256/255: Difference between revisions
Fixed the style of the archagall fifth mention to match the rest of the intervals listed Tags: Mobile edit Mobile web edit |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = charisma, charic comma, septendecimal kleisma, octave-reduced 255th subharmonic | ||
| Color name = 17ug1, sugu 1sn, Sugu comma | | Color name = 17ug1, sugu 1sn, Sugu comma | ||
| Comma = yes | | Comma = yes | ||
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{{Redirect-distinguish|Charisma|Horcrux}} | {{Redirect-distinguish|Charisma|Horcrux}} | ||
'''256/255''', the | '''256/255''', the '''charisma''', '''charic comma''' or '''septendecimal kleisma''' 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), the difference between [[128/85]] (the archagall fifth) and [[3/2]] (the just perfect fifth), and the amount by which a stack consisting of [[15/8]] and 17/16 falls short of an [[octave]]. It is a [[Mersenne comma]]. | ||
== Temperaments == | == Temperaments == | ||
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: sval mapping generators: ~2, ~3, ~5 | : sval mapping generators: ~2, ~3, ~5 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798 | |||
* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071 | |||
{{Optimal ET sequence|legend=1| 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg }} | {{Optimal ET sequence|legend=1| 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg }} | ||
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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798, ~7/4, ~11/8, ~13/8 | |||
* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071, ~7/4, ~11/8, ~13/8 | |||
{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 41, 46, 58, 77, 80, 87, 99ef, 111, 121, 152fg, 167, 198g, 256cfg, 319fgg, 377cdefgg, 507cdeefggg, 705bccdeeffggg }} | {{Optimal ET sequence|legend=1| 15, 19, 22, 31, 41, 46, 58, 77, 80, 87, 99ef, 111, 121, 152fg, 167, 198g, 256cfg, 319fgg, 377cdefgg, 507cdeefggg, 705bccdeeffggg }} | ||
=== | === Srutal archagall === | ||
By also tempering out the semitonisma ([[289/288]] = S17), an efficient but lower accuracy temperament known as [[srutal archagall]] is achieved, which has [[17/15]]~[[9/8]] and therefore makes the minor third reached by the circle of fifths equal to ~[[20/17]]. | By also tempering out the semitonisma ([[289/288]] = S17), an efficient but lower accuracy temperament known as [[srutal archagall]] is achieved, which has [[17/15]]~[[9/8]] and therefore makes the minor third reached by the circle of fifths equal to ~[[20/17]]. | ||
=== Char === | |||
The charic temperament has an immediate 2.3.5.7.17 subgroup extension, the [[Marvel family #Char|char]] temperament. It tempers out both [[225/224|S15]] and S16, as well as their sum, [[120/119]], which induces the equivalences [[17/15]]~[[8/7]] and [[20/17]]~[[7/6]]. | |||
== Etymology and history == | == Etymology and history == | ||
Before 2023, this interval was known as ''septendecimal kleisma'' or ''255th subharmonic''. | Before 2023, this interval was known as ''septendecimal kleisma'' or ''255th subharmonic''. | ||
The "char" in the name ''charisma'' (or '' | The "char" in the name ''charisma'' (or ''charic 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. 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 the [[Talk:256/255|talk page]] and [[Temperament naming #Contemporary rules]] for details. | 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 the [[Talk:256/255|talk page]] and [[Temperament naming #Contemporary rules]] for details. | ||
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* [[Small comma]] | * [[Small comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[255/128]] – its [[octave complement]] | |||
* [[85/64]] – its [[fourth complement]] | |||
[[Category:Charismic]] | [[Category:Charismic]] | ||
[[Category:Commas named after their interval size]] | [[Category:Commas named after their interval size]] | ||
[[Category:Commas referencing a famous use of a number]] | [[Category:Commas referencing a famous use of a number]] | ||