32/19: Difference between revisions
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'''32/19''' is a [[19-limit]] interval, 902.5 [[cent]]s in size, the '''utonal major sixth''' or '''octave-reduced 19th subharmonic''', which is extremely close to the major sixth of [[12edo]] (900 cents). It is an ''undevicesimal comma'' aka ''Boethius' comma'' ([[513/512]]) below the [[27/16|Pythagorean major sixth]]. | '''32/19''' is a [[19-limit]] interval, 902.5 [[cent]]s in size, the '''utonal major sixth''' or '''octave-reduced 19th subharmonic''', which is extremely close to the major sixth of [[12edo]] (900 cents). It is an ''undevicesimal comma'' aka ''Boethius' comma'' ([[513/512]]) below the [[27/16|Pythagorean major sixth]]. | ||
== Approximation == | |||
32/19 is very accurately approximated by [[121edo]] (91\121). | |||
{{Interval edo approximation|32/19}} | |||
== See also == | == See also == | ||
Latest revision as of 21:58, 13 February 2026
| Interval information |
octave-reduced 19th subharmonic
reduced subharmonic
[sound info]
32/19 is a 19-limit interval, 902.5 cents in size, the utonal major sixth or octave-reduced 19th subharmonic, which is extremely close to the major sixth of 12edo (900 cents). It is an undevicesimal comma aka Boethius' comma (513/512) below the Pythagorean major sixth.
Approximation
32/19 is very accurately approximated by 121edo (91\121).
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 3\4 | 900.00 | -2.49 | -0.83 |
| 8 | 6\8 | 900.00 | -2.49 | -1.66 |
| 12 | 9\12 | 900.00 | -2.49 | -2.49 |
| 16 | 12\16 | 900.00 | -2.49 | -3.32 |
| 20 | 15\20 | 900.00 | -2.49 | -4.14 |
| 24 | 18\24 | 900.00 | -2.49 | -4.97 |
| 28 | 21\28 | 900.00 | -2.49 | -5.80 |
| 32 | 24\32 | 900.00 | -2.49 | -6.63 |
| 36 | 27\36 | 900.00 | -2.49 | -7.46 |
| 40 | 30\40 | 900.00 | -2.49 | -8.29 |
| 44 | 33\44 | 900.00 | -2.49 | -9.12 |
| 48 | 36\48 | 900.00 | -2.49 | -9.95 |
| 73 | 55\73 | 904.11 | +1.62 | +9.87 |
| 77 | 58\77 | 903.90 | +1.41 | +9.04 |