126/125: Difference between revisions

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~~<span style~~=~~"display: block; text-align: right;">[[:de:~~126/125 ~~Deutsch]]~~</~~span~~>

{{interwiki

| de = 126/125

| en = 126/125

| es =

| ja =

}}

{{Infobox Interval

| Name = starling comma, septimal semicomma

| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma

| Comma = yes

}}

The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 ~~cents~~), is the ~~only~~ superparticular [[~~7-limit|~~7-limit]] [[~~Comma|~~comma]] which is ~~not~~ the difference between ~~two 7-limit superparticular ratios~~. ~~Instead~~, it is the amount by which [[~~12/7|~~12/7]] falls short of three [[~~6/5|~~6/5]] minor thirds. It is also the amount by which two [[5/3~~|5/3~~ major sixths]] (octave-reduced) ~~exceed~~ the [[7/5~~|7/5~~ tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6~~|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|7/6~~]] ~~subminor third, when 126/125~~ is tempered out~~, gives the~~ [[~~starling_tetrad|~~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.

[~~http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]~~ [~~[Category:7-limit~~]]

== See also ==

[[~~Category:comma~~]]

* [[Small comma]]

[[~~Category:interval~~]]

* [[Gallery of just intervals]]

[[Category:~~septimal~~]]

* [[List of superparticular intervals]]

[[Category:~~starling~~]]

[[Category:Starling]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
-<span style="display: block; text-align: right;">[[:de:126/125 Deutsch]]</span>
+{{interwiki
+| de = 126/125
+| en = 126/125
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = starling comma, septimal semicomma
+| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma
+| Comma = yes
+}}
+{{Wikipedia|Septimal semicomma}}
-The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 cents), is the only superparticular [[7-limit|7-limit]] [[Comma|comma]] which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which [[12/7|12/7]] falls short of three [[6/5|6/5]] minor thirds. It is also the amount by which two [[5/3|5/3 major sixths]] (octave-reduced) exceed the [[7/5|7/5 tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6|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|7/6]] subminor third, when 126/125 is tempered out, gives the [[starling_tetrad|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.
-[http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]      [[Category:7-limit]]
+== See also ==
-[[Category:comma]]
+* [[Small comma]]
-[[Category:interval]]
+* [[Gallery of just intervals]]
-[[Category:septimal]]
+* [[List of superparticular intervals]]
-[[Category:starling]]
+[[Category:Starling]]
+[[Category:Commas named after musical traditions]]