Electrical resonance: Difference between revisions
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[[File:Septimal semicomma.png|thumb|[[7-limit|Septimal]] semicomma as difference between 3 just [[minor third]]s plus 1 [[septimal minor third]] and 1 octaves.]] | |||
In [[music]], the '''septimal semicomma''', a [[7-limit|seven]]-[[limit (music)|limit]] [[semicomma]], is the ratio 126/125 and is equal to approximately 13.79 [[Cent (music)|cents]] ({{Audio|Septimal semicomma on C.mid|play}}).{{Citation needed|date=December 2011}} It is also called the ''small septimal comma''<ref>Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. ISBN 978-0-8247-4714-5.</ref> and the ''starling comma'' after its use in [[starling temperament]]. | |||
Factored into primes it is: <math>2*3^2*5^{-3}*7</math> | |||
Or as simple just intervals: <math>(6/5)^3*(7/6)*(2/1)^{-1}</math> | |||
Thus it is the difference between three [[minor third]]s of 6/5 plus a [[septimal minor third]] of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as [[septimal meantone temperament]]. | |||
A [[diminished seventh chord]] consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the ''septimal semicomma diminished seventh chord''. | |||
== In equal temperament == | |||
It is tempered out in [[19 equal temperament]] and [[31 equal temperament]], but not in [[22 equal temperament]], [[34 equal temperament]], [[41 equal temperament]], or [[53 equal temperament]]. | |||
==Sources== | |||
{{reflist}} | |||
{{Intervals|state=expanded}} | |||
[[Category:7-limit tuning and intervals]] | |||
[[Category:Commas]] | |||
[[Category:Superparticular intervals|0126:0125]] | |||
Revision as of 05:56, 26 January 2014
In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (My name: Lindsey Gavin
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Factored into primes it is:
Or as simple just intervals:
Thus it is the difference between three minor thirds of 6/5 plus a septimal minor third of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament.
A diminished seventh chord consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the septimal semicomma diminished seventh chord.
In equal temperament
It is tempered out in 19 equal temperament and 31 equal temperament, but not in 22 equal temperament, 34 equal temperament, 41 equal temperament, or 53 equal temperament.
Sources
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- ↑ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxvi. ISBN 978-0-8247-4714-5.