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 ==
* [[Island chords]]
* [[Semifourth]]
* [[The Archipelago]]
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]

Latest revision as of 18:34, 4 June 2026

Interval information
Ratio 676/675
Factorization 22 × 3-3 × 5-2 × 132
Monzo [2 -3 -2 0 0 2
Size in cents 2.562893¢
Names island comma,
parizekma
Color name 3oogg2, bithogu 2nd,
Bithogu comma
FJS name [math]\displaystyle{ \text{dd2}^{13,13}_{5,5} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 18.7996
Weil norm (log2 max(n, d)) 18.8018
Wilson norm (sopfr(nd)) 49
Comma size unnoticeable
S-expressions S26,
S13/S15
Open this interval in xen-calc

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

See also

Notes