19/18: Difference between revisions

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{{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

| 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 ==

== 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~~]]

@@ Line 1: / Line 1: @@
 {{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
+| 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]]