19/18: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = large undevicesimal semitone, undevicesimal limma, Boethius' semitone
| Ratio = 19/18
| Comma = yes
| Monzo = -1 -2 0 0 0 0 0 1
| Cents = 93.60301
| Name = greater undevicesimal semitone <br>greater undevicesimal limma <br>undevicesimal minor second
| Sound = jid_19_18_pluck_adu_dr220.mp3
| Color name = 19o2, ino 2nd
| Color name = 19o2, ino 2nd
| Sound = Ji-19-18-csound-foscil-220hz.mp3
}}
}}


In [[19-limit]] [[Just Intonation]], '''19/18''' is the "greater undevicesimal semitone," measuring about 93.6¢. Its [[octave complement]] is [[36/19]], the "undevicesimal major seventh".
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)^2 = 12636/12635 is tempered out in {{EDOs| 53, 130, 140, 243, 270, 422, 513, 665, 742, 795, 935, 1178, 1065, 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 ==
* [[36/19]] – its [[octave complement]], the undevicesimal major seventh
* [[20/19]] – the small undevicesimal semitone
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]


The password comma, (256/243)/(20/19) = (19/18)/(135/128) = 1216/1215 is tempered out in {{EDOs| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 EDOs}}, leading to a variety of temperaments which identifies small undevicesimal semitone with [[256/243|Pythagorean limma]] and greater undevicesimal semitone with [[135/128|major limma]] respectively.
[[Category:Semitone]]
 
[[Category:Second]]
==See also==
[[Category:Boethius]]
 
[[Category:Commas named after polymaths]]
* [[20/19]] - small undevicesimal semitone
[[Category:Commas named after their interval size]]
 
[[Category:Interval]]
[[Category:19-limit]]

Latest revision as of 16:52, 21 January 2026

Interval information
Ratio 19/18
Subgroup monzo 2.3.19 [-1 -2 1⟩
Size in cents 93.60301¢
Names large undevicesimal semitone,
undevicesimal limma,
Boethius' semitone
Color name 19o2, ino 2nd
FJS name [math]\displaystyle{ \text{m2}^{19} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 8.41785
Weil norm (log2 max(n, d)) 8.49586
Wilson norm (sopfr(nd)) 27
Comma size medium

[sound info]
Open this interval in xen-calc

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 approximations for 19/18 (93.60 ¢)
≤ 80edo, relative error ≤ 10%
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

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