676/675: Difference between revisions
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'''676/675''', otherwise known as the '''island comma''', or the '''parizekma''', is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth, and also between [[26/25]] and [[27/26]]. Tempering this comma out divides the perfect fourth into two equal halves, making [[island chords]] possible. | '''676/675''', otherwise known as the '''island comma''', or the '''parizekma''', is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth (from which its S-expression of [[169/168|S13]]/[[225/224|S15]] = (16/12)/(15/13)<sup>2</sup> is derived), and also between [[26/25]] and [[27/26]] (from which its [[S-expression]] of S26 is derived). Tempering this comma out divides the perfect fourth into two equal halves, making [[island chords]] possible. | ||
== Temperaments == | |||
See [[The Archipelago]] for the "rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments" associated with tempering out this comma, and [[Island chords]] for chords making use of the resulting structure. | |||
== Etymology == | == Etymology == | ||
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== See also == | == See also == | ||
* [[ | * [[Semifourth]] | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Latest revision as of 18:34, 4 June 2026
| Interval information |
parizekma
Bithogu comma
reduced
S13/S15
676/675, otherwise known as the island comma, or the parizekma, is the difference between two 15/13's and a 4/3 perfect fourth (from which its S-expression of S13/S15 = (16/12)/(15/13)2 is derived), and also between 26/25 and 27/26 (from which its S-expression of S26 is derived). Tempering this comma out divides the perfect fourth into two equal halves, making island chords possible.
Temperaments
See The Archipelago for the "rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments" associated with tempering out this comma, and Island chords for chords making use of the resulting structure.
Etymology
The name island comma was given by Mike Battaglia in 2011[1].
The 9-note MOS sounds like you're on some kind of tropical island off the coast of Barbados playing jubilant sun-music with the natives or something. More specifically, I feel like it takes the "island" feel of 5-equal and expands it out into diatonic and chromatic versions.
—Mike Battaglia