676/675

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.

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

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.

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

• Semifourth
• Unnoticeable comma
• List of superparticular intervals