256/255: Difference between revisions
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If char is defined as that then this comma doesn't deserve to be called the char comma. Spell 1\1 in decimal. Misc. cleanup (-weird backslash character) |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septendecimal kleisma | | Name = charisma, 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 '''septendecimal kleisma''', '''charisma | '''256/255''', the '''septendecimal kleisma''', '''charisma''' or '''octave-reduced 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), 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]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, 3/2 = 702.6467, 5/4 = 387.7981 | ||
{{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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| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, 3/2 = 702.6467, 5/4 = 387.7981, ~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 }} | ||
Revision as of 13:33, 20 April 2025
| Interval information |
septendecimal kleisma,
octave-reduced 255th subharmonic
reduced,
reduced subharmonic
- "Charisma" redirects here. Not to be confused with Horcrux.
256/255, the septendecimal kleisma, charisma or octave-reduced 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), 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
By tempering it out is defined the full 17-limit rank-6 charismic temperament or 2.3.5.17 subgroup rank-3 charic temperament, which enables the charismic chords.
Charic
Subgroup: 2.3.5.17
Sval mapping: [⟨1 0 0 8], ⟨0 1 0 -1], ⟨0 0 1 -1]]
- sval mapping generators: ~2, ~3, ~5
Optimal tuning (CTE): ~2 = 1200.0000, 3/2 = 702.6467, 5/4 = 387.7981
Optimal ET sequence: 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg
Charismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 1 | 0 | 0 | 0 | 0 | 0 | 8 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
Optimal tuning (CTE): ~2 = 1200.0000, 3/2 = 702.6467, 5/4 = 387.7981, ~7/4, ~11/8, ~13/8
Optimal ET sequence: 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.
Char
Char temperament is a 2.3.5.7.17 subgroup extension tempering out both S15 and S16, which has 17/15~8/7 and 20/17~7/6.
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 the talk page 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.