Halftone - Revision history

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:23:55Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:23, 29 April 2025
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	[[Category:Halftone\| ]] <!-- main article -->		[[Category:Halftone\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup~~ temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave~~]]

FloraC: - parent category

2025-04-28T14:13:48Z

- parent category

← Older revision		Revision as of 14:13, 28 April 2025
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	{\|class="wikitable"		{\|class="wikitable"
	\|-		\|-
	\|53.040		\| 53.040
	\|182.823		\| 182.823
	\|312.606		\| 312.606
	\|442.389		\| 442.389
	\|572.172		\| 572.172
	\|0		\| 0
	\|129.783		\| 129.783
	\|259.566		\| 259.566
	\|389.349		\| 389.349
	\|519.132		\| 519.132
	\|648.915		\| 648.915
	\|-		\|-
	\|[[28/27]]		\| [[28/27]]
	\|[[10/9]]		\| [[10/9]]
	\|[[25/21]]		\| [[25/21]]
	\|125/98~98/75		\| 125/98~98/75
	\|[[7/5]]		\| [[7/5]]
	\|[[1/1]]		\| [[1/1]]
	\|[[15/14]]		\| [[15/14]]
	\|225/196~147/125		\| 225/196~147/125
	\|[[63/50]]		\| [[63/50]]
	\|[[27/20]]		\| [[27/20]]
	\|81/56		\| 81/56
	\|}		\|}

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

Lériendil at 23:08, 19 April 2025

2025-04-19T23:08:35Z

← Older revision		Revision as of 23:08, 19 April 2025
Line 40:		Line 40:

	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

CompactStar at 01:09, 10 June 2023

2023-06-10T01:09:57Z

← Older revision		Revision as of 01:09, 10 June 2023
Line 1:		Line 1:
	[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]		[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]

	'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone include [[~~6edf~~]], [[~~11edf~~]], [[~~16edf~~]], [[~~17edf~~]] ~~(not in the patent val)~~, [[21edf]], and [[27edf]].		'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone include [[5edf]], [[6edf]], [[11edf]], [[16edf]], [[21edf]], and [[27edf]].

	If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].		If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].

CompactStar at 01:09, 10 June 2023

2023-06-10T01:09:22Z

← Older revision		Revision as of 01:09, 10 June 2023
Line 1:		Line 1:
	[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]		[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]

	'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone ~~with relatively low error~~ include [[11edf]], [[16edf]], ~~and~~ [[17edf]] (not in the patent val)~~. 11edf particularly is an interesting case because it is also a close approximation of~~ [[~~19edo~~]], ~~which allows for playing both meantone~~ and ~~halftone music~~.		'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone include [[6edf]], [[11edf]], [[16edf]], [[17edf]] (not in the patent val), [[21edf]], and [[27edf]].

	If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].		If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].

CompactStar at 01:08, 10 June 2023

2023-06-10T01:08:03Z

← Older revision		Revision as of 01:08, 10 June 2023
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	== MOS scales ==		== MOS scales ==
	Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ( ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)\|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.		Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)\|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.


	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

CompactStar at 00:24, 10 June 2023

2023-06-10T00:24:38Z

← Older revision		Revision as of 00:24, 10 June 2023
Line 40:		Line 40:

	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Nonoctave]]

CompactStar at 00:24, 10 June 2023

2023-06-10T00:24:31Z

← Older revision		Revision as of 00:24, 10 June 2023
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	== MOS scales ==		== MOS scales ==
	Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ( ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)\|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.		Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ( ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)\|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.


			[[Category:Temperaments]]

CompactStar at 00:19, 10 June 2023

2023-06-10T00:19:34Z

← Older revision		Revision as of 00:19, 10 June 2023
Line 1:		Line 1:
	[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]		[[File:halftone6.wav\|thumb\|Halftone[6] example in 16edf and 4<nowiki>\|</nowiki>1 mode]]

	'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone with relatively low error include [[11edf]], [[16edf]], and [[17edf]] (not in the patent val). 11edf particularly is an interesting case because it is also an approximation of [[19edo]], which allows for playing both meantone and halftone music.		'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone with relatively low error include [[11edf]], [[16edf]], and [[17edf]] (not in the patent val). 11edf particularly is an interesting case because it is also a close approximation of [[19edo]], which allows for playing both meantone and halftone music.

	If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].		If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].

CompactStar at 00:14, 10 June 2023

2023-06-10T00:14:43Z

← Older revision		Revision as of 00:14, 10 June 2023
Line 36:		Line 36:

	== MOS scales ==		== MOS scales ==
	Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ( ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.		Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)\|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)\|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)\|5L 1s⟨3/2⟩]]) and 11 ( ([[5L 6s (3/2-equivalent)\|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)\|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.