256/255 - Revision history

FloraC: /* Temperaments */ update data

2026-03-21T14:33:22Z

Temperaments: update data

← Older revision		Revision as of 14:33, 21 March 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~{{c}}, 3/2 = 702.~~647~~{{c}}, 5/4 = 387.~~798~~{{c}}		* [[WE]]: ~2 = 1199.3878{{c}}, 3/2 = 702.7586{{c}}, 5/4 = 387.9493{{c}}
	* [[CWE]]: ~2 = 1200.~~000~~{{c}}, 3/2 = 703.~~015~~{{c}}, 5/4 = 388.~~071~~{{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 }}		{{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 ===		=== Charismic ===
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~{{c}}, 3/2 = 702.~~647~~{{c}}, 5/4 = 387.~~798~~{{c}}, ~7/4, ~11/8, ~13/8		* [[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.~~000~~{{c}}, 3/2 = 703.~~015~~{{c}}, 5/4 = 388.~~071~~{{c}}, ~7/4, ~11/8, ~13/8		* [[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 }}		{{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 ==		== Etymology and history ==

FloraC: Rework intro to temps. Also, "octave-reduced 255th subharmonic" isn't even a descriptive name, just a statement of fact

2026-03-21T12:36:55Z

Rework intro to temps. Also, "octave-reduced 255th subharmonic" isn't even a descriptive name, just a statement of fact

← Older revision		Revision as of 12:36, 21 March 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = charisma, charic comma, septendecimal kleisma~~, octave-reduced 255th subharmonic~~		\| Name = charisma, charic comma, septendecimal kleisma
	\| Color name = 17ug1, sugu 1sn, Sugu comma		\| Color name = 17ug1, sugu 1sn, Sugu comma
	\| Comma = yes		\| Comma = yes
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	{{Redirect\|Charisma\|the temperament that used to go by this name\|Horcrux}}		{{Redirect\|Charisma\|the temperament that used to go by this name\|Horcrux}}

	'''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]].		'''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 ==		== 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]].		[[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 ===		=== Charic ===
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	{{Mapping\|legend=2\| 1 0 0 8 \| 0 1 0 -1 \| 0 0 1 -1 }}		{{Mapping\|legend=2\| 1 0 0 8 \| 0 1 0 -1 \| 0 0 1 -1 }}
			: mapping generators: ~2, ~3, ~5
	: ~~sval~~ mapping generators: ~2, ~3, ~5

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798		* [[CTE]]: ~2 = 1200.000{{c}}, 3/2 = 702.647{{c}}, 5/4 = 387.798{{c}}
	* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071		* [[CWE]]: ~2 = 1200.000{{c}}, 3/2 = 703.015{{c}}, 5/4 = 388.071{{c}}

	{{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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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000, 3/2 = 702.647, 5/4 = 387.798, ~7/4, ~11/8, ~13/8		* [[CTE]]: ~2 = 1200.000{{c}}, 3/2 = 702.647{{c}}, 5/4 = 387.798{{c}}, ~7/4, ~11/8, ~13/8
	* [[CWE]]: ~2 = 1200.000, 3/2 = 703.015, 5/4 = 388.071, ~7/4, ~11/8, ~13/8		* [[CWE]]: ~2 = 1200.000{{c}}, 3/2 = 703.015{{c}}, 5/4 = 388.071{{c}}, ~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]].

	~~=== 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''~~.		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 "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 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 [[~~User:Godtone\|~~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.		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 ==
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[255/128]] – its [[octave complement]]		* [[255/128]] – its [[octave complement]]

FloraC at 14:49, 22 February 2026

2026-02-22T14:49:25Z

← Older revision		Revision as of 14:49, 22 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	{{Redirect\|Charisma\|temperament that used to go by this name\|Horcrux}}		{{Redirect\|Charisma\|the temperament that used to go by this name\|Horcrux}}

	'''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]].		'''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]].

