126/125: Difference between revisions

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{{Infobox Interval

~~| Ratio = 126/125~~

| Name = starling comma, septimal semicomma

~~| Monzo = 1 2 -3 1~~

| Color name = zg32, zotrigu 2nd, Zotrigu comma

~~| Cents = 13.79477~~

| Comma = yes

| Name = ~~Starling~~ comma, ~~ ~~ septimal semicomma

| Color name = zg32, zotrigu ~~comma~~

~~| FJS name = d2~~<~~sup>7125</sub~~>

| ~~Sound~~ =

}}

The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 ~~cents~~), is the superparticular [[7-limit]] [[comma]] which is the difference between ~~the~~ [[36/35]] septimal quartertone and ~~the~~ [[50/49]] jubilisma. In terms of just intervals, it is the amount by which [[12/7]] falls short of three [[6/5]] minor thirds. It is also the amount by which two [[5/3]] major sixths (octave-reduced) ~~exceed~~ the [[7/5]] [[tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6]] septimal minor third~~. It can be found as the difference between [[25/18]] and [[7/5]]~~. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.

The '''starling comma''' or '''septimal semicomma''', '''126/125''' (about 13.8 [[cent]]s), is the [[superparticular]] [[7-limit]] [[comma]] which is the difference between [[36/35]] (septimal quartertone) and [[50/49]] (jubilisma). In terms of just intervals, it is the amount by which [[12/7]] falls short of three [[6/5]] minor thirds. It is also the amount by which two [[5/3]] major sixths (octave-reduced, [[25/18]]) fall short of the [[7/5]] [[tritone]], and the amount by which three 5/3's (octave-reduced) fall short of the [[7/6]] septimal minor third. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest [[Bohlen–Pierce]] intervals.

== Temperaments ==

Tempering it out leads to the [[~~Starling family #Starling|~~starling ~~temperament~~]], and ~~three minor thirds plus a~~ [[~~7/6~~]] ~~subminor third, when 126/125~~ is tempered out~~, gives the~~ [[starling ~~tetrad~~]] ~~or septimal semicomma diminished seventh chord~~.

Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out.

== See also ==

* [[Starling family]], the rank-3 temperament family where it is tempered out

* [[Starling temperaments]], a collection of rank-2 temperaments where it is tempered out

* [[Starling chords]]

* [[Small comma]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

~~[[Category:7-limit]]~~

~~[[Category:Small commas]]~~

[[Category:Starling]]

[[Category:~~Superparticular~~]]

[[Category:Commas named after musical traditions]]

@@ Line 6: / Line 6: @@
 }}
 {{Infobox Interval
-| Ratio = 126/125
+| Name = starling comma, septimal semicomma
-| Monzo = 1 2 -3 1
+| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma
-| Cents = 13.79477
+| Comma = yes
-| Name = Starling comma, <br> septimal semicomma
-| Color name = zg<sup>3</sup>2, zotrigu comma
-| FJS name = d2<sup>7</sup><sub>125</sub>
-| Sound =
 }}
 {{Wikipedia|Septimal semicomma}}
-The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 cents), is the superparticular [[7-limit]] [[comma]] which is the difference between the [[36/35]] septimal quartertone and the [[50/49]] jubilisma. In terms of just intervals, it is the amount by which [[12/7]] falls short of three [[6/5]] minor thirds. It is also the amount by which two [[5/3]] major sixths (octave-reduced) exceed the [[7/5]] [[tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6]] septimal minor third. It can be found as the difference between [[25/18]] and [[7/5]]. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.
+The '''starling comma''' or '''septimal semicomma''', '''126/125''' (about 13.8 [[cent]]s), is the [[superparticular]] [[7-limit]] [[comma]] which is the difference between [[36/35]] (septimal quartertone) and [[50/49]] (jubilisma). In terms of just intervals, it is the amount by which [[12/7]] falls short of three [[6/5]] minor thirds. It is also the amount by which two [[5/3]] major sixths (octave-reduced, [[25/18]]) fall short of the [[7/5]] [[tritone]], and the amount by which three 5/3's (octave-reduced) fall short of the [[7/6]] septimal minor third. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest [[Bohlen–Pierce]] intervals.
 == Temperaments ==
-Tempering it out leads to the [[Starling family #Starling|starling temperament]], and three minor thirds plus a [[7/6]] subminor third, when 126/125 is tempered out, gives the [[starling tetrad]] or septimal semicomma diminished seventh chord.
+Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out.
 == See also ==
-* [[Starling family]], the rank-3 temperament family where it is tempered out
-* [[Starling temperaments]], a collection of rank-2 temperaments where it is tempered out
-* [[Starling chords]]
 * [[Small comma]]
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-[[Category:7-limit]]
-[[Category:Small commas]]
 [[Category:Starling]]
-[[Category:Superparticular]]
+[[Category:Commas named after musical traditions]]