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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.]]
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| 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]].
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| Factored into primes it is: <math>2*3^2*5^{-3}*7</math>
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| Or as simple just intervals: <math>(6/5)^3*(7/6)*(2/1)^{-1}</math>
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| 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]].
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| 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''.
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| == In equal temperament ==
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| 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]].
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| ==Sources==
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| {{reflist}}
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| {{Intervals|state=expanded}}
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| [[Category:7-limit tuning and intervals]] | |
| [[Category:Commas]]
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| [[Category:Superparticular intervals|0126:0125]]
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Latest revision as of 11:02, 6 September 2014
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