289/288 - Revision history

FloraC at 14:41, 21 March 2026

2026-03-21T14:41:13Z

← Older revision		Revision as of 14:41, 21 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].		'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[small comma\|small]] [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].

	== Commatic relations ==		== Commatic relations ==
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	== See also ==		== See also ==
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:Semitonismic]]		[[Category:Semitonismic]]
	[[Category:Commas named for the intervals they stack]]		[[Category:Commas named for the intervals they stack]]

FloraC: Update data

2026-03-21T14:38:56Z

Update data

← Older revision		Revision as of 14:38, 21 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}

	'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].		'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].

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	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic ~~temperament~~''', or in the 2.3.17 subgroup, the rank-2 '''semitonic ~~temperament~~'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.		[[Tempering out]] this comma in the full 17-limit results in the rank-6 '''semitonismic''' temperament, or in the 2.3.17 subgroup, the rank-2 '''semitonic''' temperament. In either case the [[2/1\|octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

	=== Semitonic ===		=== Semitonic ===
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}

	: mapping generators: ~17/12, ~3, ~5, ~7, ~11, ~13		: mapping generators: ~17/12, ~3, ~5, ~7, ~11, ~13

	[[Optimal tuning]] ([[~~CTE~~]]): ~17/12 = 1\2, ~3/2 = 702.~~3472~~, 5/4, 7/4, 11/8, 13/8		[[Optimal tuning]]s:
			* [[WE]]: ~17/12 = 600.1471{{c}}, ~3/2 = 701.9563{{c}}, ~5/4 = 385.7246{{c}}, ~7/4 = 968.2366{{c}}, ~11/8 = 550.4343{{c}}, ~13/8 = 839.6439{{c}}
			* [[CWE]]: ~17/12 = 600.0000{{c}}, ~3/2 = 702.0260{{c}}, ~5/4 = 385.9237{{c}}, ~7/4 = 968.3544{{c}}, ~11/8 = 550.7369{{c}}, ~13/8 = 839.9061{{c}}

	{{Optimal ET sequence\|legend=1\| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}*		{{Optimal ET sequence\|legend=1\| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }} *

	<nowiki>*</nowiki> [[optimal patent val]]: [[280edo\|280]]		<nowiki>*</nowiki> [[optimal patent val]]: [[280edo\|280]]

			[[Badness]] (Sintel): 3.70

	== Etymology ==		== Etymology ==

BudjarnLambeth at 00:39, 16 November 2024

2024-11-16T00:39:51Z

← Older revision		Revision as of 00:39, 16 November 2024
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	[[Category:Semitonismic]]		[[Category:Semitonismic]]
			[[Category:Commas named for the intervals they stack]]

BudjarnLambeth: Add to info box the names mentioned in body of text

2024-10-25T04:28:22Z

Add to info box the names mentioned in body of text

← Older revision		Revision as of 04:28, 25 October 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = semitonisma		\| Name = semitonisma, septendecimal semitones comma, septendecimal 6-cent comma
	\| Color name = 17oo2, soso 2nd,<br>Soso comma		\| Color name = 17oo2, soso 2nd,<br>Soso comma
	\| Comma = yes		\| Comma = yes

FloraC: /* Temperaments */ -duplicate data

2024-10-20T08:12:27Z

Temperaments: -duplicate data

← Older revision		Revision as of 08:12, 20 October 2024
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	=== Semitonic ===		=== Semitonic ===
	[[~~Subgroup~~]]~~: 2~~.~~3.17~~		See [[No-fives subgroup temperaments #Semitonic]].

	~~{{Mapping\|legend=2\| 2 0 5 \| 0 1 1 }}~~

	~~: sval mapping generators: ~17/12, ~3~~

	~~[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)~~

	~~{{Optimal ET sequence\|legend=1\| 10, 12, 58, 70, 82, 94, 106, 118, 224g }}~~

	=== Semitonismic ===		=== Semitonismic ===

FloraC: /* Temperaments */ OPV

2024-03-12T09:47:02Z

Temperaments: OPV

← Older revision		Revision as of 09:47, 12 March 2024
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	[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)		[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)

	{{Optimal ET sequence\|legend=1\| 12, 58, 70, 82, 94, 106, 118, 224g }}		{{Optimal ET sequence\|legend=1\| 10, 12, 58, 70, 82, 94, 106, 118, 224g }}

	=== Semitonismic ===		=== Semitonismic ===
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	[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8		[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8

	{{Optimal ET sequence\|legend=1\| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}		{{Optimal ET sequence\|legend=1\| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}*

			<nowiki>*</nowiki> [[optimal patent val]]: [[280edo\|280]]

	== Etymology ==		== Etymology ==

FloraC: /* Temperaments */ swap them to impress the reader of the "simpler" temp first

2024-01-19T07:25:13Z

Temperaments: swap them to impress the reader of the "simpler" temp first

@@ Line 21: / Line 21: @@
 == Temperaments ==
 Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
 === Semitonismic ===
@@ Line 46: / Line 57: @@
 {{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}
 == Etymology ==

FloraC: Restore certain parts that are helpful for clarity

2024-01-18T11:48:25Z

Restore certain parts that are helpful for clarity

← Older revision		Revision as of 11:48, 18 January 2024
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.		Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

	=== Semitonismic ===		=== Semitonismic ===

FloraC: Revert to original normalized state

2024-01-18T11:45:44Z

Revert to original normalized state

@@ Line 20: / Line 20: @@
 == Temperaments ==
-Tempering out this comma results in the rank-2 '''semitonic temperament''' in the 2.3.17 subgroup, or the rank-6 '''semitonismic temperament''' in the full [[17-limit]]. In either case, the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
+Tempering out this comma results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
 === Semitonismic ===
@@ Line 55: / Line 46: @@
 {{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}
 == Etymology ==

Godtone: /* Temperaments */

2024-01-16T16:57:10Z

Temperaments

← Older revision		Revision as of 16:57, 16 January 2024
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	{{Optimal ET sequence\|legend=1\| 12, 58, 70, 82, 94, 106, 118, 224g }}		{{Optimal ET sequence\|legend=1\| 12, 58, 70, 82, 94, 106, 118, 224g }}

	{{Mapping\|legend=2\| 2 2 7 \| 0 1 1 }}		{{Mapping\|legend=1\| 2 2 7 \| 0 1 1 }}

	[[CTE]] generators: ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)		[[CTE]] generators: ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)