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{{Infobox Interval | {{Infobox Interval | ||
| Name = charisma, charic comma, septendecimal kleisma | |||
| Color name = 17ug1, sugu 1sn, Sugu comma | |||
| Comma = yes | |||
| Name = septendecimal kleisma | |||
| Color name = | |||
| | |||
}} | }} | ||
{{Redirect|Charisma|the temperament that used to go by this name|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 the octave-reduced 255th subharmonic. By virtue of {{nowrap| 255 {{=}} 2<sup>8</sup> - 1 }}, it is a [[Mersenne comma]]. | |||
== Temperaments == | |||
[[Tempering out]] this comma defines the full 17-limit rank-6 '''charismic''' temperament or 2.3.5.17-subgroup rank-3 '''charic''' temperament. In either case, it enables the [[charismic chords]]. | |||
By also tempering out the semitonisma, [[289/288]] ({{S|17}}), charic can be tempered to an efficient but lower-accuracy rank-2 temperament known as [[srutal archagall]], which has [[17/15]]~[[9/8]] and therefore makes the minor third reached by the circle of fifths equal to ~[[20/17]]. Alternatively, by tempering out the marvel comma, [[225/224]] ({{S|15}}), charic can be extended to the 2.3.5.7.17 subgroup, known as [[char]], which is also of lower accuracy compared to either charic or [[marvel]] as it introduces the equivalences [[17/15]]~[[8/7]] and [[20/17]]~[[7/6]]. | |||
=== Charic === | |||
[[Subgroup]]: 2.3.5.17 | |||
{{Mapping|legend=2| 1 0 0 8 | 0 1 0 -1 | 0 0 1 -1 }} | |||
: mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.3878{{c}}, 3/2 = 702.7586{{c}}, 5/4 = 387.9493{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, 3/2 = 703.0148{{c}}, 5/4 = 388.0713{{c}} | |||
{{Optimal ET sequence|legend=1| 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg }} | |||
[[Badness]] (Sintel): 0.157 | |||
=== Charismic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Mapping]]: | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 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]]s: | |||
* [[WE]]: ~2 = 1199.3878{{c}}, 3/2 = 702.7586{{c}}, 5/4 = 387.9493{{c}}, ~7/4 = 970.0490{{c}}, ~11/8 = 553.1530{{c}}, ~13/8 = 842.3626{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, 3/2 = 703.0148{{c}}, 5/4 = 388.0713{{c}}, ~7/4 = 970.1701{{c}}, ~11/8 = 552.9744{{c}}, ~13/8 = 842.2995{{c}} | |||
{{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 }} | |||
[[Badness]] (Sintel): 2.75 | |||
== Etymology and history == | |||
This interval was described as ''septendecimal kleisma'' as early as 2020. | |||
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 seconds (i.e. [[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 out that comma in the corresponding prime limit). | |||
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. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[255/128]] – its [[octave complement]] | |||
* [[85/64]] – its [[fourth complement]] | |||
[[Category: | [[Category:Charismic]] | ||
[[Category: | [[Category:Commas named after their interval size]] | ||
[[Category: | [[Category:Commas referencing a famous use of a number]] | ||
Latest revision as of 14:33, 21 March 2026
| Interval information |
charic comma,
septendecimal kleisma
reduced,
reduced subharmonic
- "Charisma" redirects here. For the temperament that used to go by this name, see Horcrux.
256/255, the charisma, charic comma or septendecimal kleisma 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 the octave-reduced 255th subharmonic. By virtue of 255 = 28 - 1, it is a Mersenne comma.
Temperaments
Tempering out this comma defines the full 17-limit rank-6 charismic temperament or 2.3.5.17-subgroup rank-3 charic temperament. In either case, it enables the charismic chords.
By also tempering out the semitonisma, 289/288 (S17), charic can be tempered to an efficient but lower-accuracy rank-2 temperament known as srutal archagall, which has 17/15~9/8 and therefore makes the minor third reached by the circle of fifths equal to ~20/17. Alternatively, by tempering out the marvel comma, 225/224 (S15), charic can be extended to the 2.3.5.7.17 subgroup, known as char, which is also of lower accuracy compared to either charic or marvel as it introduces the equivalences 17/15~8/7 and 20/17~7/6.
Charic
Subgroup: 2.3.5.17
Subgroup-val mapping: [⟨1 0 0 8], ⟨0 1 0 -1], ⟨0 0 1 -1]]
- mapping generators: ~2, ~3, ~5
- WE: ~2 = 1199.3878 ¢, 3/2 = 702.7586 ¢, 5/4 = 387.9493 ¢
- CWE: ~2 = 1200.0000 ¢, 3/2 = 703.0148 ¢, 5/4 = 388.0713 ¢
Optimal ET sequence: 5, 7, 9, 10, 12, 22, 31, 34, 65, 87, 99, 343cgg, 442cgg, 541bcggg, 640bcgggg
Badness (Sintel): 0.157
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
- WE: ~2 = 1199.3878 ¢, 3/2 = 702.7586 ¢, 5/4 = 387.9493 ¢, ~7/4 = 970.0490 ¢, ~11/8 = 553.1530 ¢, ~13/8 = 842.3626 ¢
- CWE: ~2 = 1200.0000 ¢, 3/2 = 703.0148 ¢, 5/4 = 388.0713 ¢, ~7/4 = 970.1701 ¢, ~11/8 = 552.9744 ¢, ~13/8 = 842.2995 ¢
Optimal ET sequence: 15, 19, 22, 31, 41, 46, 58, 77, 80, 87, 99ef, 111, 121, 152fg, 167, 198g, 256cfg, 319fgg, 377cdefgg, 507cdeefggg, 705bccdeeffggg
Badness (Sintel): 2.75
Etymology and history
This interval was described as septendecimal kleisma as early as 2020.
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 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 seconds (i.e. 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 out that comma in the corresponding prime limit).
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.