Harry - Revision history

Overthink: /* Interval chain */ start section

2026-04-08T18:48:24Z

Interval chain: start section

← Older revision		Revision as of 18:48, 8 April 2026
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	\| '''16/11'''		\| '''16/11'''
	\|}		\|}

			=== As a detemperament of 14et ===
			Harry is naturally considered a detemperament of [[14edo\|14 equal temperament]], thus containing both diatonic and interordinal interval catgories. The small step at 1/2 octave minus seven ~21/20 generators serves as a spacer between intervals in the same category, representing 81/80~91/90~99/98~100/99~105/104~121/120.

			{{Todo\|complete section}}

	== Chords and harmony ==		== Chords and harmony ==

FloraC: + infobox

2026-03-26T13:45:05Z

+ infobox

← Older revision		Revision as of 13:45, 26 March 2026
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	'''Harry''' is the rank-2 [[~~Regular~~ temperament\|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993\|made]] a third of [[4/3]]) and three of which [[1001/1000\|made]] equal to [[15/13]] (which is [[676/675\|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].		{{Infobox regtemp
			\| Title = Harry
			\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
			\| Comma basis = [[2401/2400]], [[19683/19600]] (7-limit); <br>[[243/242]], [[441/440]], [[4000/3993]] (11-limit); <br>[[243/242]], [[351/350]], [[364/363]], [[441/440]]<br>(13-limit)
			\| Edo join 1 = 58 \| Edo join 2 = 72
			\| Mapping = 2; -6 -17 -10 -15 -26
			\| Generators = 21/20 \| Generators tuning = 83.1 \| Optimization method = CWE
			\| MOS scales = [[2L 12s]], [[14L 2s]], [[14L 16s]], [[14L 30s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 1.81 \| Complexity 1 = 44
			\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 3.30 \| Complexity 2 = 58
			}}
			'''Harry''' is the rank-2 [[regular temperament\|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993\|made]] a third of [[4/3]]) and three of which [[1001/1000\|made]] equal to [[15/13]] (which is [[676/675\|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].

	Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.		Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.

FloraC: /* Chords */ -> chords and harmony

2025-12-07T10:04:09Z

Chords: -> chords and harmony

← Older revision		Revision as of 10:04, 7 December 2025
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	\|}		\|}

	== Chords ==		== Chords and harmony ==
	{{~~Main~~\| Chords of harry }}		{{See also\| Chords of harry }}

	== Scales ==		== Scales ==

FloraC: /* Tuning spectrum */ + basic norm-based tunings

2025-12-07T10:02:43Z

Tuning spectrum: + basic norm-based tunings

@@ Line 121: / Line 121: @@
 * [[Harry58]]
-== Tuning spectrum ==
+== Tunings ==
 {| class="wikitable center-all left-4"
 |-

FloraC: /* Tuning spectrum */ note vals. Simplify ratios under octave equivalence. Style

2025-12-07T09:57:04Z

Tuning spectrum: note vals. Simplify ratios under octave equivalence. Style

← Older revision		Revision as of 09:57, 7 December 2025
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! ~~EDO~~<br>generator		! Edo<br>generator
	! [[~~eigenmonzo~~\|~~eigenmonzo~~<br>(unchanged interval)]]		! [[Eigenmonzo\|Eigenmonzo<br>(unchanged interval)]]
	! ~~generator~~<br>(¢)		! Generator<br>(¢)
	! ~~comments~~		! Comments
	\|-		\|-
	\| 3\44		\| 3\44
	\|		\|
	\| 81.818		\| 81.818
	\| ~~Lower~~ bound of 7- ~~and~~ 11-odd-limit diamond monotone		\| 44ceff val, lower bound of 7- to 11-odd-limit diamond monotone
	\|-		\|-
	\|		\|
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	\|-		\|-
	\|		\|
	\| 4/3		\| 3/2
	\| 83.007		\| 83.007
	\|		\|
	\|-		\|-
	\|		\|
	\| 14/13		\| 13/7
	\| 83.019		\| 83.019
	\|		\|
	\|-		\|-
	\|		\|
	\| 16/13		\| 13/8
	\| 83.057		\| 83.057
	\|		\|
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	\|-		\|-
	\|		\|
	\| 18/13		\| 13/9
	\| 83.099		\| 83.099
	\| 13- and 15-odd-limit minimax		\| 13- and 15-odd-limit minimax
	\|-		\|-
	\|		\|
	\| 8/7		\| 7/4
	\| 83.117		\| 83.117
	\|		\|
	\|-		\|-
	\|		\|
	\| 16/15		\| 15/8
	\| 83.119		\| 83.119
	\|		\|
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	\|-		\|-
	\|		\|
	\| 6/5		\| 5/3
	\| 83.240		\| 83.240
	\|		\|
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	\|-		\|-
	\|		\|
	\| 12/11		\| 11/6
	\| 83.404		\| 83.404
	\|		\|
	\|-		\|-
	\|		\|
	\| 14/11		\| 11/7
	\| 83.502		\| 83.502
	\|		\|
	\|-		\|-
	\|		\|
	\| 10/9		\| 9/5
	\| 83.519		\| 83.519
	\|		\|
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	\|		\|
	\| 83.721		\| 83.721
	\|		\| 86ceff val
	\|-		\|-
	\|		\|

