82/81 - Revision history

FloraC: Improve links

2026-05-11T17:43:30Z

Improve links

← Older revision		Revision as of 17:43, 11 May 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[~~HEJI~~]], is a 2.3.41-subgroup [[comma]]. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]].		'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[Helmholtz–Ellis notation]], is a 2.3.41-subgroup [[comma]]. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]].

	This interval is significant in the [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.		This interval is significant in the [[Functional Just System]] and Helmholtz–Ellis notation as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.

	== Temperaments ==		== Temperaments ==

FloraC: Recognize reversed meantone as a name

2026-05-11T17:39:35Z

Recognize reversed meantone as a name

← Older revision		Revision as of 17:39, 11 May 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 82/81		\| Ratio = 82/81
	\| Name = 41-limit Johnston comma (HEJI)		\| Name = reversed meantone comma, 41-limit Johnston comma (HEJI)
	\| Color name = 41o1, fowo unison		\| Color name = 41o1, fowo unison
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''82/81''', or the '''41-limit Johnston comma ~~(HEJI)~~''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560~~]]. It is the parent comma for the [[reversed meantone clan~~]].		'''82/81''', the '''reversed meantone comma''', or the '''41-limit Johnston comma''' in [[HEJI]], is a 2.3.41-subgroup [[comma]]. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]].

	This interval is significant in the [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.		This interval is significant in the [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.

			== Temperaments ==
			[[Tempering out]] this comma in the 2.3.41 subgroup leads to a rank-2 temperament known as [[reversed meantone]].

			[[Category:Reversed meantone]]
	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: Clarify

2025-07-12T13:43:34Z

Clarify

← Older revision		Revision as of 13:43, 12 July 2025
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	'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is the parent comma for the [[reversed meantone clan]].		'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is the parent comma for the [[reversed meantone clan]].

	This interval is significant in the [[Functional Just System]] and [[~~Helmholtz-Ellis~~ notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In ~~Helmholtz-Ellis~~ notation, the symbols ~~being used~~ are ~~virtually identical to~~ [[Ben Johnston]]'s plus and minus signs representing 81/80.		This interval is significant in the [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz–Ellis notation, the symbols are adapted from [[Ben Johnston]]'s plus and minus signs representing 81/80.

	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: +short explanation on its look in HEJI and hopefully this helps to understand the current name

2024-11-28T18:05:48Z

+short explanation on its look in HEJI and hopefully this helps to understand the current name

← Older revision		Revision as of 18:05, 28 November 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. ~~It is the parent comma for~~ the [[~~reversed meantone clan~~]].		'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is the parent comma for the [[reversed meantone clan]].

			This interval is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. In Helmholtz-Ellis notation, the symbols being used are virtually identical to [[Ben Johnston]]'s plus and minus signs representing 81/80.

	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

FloraC: +significance in FJS and misc. rework

2024-11-28T17:19:50Z

+significance in FJS and misc. rework

← Older revision		Revision as of 17:19, 28 November 2024
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	{{Infobox Interval		{{Infobox Interval
	\|Ratio = 82/81		\| Ratio = 82/81
	\|Name = 41-limit Johnston comma (HEJI)		\| Name = 41-limit Johnston comma (HEJI)
	\|Color name = 41o1, fowo unison		\| Color name = 41o1, fowo unison
	\|Comma = yes		\| Comma = yes
	}}		}}
	'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 ~~(the 41st harmonic)~~ exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit ~~(prefix???~~) interval. It is the parent comma for the [[reversed meantone clan]].		'''82/81''', or the '''41-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which the octave-reduced 41st harmonic [[41/32]] exceeds the Pythagorean major third (ditone) of [[81/64]], and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in the [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby quadracesimoprimal (41-limit) interval. It is the parent comma for the [[reversed meantone clan]].

	[[Category:Commas named after composers]]		[[Category:Commas named after composers]]
	[[Category:Commas named after music theorists]]		[[Category:Commas named after music theorists]]

BudjarnLambeth at 01:37, 16 November 2024

2024-11-16T01:37:49Z

← Older revision		Revision as of 01:37, 16 November 2024
Line 6:		Line 6:
	}}		}}
	'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval. It is the parent comma for the [[reversed meantone clan]].		'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval. It is the parent comma for the [[reversed meantone clan]].

			[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

BudjarnLambeth: Add link to orphan page

2024-09-19T03:51:04Z

Add link to orphan page

← Older revision		Revision as of 03:51, 19 September 2024
Line 5:		Line 5:
	\|Comma = yes		\|Comma = yes
	}}		}}
	'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.		'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval. It is the parent comma for the [[reversed meantone clan]].

Lériendil at 12:46, 23 July 2024

2024-07-23T12:46:20Z

← Older revision		Revision as of 12:46, 23 July 2024
Line 5:		Line 5:
	\|Comma = yes		\|Comma = yes
	}}		}}
	'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.		'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64, and differs from the syntonic comma ([[81/80]]) by [[6561/6560]]. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.

Francium: Added Infobox Interval

2023-09-24T10:01:31Z

Added Infobox Interval

← Older revision		Revision as of 10:01, 24 September 2023
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	{~~\| class="wikitable"~~		{{Infobox Interval
	\|+Interval ~~information~~		\|Ratio = 82/81
	\|Ratio		\|Name = 41-limit Johnston comma (HEJI)
	\|82/81		\|Color name = 41o1, fowo unison
	\|-		\|Comma = yes
	~~\|[[Smonzos and svals\|Subgroup monzo]]~~		}}
	~~\|2.3.41 [1 -4 1⟩~~
	\|-
	~~\|Size in [[Cent\|cents]]~~
	~~\|21.242402¢~~
	\|-
	~~\|Names~~
	\|41-limit Johnston comma (HEJI)
	\|}
	'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.		'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.

Stephen Weigel: Created for HEJI

2023-09-24T03:54:46Z

Created for HEJI

New page

{| class="wikitable"
|+Interval information
|Ratio
|82/81
|-
|[[Smonzos and svals|Subgroup monzo]]
|2.3.41 [1 -4 1⟩
|-
|Size in [[Cent|cents]]
|21.242402¢
|-
|Names
|41-limit Johnston comma (HEJI)
|}
'''82/81''', or the 41'''-limit Johnston comma (HEJI)''', is a 2.3.41 subgroup comma. It is the amount by which 41/32 (the 41st harmonic) exceeds the Pythagorean major third (ditone) of 81/64. It is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby 41-limit (prefix???) interval.