256/255

Interval information

Ratio	256/255
Factorization	28 × 3-1 × 5-1 × 17-1
Monzo	[8 -1 -1 0 0 0 -1⟩
Size in cents	6.775876¢
Names	septendecimal kleisma, charsma, diasemisma, 255th subharmonic
Color name	17ug1, sugu 1sn, Sugu comma
FJS name	[math]\displaystyle{ \text{P1}_{5,17} }[/math]
Special properties	square superparticular, reduced, reduced subharmonic
Tenney height (log2 nd)	15.9944
Weil height (log2 max(n, d))	16
Wilson height (sopfr(nd))	41
Comma size	small
S-expression	S16
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256/255, the septendecimal kleisma, charsma, diasemisma or 255th subharmonic is a small 17-limit superparticular comma about 6.8 cents in size. It is the difference between 16/15 (classical diatonic semitone) and 17/16 (large septendecimal semitone, also called as minor diatonic semitone), and forms the amount by which a stack consisting of 15/8 and 17/16 falls short of an octave. It differs from 352/351 (the minthma) by 936/935 – an unnoticeable comma measuring about 1.85 cents.

By tempering it out is defined the charsmic temperament (full 17-limit rank-6) or charic temperament (2.3.5.17 subgroup rank-3), which enables the charsmic chords.

Etymology

The name diasemisma was named by Xenllium in May 2023. It is a contraction of diatonic semitone into a single word; it is unrelated to the diasem scale structure. However, septendecimal kleisma and 255th subharmonic were attested much earlier.

Godtone named this comma charisma in December 2023, referring to the comma being a superparticular ratio with the numerator is 2⁸ (the number of combinations in a byte, often referred to as a char in programming). Later, this name was revised to charsma (no-i spelling) by Xenllium in January 2024 for disambiguation (formerly charisma and charismic were used for horcrux extensions).

See also

• Small comma
• List of superparticular intervals