126/125: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = starling comma, septimal semicomma

~~| Ratio = 126/125~~

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

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

| Comma = yes

~~| Cents = 13.79477~~

| 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 ~~only~~ superparticular [[7-limit]] [[comma]] which is ~~not~~ the difference between ~~two 7-limit superparticular ratios~~. ~~Instead~~, 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 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.

Tempering it out leads to [[~~Starling_temperaments#Starling comma|~~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~~.

== Temperaments ==

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 ==

* [[Small comma]]

* [[Gallery of just intervals]]

* [~~http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma~~]

* [[List of superparticular intervals]]

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

~~[[Category:Small comma]]~~

~~[[Category:Interval]]~~

[[Category:Starling]]

[[Category:~~Superparticular~~]]

[[Category:Commas named after musical traditions]]

@@ Line 6: / Line 6: @@
 }}
 {{Infobox Interval
-| Icon =
+| Name = starling comma, septimal semicomma
-| Ratio = 126/125
+| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma
-| Monzo = 2 3 -3 1
+| Comma = yes
-| Cents = 13.79477
-| 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 only superparticular [[7-limit]] [[comma]] which is not the difference between two 7-limit superparticular ratios. Instead, 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 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.
-Tempering it out leads to [[Starling_temperaments#Starling comma|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.
+== Temperaments ==
+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 ==
+* [[Small comma]]
 * [[Gallery of just intervals]]
-* [http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]
+* [[List of superparticular intervals]]
-[[Category:7-limit]]
-[[Category:Small comma]]
-[[Category:Interval]]
 [[Category:Starling]]
-[[Category:Superparticular]]
+[[Category:Commas named after musical traditions]]