33/32: Difference between revisions
Clarified that the attestation of a 16/15 semitone on Wikipedia is indirect |
m Mention its significance in HE notation; add link to fifth complement |
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Because of its close proximity to [[28/27]], form which it differs only by [[Pentacircle comma|896/891]], one could reasonably argue that 33/32 is the undecimal counterpart to 28/27 in a way, particularly if treated as an interval in its own right. However, despite this, 33/32 generally has properties more akin to a chromatic interval than to anything resembling a diatonic interval. In addition, 33/32 could arguably have been used as a melodic interval in the Greek Enharmonic Genus, and if so, there are several possibilities for the resulting tetrachord. The most obvious of these possibilities would be to include 32:33:34 within the interval of a perfect fourth, in which case this ancient Greek scale can be approximated in [[22edo]] and [[24edo]], with the comma 1089/1088 being tempered out so that 33/32 and 34/33 are equated. Another possibility, however, is that the semitone was [[16/15]], which, according to [https://en.wikipedia.org/wiki/Genus_(music) Wikipedia], is indirectly attested to in the writings of Ptolemy, and thus, if 33/32 was in fact used, it would have been paired with [[512/495]]. | Because of its close proximity to [[28/27]], form which it differs only by [[Pentacircle comma|896/891]], one could reasonably argue that 33/32 is the undecimal counterpart to 28/27 in a way, particularly if treated as an interval in its own right. However, despite this, 33/32 generally has properties more akin to a chromatic interval than to anything resembling a diatonic interval. In addition, 33/32 could arguably have been used as a melodic interval in the Greek Enharmonic Genus, and if so, there are several possibilities for the resulting tetrachord. The most obvious of these possibilities would be to include 32:33:34 within the interval of a perfect fourth, in which case this ancient Greek scale can be approximated in [[22edo]] and [[24edo]], with the comma 1089/1088 being tempered out so that 33/32 and 34/33 are equated. Another possibility, however, is that the semitone was [[16/15]], which, according to [https://en.wikipedia.org/wiki/Genus_(music) Wikipedia], is indirectly attested to in the writings of Ptolemy, and thus, if 33/32 was in fact used, it would have been paired with [[512/495]]. | ||
33/32 is significant in [[Functional Just System]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. Apart from the aforementioned relationship between 4/3 and 11/8, it is also the interval between [[32/27]] and [[11/9]], and between [[9/8]] and [[12/11]]. | 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. Apart from the aforementioned relationship between 4/3 and 11/8, it is also the interval between [[32/27]] and [[11/9]], and between [[9/8]] and [[12/11]]. | ||
== See also == | == See also == | ||
* [[64/33]] – its [[octave complement]] | * [[64/33]] – its [[octave complement]] | ||
* [[16/11]] – its [[fifth complement]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[32/31]] | * [[32/31]] | ||