256/255: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septendecimal kleisma, <br>charisma, <br>255th subharmonic | | Name = septendecimal kleisma, <br>charisma, char comma, <br>255th subharmonic | ||
| Color name = 17ug1, sugu 1sn, <br>Sugu comma | | Color name = 17ug1, sugu 1sn, <br>Sugu comma | ||
| Comma = yes | | Comma = yes | ||
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{{Redirect-distinguish|Charisma|Horcrux}} | {{Redirect-distinguish|Charisma|Horcrux}} | ||
'''256/255''', the '''septendecimal kleisma''', '''charisma''' 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]] (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. | '''256/255''', the '''septendecimal kleisma''', '''charisma''', '''char comma''' 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]] (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 == | == 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]]. | 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 === | === Charic === | ||
[[Subgroup]]: 2.3.5.17 | [[Subgroup]]: 2.3.5.17 | ||
Patent EDO tunings with [[relative error]] | 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 | ||
{{mapping|legend=1| 1 1 2 5 | 0 1 0 -1 | 0 0 1 -1 }} | {{mapping|legend=1| 1 1 2 5 | 0 1 0 -1 | 0 0 1 -1 }} | ||
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[[Mapping]]: [same as charic plus trivial pure extra primes] | [[Mapping]]: [same as charic plus trivial pure extra primes] | ||
Patent EDO tunings with [[relative error]] | Patent EDO tunings with [[relative error]] < 1/3 for all generators: 9, 31, 43, 46, 56 | ||
[[CTE]] generators: [same as charic plus trivial pure extra primes] | [[CTE]] generators: [same as charic plus trivial pure extra primes] | ||
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== Etymology and history == | == Etymology and history == | ||
The "char" in the name | Before 2023, this interval was known as ''septendecimal kleisma'' or ''255th subharmonic''. | ||
The "char" in the name ''charisma'' (or ''char comma'') 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 [[User:Xenllium|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 [[ | The former name ''diasemisma'' was proposed by [[User:Xenllium|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 [[User:Godtone|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. | 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 [[User:Godtone|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 == | == See also == | ||