24/19: Difference between revisions
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'''24/19''', the '''small undevicesimal major third''' or '''Boethius' major third''', is a [[19-limit]] interval that is very close to the major third of [[12edo]] (400 cents). It is an ''undevicesimal comma'' aka ''Boethius' comma'' ([[513/512]]) below the Pythagorean major third ([[81/64]]). | '''24/19''', the '''small undevicesimal major third''' or '''Boethius' major third''', is a [[19-limit]] interval that is very close to the major third of [[12edo]] (400 cents). It is an ''undevicesimal comma'' aka ''Boethius' comma'' ([[513/512]]) below the Pythagorean major third ([[81/64]]). | ||
== Approximation == | == Approximation == | ||
24/19 is very accurately approximated by [[89edo]] (30\89), although technically there is a slight difference, as that of 89edo is 0.0524 cents sharper. | |||
{{Interval edo approximation|24/19}} | {{Interval edo approximation|24/19}} | ||
== See also == | == See also == | ||
* [[19/12]] – its [[octave complement]] | * [[19/12]] – its [[octave complement]] | ||
Latest revision as of 22:00, 13 February 2026
| Interval information |
Boethius' major third
[sound info]
24/19, the small undevicesimal major third or Boethius' major third, is a 19-limit interval that is very close to the major third of 12edo (400 cents). It is an undevicesimal comma aka Boethius' comma (513/512) below the Pythagorean major third (81/64).
Approximation
24/19 is very accurately approximated by 89edo (30\89), although technically there is a slight difference, as that of 89edo is 0.0524 cents sharper.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 1\3 | 400.00 | -4.44 | -1.11 |
| 6 | 2\6 | 400.00 | -4.44 | -2.22 |
| 9 | 3\9 | 400.00 | -4.44 | -3.33 |
| 12 | 4\12 | 400.00 | -4.44 | -4.44 |
| 15 | 5\15 | 400.00 | -4.44 | -5.55 |
| 18 | 6\18 | 400.00 | -4.44 | -6.66 |
| 21 | 7\21 | 400.00 | -4.44 | -7.77 |
| 24 | 8\24 | 400.00 | -4.44 | -8.88 |
| 27 | 9\27 | 400.00 | -4.44 | -9.99 |
| 65 | 22\65 | 406.15 | +1.71 | +9.27 |
| 68 | 23\68 | 405.88 | +1.44 | +8.16 |
| 71 | 24\71 | 405.63 | +1.19 | +7.05 |
| 74 | 25\74 | 405.41 | +0.96 | +5.94 |
| 77 | 26\77 | 405.19 | +0.75 | +4.83 |
| 80 | 27\80 | 405.00 | +0.56 | +3.72 |
See also
- 19/12 – its octave complement
- 19/16 – its fifth complement
- 19/15 – the large undevicesimal major third
- Gallery of just intervals