256/255: Difference between revisions
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{{Redirect-distinguish|Charisma|Horcrux}} | {{Redirect-distinguish|Charisma|Horcrux}} | ||
'''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]] | '''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]]. | ||
== Temperaments == | == Temperaments == | ||
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[[Subgroup]]: 2.3.5.17 | [[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 | Patent EDO tunings with [[relative error]] < 1/3 for all generators: {{Optimal ET sequence|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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=== Charismic === | === Charismic === | ||
[[Subgroup]]: [[17-limit]] | [[Subgroup]]: full [[17-limit]] | ||
[[Mapping]]: | [[Mapping]]: same as charic plus trivial pure extra primes | ||
Patent EDO tunings with [[relative error]] < 1/3 for all generators: 9, 31, 43, 46, 56 | Patent EDO tunings with [[relative error]] < 1/3 for all generators: {{Optimal ET sequence|9, 31, 43, 46, 56 }} | ||
[[CTE]] generators: | [[CTE]] generators: same as charic plus trivial pure extra primes | ||
=== [[Srutal archagall]] === | === [[Srutal archagall]] === | ||
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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 "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, | The former name ''diasemisma'' was proposed by [[User:Xenllium|Xenllium]] in May 2023. It is a contraction of ''diatonic semitone'' into a single word. In some contexts, both [[16/15]] and [[17/16]] are considered minor second (ie. [[diatonic semitone]]), namely classical diatonic semitone and minor diatonic semitone respectively. 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. | ||
Revision as of 11:30, 27 January 2024
| Interval information |
charisma,
char comma,
255th subharmonic
Sugu comma
reduced,
reduced subharmonic
- "Charisma" redirects here. Not to be confused with Horcrux.
256/255, the septendecimal kleisma, charisma, char comma 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.
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
Mapping: [⟨1 1 2 5], ⟨0 1 0 -1], ⟨0 0 1 -1]]
CTE generators: (2/1,) 3/2 = 702.647, 5/4 = 387.798
Charismic
Mapping: same as charic plus trivial pure extra primes
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
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
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 Xenllium in May 2023. It is a contraction of diatonic semitone into a single word. In some contexts, both 16/15 and 17/16 are considered minor second (ie. diatonic semitone), namely classical diatonic semitone and minor diatonic semitone respectively. 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.