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, charisma, 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
Open this interval in xen-calc

256/255, the septendecimal kleisma, charisma or 255th subharmonic is a small 17-limit superparticular comma about 6.8 cents in size. It is the difference between 16/15 (the classical diatonic semitone) and 17/16 (the large septendecimal 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.

Temperaments

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

Charic

Subgroup: 2.3.5.17

Patent EDO tunings with relative error < 1/3 for all generators: 3, 9, 10, 12, 15, 21, 22, 24, 31, 32, 34, 43, 44, 46, 55, 56, 58, 65, 68, 77, 80, 111, 114, 145

CTE generators: (2/1,) 3/2 = 702.647, 5/4 = 387.798

Charismic

Subgroup: 17-limit

Patent EDO tunings with relative error < 1/3 for all generators: 9, 31, 43, 46, 56

CTE generators: [same as charic plus pure extra primes]

Srutal archagall

By also tempering the semitonisma, 256/255, an efficient temperament known as Srutal archagall is achieved, which is equivalently described as charic semitonic.

This is because of a general fact of S-expressions; in this case it manifests as that: {S16² × S17 , S16/S17} = {S16, S17}

Etymology and history

The "char" in the name "charisma" refers to the char data type in C-derived programming languages, where the char represents a byte of at least or exactly 8 bits. Thereby, the maximum unsigned value for an 8-bit char is 255 and the number of values an 8-bit char can take is 256, hence 256/255.

The former name diasemisma was proposed by Xenllium in May 2023. It is a contraction of diatonic semitone into a single word, however, a rename to charisma was proposed as part of an effort to make naming more standardised and for a number of reasons including potential confusion with diasem and the former nonconforming naming of horcrux in the 11- and 13-limit (which were formerly named "charisma" and "charismic", creating a potential false impression that the former was a comma, not a temperament, and that the latter was the temperament defined by tempering that comma in the corresponding prime limit); specifically, see Talk:256/255 and Temperament_naming#Contemporary_rules for details.

The rename took place as Starshine (from the XA Discord server) suggested (half-jokingly) that a chance had been missed to name it the charisma in December 2023, a name which Godtone took favor to and championed which then caused awareness of nonconforming names of two horcrux temeraments. A revision to charsma (no-i spelling) was proposed by Xenllium in January 2024 for disambiguation but this would cause inconsistency with the -ic -ismic -isma rule which is a reason that those same temperaments were already being proposed to be renamed.

See also

• Small comma
• List of superparticular intervals