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Cmloegcmluin (talk | contribs) add section for this comma's use in Sagittal notation |
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== Approximation == | == Approximation == | ||
If one wants to treat Archytas' comma as a musical interval in its own right as opposed to tempering it out, you will find that it acts as a sort of chroma – specifically, it functions as a septimal equivalent of [[55/54]], from which it differs by a [[385/384|keenanisma]], or of [[56/55]], from which it differs by a [[441/440|Werckisma]]. In addition, its incredible proximity to 1/44th of the octave – to the point where the [[Septimal ruthenia|44-64/63 comma]] is tempered out in edos as large as tens of thousands – enables the tuning of [[ruthenium]] temperament. As a result, the major second of [[22edo]] is a good approximation to [[17/15]], due to it being the [[mediant]] of [[9/8]] and [[8/7]], so that the ~7:8:9 chord is much more accurately a 17/15–17/15 chord, with the outer dyad as 9/7, by tempering out [[2025/2023]]. | If one wants to treat Archytas' comma as a musical interval in its own right as opposed to tempering it out, you will find that it acts as a sort of chroma – specifically, it functions as a septimal equivalent of [[55/54]], from which it differs by a [[385/384|keenanisma]], or of [[56/55]], from which it differs by a [[441/440|Werckisma]]. In addition, its incredible proximity to 1/44th of the octave – to the point where the [[Septimal ruthenia|44-64/63 comma]] is tempered out in edos as large as tens of thousands – enables the tuning of [[ruthenium]] temperament. As a result, the major second of [[22edo]] is a good approximation to [[17/15]], due to it being the [[mediant]] of [[9/8]] and [[8/7]], so that the ~7:8:9 chord is much more accurately a 17/15–17/15 chord, with the outer dyad as 9/7, by tempering out [[2025/2023]]. | ||
== Sagittal notation == | |||
In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | !) }} and is called the '''7 comma''', or '''7C''' for short, because the simplest ratio it notates is 4:7, as for example in G:F{{sagittal | !) }}. | |||
== See also == | == See also == | ||