256/255: Difference between revisions
this is a silly reason, it's clear to any1 working with the commas (& more clear if we use S-expression notation, so i've added that to clarify, altho it was already present) that there is more damage implied, but srutal archagall is notable as being the way of making diaschismic much more accurate and interesting and giving it more interpretations, & it's natural to see it at least mentioned here; i avoided for 289/288 cuz it's more debatable there, but even then its omission feels out of place Tag: Undo |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = charisma, charic comma, septendecimal kleisma, octave-reduced 255th subharmonic | ||
| Color name = 17ug1, sugu 1sn, | | Color name = 17ug1, sugu 1sn, Sugu comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{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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[[Subgroup]]: 2.3.5.7.11.13.17 | [[Subgroup]]: 2.3.5.7.11.13.17 | ||
[[Mapping]]: | [[Mapping]]: | ||
{| class="right-all" | {| class="right-all" | ||
|- | |- | ||
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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 === | === Srutal archagall === | ||
By also tempering the semitonisma ([[289/288]] = S17), an efficient | 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 referencing a famous use of a number]] | |||