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If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both [[9/8]] and [[8/7]]: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.

~~On the other hand, if~~ one ~~should be so bold as~~ to treat ~~the~~ Archytas' comma as a musical interval in its own right, you will find that it acts as a sort of chroma – specifically, it functions as ~~the~~ septimal equivalent of [[55/54]], from which it differs by a [[385/384|keenanisma]]. In addition, its incredible proximity to 1/44th of the octave - to the point where [[Septimal ruthenia|44-64/63 comma]] is tempered out in EDOs as large as tens of thousands - enables the tuning of [[ruthenium]] temperament.

If one wants to treat Archytas' comma as a musical interval in its own right as opposed to tempering it out (which in higher-accuracy contexts causes significant damage to the [[7-limit]]), 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 [[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 [[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 [[2025/2023]].

== See also ==

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 If you are using 9/7 major thirds, this also implies that the major third is split into two equal steps that represent both [[9/8]] and [[8/7]]: If a stack of four fifths gets you to (octave-equivalent) 9/7, and a stack of two fifths gets you to 9/8, then the difference must be (9/7)/(9/8) = 8/7. The 8/7 and 9/8 intervals are equal, however, as a result of the generation process.
-On the other hand, if one should be so bold as to treat the Archytas' comma as a musical interval in its own right, you will find that it acts as a sort of chroma – specifically, it functions as the septimal equivalent of [[55/54]], from which it differs by a [[385/384|keenanisma]]. In addition, its incredible proximity to 1/44th of the octave - to the point where [[Septimal ruthenia|44-64/63 comma]] is tempered out in EDOs as large as tens of thousands - enables the tuning of [[ruthenium]] temperament.
+If one wants to treat Archytas' comma as a musical interval in its own right as opposed to tempering it out (which in higher-accuracy contexts causes significant damage to the [[7-limit]]), 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 [[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 [[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 [[2025/2023]].
 == See also ==