256/255: Difference between revisions

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'''256/255''', the '''septendecimal kleisma''', '''diasemisma''' or '''255th subharmonic''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s 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.
'''256/255''', the '''septendecimal kleisma''', '''charisma''', '''diasemisma''' or '''255th subharmonic''', is a [[small comma|small]] [[17-limit]] [[superparticular]] comma about 6.8 [[cent]]s 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 '''diasemismic temperament''', which enables the [[diasemismic chords]].
By tempering it out is defined the '''charismic temperament''' or '''diasemismic temperament''', which enables the [[charismic chords]].


== Etymology ==
== Etymology ==
The name ''diasemisma'' was named by [[User:Xenllium|Xenllium]] in 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 ''diasemisma'' was named by [[User:Xenllium|Xenllium]] in 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'' was named by [[User:Godtone|Godtone]] in 2023, and refers to the comma being a superparticular ratio with the numerator is 2^8 (the number of combinations in a byte, often referred to as a char in programming).
== See also ==
== See also ==
* [[Small comma]]
* [[Small comma]]

Revision as of 03:46, 6 January 2024

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,
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 norm (log2 nd) 15.9944
Weil norm (log2 max(n, d)) 16
Wilson norm (sopfr(nd)) 41
Comma size small
S-expression S16
Open this interval in xen-calc

256/255, the septendecimal kleisma, charisma, 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 charismic temperament or diasemismic temperament, which enables the charismic chords.

Etymology

The name diasemisma was named by Xenllium in 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 was named by Godtone in 2023, and refers to the comma being a superparticular ratio with the numerator is 2^8 (the number of combinations in a byte, often referred to as a char in programming).

See also