256/255: Difference between revisions
Don't fight me on this. Char has a lower accuracy that is more associated with 120/119 than with this comma. If that temp should make this a char comma then it'd also make the marvel comma a char comma |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = charisma, septendecimal kleisma, octave-reduced 255th subharmonic | | Name = charisma, char 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 '''charisma''', ''' | '''256/255''', the '''charisma''', '''char 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]] (octave-reduced 255th subharmonic). | ||
== 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 (1<span style="font-family:'Arial', sans-serif">\</span>1), 3/2 = 702.647, 5/4 = 387.798 | |||
* [[CWE]]: ~2 = 1200.000 (1<span style="font-family:'Arial', sans-serif">\</span>1), 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 }} | ||
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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 === | === Char (2.3.5.7.17 temperament) === | ||
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]]. | 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]]. | ||