FloraC at 14:49, 22 February 2026

2026-02-22T14:49:16Z

← Older revision		Revision as of 14:49, 22 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	{{Redirect~~-distinguish~~\|Charisma\|Horcrux}}		{{Redirect\|Charisma\|temperament that used to go by this name\|Horcrux}}

	'''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]].		'''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]].

Xenllium at 12:44, 23 April 2025

2025-04-23T12:44:00Z

← Older revision		Revision as of 12:44, 23 April 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = charisma, septendecimal kleisma, octave-reduced 255th subharmonic		\| 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
Line 6:		Line 6:
	{{Redirect-distinguish\|Charisma\|Horcrux}}		{{Redirect-distinguish\|Charisma\|Horcrux}}

	'''256/255''', the '''charisma''' 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)~~.		'''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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	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 ''~~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 "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]]

FloraC: As I said, 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

2025-04-21T08:56:02Z

As I said, 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

← Older revision		Revision as of 08:56, 21 April 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = charisma~~, char comma~~, septendecimal kleisma, octave-reduced 255th subharmonic		\| 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
Line 6:		Line 6:
	{{Redirect-distinguish\|Charisma\|Horcrux}}		{{Redirect-distinguish\|Charisma\|Horcrux}}

	'''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).		'''256/255''', the '''charisma''' 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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	[[Optimal tuning]]s:		[[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		* [[CTE]]: ~2 = 1200.000, 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		* [[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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	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 ~~(2.3.5.7.17 temperament)~~ ===		=== 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]].		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]].

Xenllium at 22:42, 20 April 2025

2025-04-20T22:42:40Z

← Older revision		Revision as of 22:42, 20 April 2025
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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''', '''~~septendecimal kleisma~~''', 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]].		'''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]] ([[CTE]]): ~2 = 1200.~~0000~~, 3/2 = 702.~~6467~~, 5/4 = 387.~~7981~~		[[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 }}
Line 43:		Line 45:
	: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13		: 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 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 }}
Line 50:		Line 54:
	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]].

FloraC: 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

2025-04-20T16:16:56Z

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

← Older revision		Revision as of 16:16, 20 April 2025
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = charisma~~, char comma~~, septendecimal kleisma, octave-reduced 255th subharmonic		\| 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
Line 6:		Line 6:
	{{Redirect-distinguish\|Charisma\|Horcrux}}		{{Redirect-distinguish\|Charisma\|Horcrux}}

	'''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]].		'''256/255''', the '''charisma''', '''septendecimal kleisma''', 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 ==
Line 50:		Line 50:
	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 ~~temperament~~ ===		=== 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, which ~~has~~ [[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]].

	== Etymology and history ==		== Etymology and history ==

Xenllium at 15:05, 20 April 2025

2025-04-20T15:05:26Z

← Older revision		Revision as of 15:05, 20 April 2025
Line 1:		Line 1:
	{{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
Line 50:		Line 50:
	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 temperament ===
	~~[[Marvel family #Char\|Char~~ temperament~~]] is a~~ 2.3.5.7.17 subgroup extension ~~tempering~~ out both [[225/224\|S15]] and S16, which has [[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, which has [[17/15]]~[[8/7]] and [[20/17]]~[[7/6]].

	== Etymology and history ==		== Etymology and history ==

FloraC: 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)

2025-04-20T13:33:14Z

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)

← Older revision		Revision as of 13:33, 20 April 2025
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = septendecimal kleisma~~, charisma, char comma~~, octave-reduced 255th subharmonic		\| 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
Line 6:		Line 6:
	{{Redirect-distinguish\|Charisma\|Horcrux}}		{{Redirect-distinguish\|Charisma\|Horcrux}}

	'''256/255''', the '''septendecimal kleisma''', '''charisma~~''', '''char comma~~''' 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]].		'''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 = ~~1＼1~~, 3/2 = 702.6467, 5/4 = 387.7981		[[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 }}
Line 41:		Line 41:
	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}
	: ~~Mapping~~ generators: ~2, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1＼1~~, 3/2 = 702.6467, 5/4 = 387.7981, ~7/4, ~11/8, ~13/8		[[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 }}