19/18: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = large undevicesimal semitone, undevicesimal limma, Boethius' semitone | |||
| Comma = yes | |||
| Name = large undevicesimal semitone | |||
| Color name = 19o2, ino 2nd | | Color name = 19o2, ino 2nd | ||
| Sound = Ji-19-18-csound-foscil-220hz.mp3 | | Sound = Ji-19-18-csound-foscil-220hz.mp3 | ||
}} | }} | ||
| Line 11: | Line 8: | ||
In [[19-limit]] [[just intonation]], '''19/18''' is the '''large undevicesimal semitone''' or '''Boethius' semitone''', measuring about 93.6¢. It is sharp of the [[256/243|Pythagorean limma (256/243)]] by [[513/512]], the ''undevicesimal comma'' aka ''Boethius' comma''. | In [[19-limit]] [[just intonation]], '''19/18''' is the '''large undevicesimal semitone''' or '''Boethius' semitone''', measuring about 93.6¢. It is sharp of the [[256/243|Pythagorean limma (256/243)]] by [[513/512]], the ''undevicesimal comma'' aka ''Boethius' comma''. | ||
The small comma (39/35)/(19/18)<sup>2</sup> = 12636/12635 is tempered out in {{EDOs| 53, 130, 140, 243, 270, 422, 513, 665, 742, 795, 935, 1065, 1178, 1205, 1308, 1395, 1448, 1578, 2000, 2190, 2243, 2460, 3125, 3178, 3395, and 4703 EDOs}}. | The small comma ([[39/35]])/(19/18)<sup>2</sup> = [[12636/12635]] is tempered out in {{EDOs| 53, 130, 140, 243, 270, 422, 513, 665, 742, 795, 935, 1065, 1178, 1205, 1308, 1395, 1448, 1578, 2000, 2190, 2243, 2460, 3125, 3178, 3395, and 4703 EDOs}}. | ||
== Approximation == | |||
{{Interval edo approximation|19/18}} | |||
== See also == | == See also == | ||
* [[36/19]] – its [[octave complement]], the undevicesimal major seventh | * [[36/19]] – its [[octave complement]], the undevicesimal major seventh | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Boethius]] | [[Category:Boethius]] | ||
[[Category: | [[Category:Commas named after polymaths]] | ||
[[Category:Commas named after their interval size]] | |||
Latest revision as of 16:52, 21 January 2026
| Interval information |
undevicesimal limma,
Boethius' semitone
reduced
[sound info]
In 19-limit just intonation, 19/18 is the large undevicesimal semitone or Boethius' semitone, measuring about 93.6¢. It is sharp of the Pythagorean limma (256/243) by 513/512, the undevicesimal comma aka Boethius' comma.
The small comma (39/35)/(19/18)2 = 12636/12635 is tempered out in 53, 130, 140, 243, 270, 422, 513, 665, 742, 795, 935, 1065, 1178, 1205, 1308, 1395, 1448, 1578, 2000, 2190, 2243, 2460, 3125, 3178, 3395, and 4703 EDOs.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 12 | 1\12 | 100.00 | +6.40 | +6.40 |
| 13 | 1\13 | 92.31 | -1.30 | -1.40 |
| 14 | 1\14 | 85.71 | -7.89 | -9.20 |
| 25 | 2\25 | 96.00 | +2.40 | +4.99 |
| 26 | 2\26 | 92.31 | -1.30 | -2.81 |
| 38 | 3\38 | 94.74 | +1.13 | +3.59 |
| 39 | 3\39 | 92.31 | -1.30 | -4.21 |
| 50 | 4\50 | 96.00 | +2.40 | +9.99 |
| 51 | 4\51 | 94.12 | +0.51 | +2.19 |
| 52 | 4\52 | 92.31 | -1.30 | -5.61 |
| 63 | 5\63 | 95.24 | +1.64 | +8.58 |
| 64 | 5\64 | 93.75 | +0.15 | +0.78 |
| 65 | 5\65 | 92.31 | -1.30 | -7.02 |
| 76 | 6\76 | 94.74 | +1.13 | +7.18 |
| 77 | 6\77 | 93.51 | -0.10 | -0.62 |
| 78 | 6\78 | 92.31 | -1.30 | -8.42 |
See also
- 36/19 – its octave complement, the undevicesimal major seventh
- 20/19 – the small undevicesimal semitone
- Gallery of just intervals
- List of superparticular intervals