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 or diasemismic temperament, 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.

The name charisma for this comma was named by Godtone in December 2023, and refers 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 are used for horcrux extensions).

See also

• Small comma
• List of superparticular intervals