Overthink: /* Tuning spectrum */ fixed monotone tuning (6\86 swaps 13/12 and 14/13)

2025-12-06T22:11:23Z

Tuning spectrum: fixed monotone tuning (6\86 swaps 13/12 and 14/13)

← Older revision		Revision as of 22:11, 6 December 2025
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	\|		\|
	\| 83.333		\| 83.333
	\|		\| Upper bound of 13-odd-limit diamond monotone
	\|-		\|-
	\|		\|
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	\|		\|
	\| 83.721		\| 83.721
	\| ~~Upper bound of 13-odd-limit diamond monotone~~		\|
	\|-		\|-
	\|		\|

Squib: 4/3 is split into six, not twelve

2025-06-29T16:39:31Z

4/3 is split into six, not twelve

← Older revision		Revision as of 16:39, 29 June 2025
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	'''Harry''' is the rank-2 [[Regular temperament\|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993\|made]] a third of [[4/3]]) and three of which [[1001/1000\|made]] equal to [[15/13]] (which is [[676/675\|made]] a half of 4/3). This means that harry splits 4/3 into 12 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].		'''Harry''' is the rank-2 [[Regular temperament\|temperament]] with a [[period]] of half an [[octave]] and a [[generator]] somewhere between [[22/21]] and [[21/20]] (which are tempered together in harry), or around 83 [[cent]]s. Two generators are thus equal to [[11/10]] (which is [[4000/3993\|made]] a third of [[4/3]]) and three of which [[1001/1000\|made]] equal to [[15/13]] (which is [[676/675\|made]] a half of 4/3). This means that harry splits 4/3 into 6 equal parts, a highly composite number, and splitting 2/1 into two equal parts (representing [[24/17]]~[[99/70]]) means it also splits 3/2 into two equal parts (representing [[11/9]]~[[49/40]]). Alternatively, it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[mos]] of harry has the shape [[2L 12s]].

	Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.		Harry was named after [[Harry Partch]], which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.
Line 5:		Line 5:
	This particular rank-2 temperament might be called "harry" because the lowest [[edo]] in which [[Harry Partch's 43-tone scale]] is represented distinctly is [[58edo]], and harry is one of the best temperaments supported by 58edo (it is 58 & 72). Alternatively, if you look at the tempered image of the 43-tone JI scale in this temperament, it is relatively compact and never "backtracks" from one of the 14 clusters to the previous one. In fact, the entire temperament can be derived from knowing that the fragment [12/11, 11/10, 10/9, 9/8] is supposed to be equidistant, and [14/11, 9/7] also has that same separation. The steps of those scale fragments are 121/120, 100/99, 81/80, and 99/98. Tempering these together means that 4000/3993, 243/242, and 9801/9800 are all tempered out, and harry is the unique 11-limit rank-2 temperament tempering those out.		This particular rank-2 temperament might be called "harry" because the lowest [[edo]] in which [[Harry Partch's 43-tone scale]] is represented distinctly is [[58edo]], and harry is one of the best temperaments supported by 58edo (it is 58 & 72). Alternatively, if you look at the tempered image of the 43-tone JI scale in this temperament, it is relatively compact and never "backtracks" from one of the 14 clusters to the previous one. In fact, the entire temperament can be derived from knowing that the fragment [12/11, 11/10, 10/9, 9/8] is supposed to be equidistant, and [14/11, 9/7] also has that same separation. The steps of those scale fragments are 121/120, 100/99, 81/80, and 99/98. Tempering these together means that 4000/3993, 243/242, and 9801/9800 are all tempered out, and harry is the unique 11-limit rank-2 temperament tempering those out.

	See [[Gravity family #Harry]] for more technical data.		See [[Gravity family #Harry]] for more technical data.

	== Interval chain ==		== Interval chain ==

Lériendil: Text replacement - "(unchanged-interval)" to "(unchanged interval)"

2025-06-21T06:59:25Z

Text replacement - "(unchanged-interval)" to "(unchanged interval)"

← Older revision		Revision as of 06:59, 21 June 2025
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	\|-		\|-
	! EDO<br>generator		! EDO<br>generator
	! [[eigenmonzo\|eigenmonzo<br>(unchanged-interval)]]		! [[eigenmonzo\|eigenmonzo<br>(unchanged interval)]]
	! generator<br>(¢)		! generator<br>(¢)
	! comments		! comments

FloraC: - parent category

2025-04-28T14:14:13Z

- parent category

← Older revision		Revision as of 14:14, 28 April 2025
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	* [[Lumatone mapping for harry]]		* [[Lumatone mapping for harry]]

	~~[[Category:Temperaments]]~~
	[[Category:Harry\| ]] <!-- main article -->		[[Category:Harry\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Lériendil at 23:09, 19 April 2025

2025-04-19T23:09:10Z

← Older revision		Revision as of 23:09, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Harry\| ]] <!-- main article -->		[[Category:Harry\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
	[[Category:Gravity family]]		[[Category:Gravity family]]
	[[Category:Stearnsmic clan]]		[[Category:Stearnsmic clan]]
	[[Category:Breedsmic temperaments]]		[[Category:Breedsmic temperaments]]
	[[Category:Cataharry temperaments]]		[[Category:Cataharry temperaments]]