17
| Interval information |
septendecimal diminished octave
reduced subharmonic
[sound info]
In 17-limit just intonation, 32/17 is the septendecimal major seventh or the septendecimal diminished octave, depending on how one views it. It is also the octave-reduced 17th subharmonic. Its inversion is 17/16, the octave-reduced 17th harmonic. Measuring about 1095 ¢, it is the mediant between 15/8 and 17/9.
Terminology and notation
There exists a disagreement in different conceptualization systems on whether 32/17 should be a major seventh or a diminished octave. The major seventh view corresponds to Functional Just System, with the formal comma 4131/4096 separating it from 243/128, the Pythagorean major seventh. The diminished octave view corresponds to Helmholtz-Ellis notation, with the formal comma 2187/2176 separating it from 4096/2187, the Pythagorean diminished octave.
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 | -4.14 | -3.79 |
| 12 | 11\12 | 1100.00 | +4.96 | +4.96 |
| 22 | 20\22 | 1090.91 | -4.14 | -7.58 |
| 23 | 21\23 | 1095.65 | +0.61 | +1.16 |
| 24 | 22\24 | 1100.00 | +4.96 | +9.91 |
| 34 | 31\34 | 1094.12 | -0.93 | -2.63 |
| 35 | 32\35 | 1097.14 | +2.10 | +6.12 |
| 45 | 41\45 | 1093.33 | -1.71 | -6.42 |
| 46 | 42\46 | 1095.65 | +0.61 | +2.33 |
| 57 | 52\57 | 1094.74 | -0.31 | -1.46 |
| 58 | 53\58 | 1096.55 | +1.51 | +7.28 |
| 68 | 62\68 | 1094.12 | -0.93 | -5.25 |
| 69 | 63\69 | 1095.65 | +0.61 | +3.49 |
| 79 | 72\79 | 1093.67 | -1.37 | -9.04 |
| 80 | 73\80 | 1095.00 | -0.04 | -0.30 |