Angel - Revision history

Dummy index: link target changed

2025-06-03T14:42:18Z

link target changed

← Older revision		Revision as of 14:42, 3 June 2025
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	If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.		If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.

	More specifically, the term angel may refer to various [[MOS scale\|mosses]] and [[MODMOS scale\|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[~~diatonic, chromatic, enharmonic, subchromatic~~\|pentic, diatonic, chromatic, and enharmonic]] scales respectively.		More specifically, the term angel may refer to various [[MOS scale\|mosses]] and [[MODMOS scale\|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[meantone #Scales\|pentic, diatonic, chromatic, and enharmonic]] scales respectively.

	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You do not even have to train yourself to hear the 5th harmonic as [[equivalence\|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You do not even have to train yourself to hear the 5th harmonic as [[equivalence\|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

ArrowHead294 at 14:02, 20 March 2025

2025-03-20T14:02:04Z

← Older revision		Revision as of 14:02, 20 March 2025
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	If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.		If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.

	More specifically, the term angel may refer to various [[MOS scale\|mosses]] and [[MODMOS scale\|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[~~Diatonic~~, ~~Chromatic~~, ~~Enharmonic~~, ~~Subchromatic~~\|pentic, diatonic, chromatic, and enharmonic]] scales respectively.		More specifically, the term angel may refer to various [[MOS scale\|mosses]] and [[MODMOS scale\|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[diatonic, chromatic, enharmonic, subchromatic\|pentic, diatonic, chromatic, and enharmonic]] scales respectively.

	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You do not even have to train yourself to hear the 5th harmonic as [[equivalence\|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You do not even have to train yourself to hear the 5th harmonic as [[equivalence\|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

FloraC: Review

2024-10-15T13:49:45Z

Review

← Older revision		Revision as of 13:49, 15 October 2024
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	'''Angel''' is ~~a name* proposed by Mason Green for the temperament that tempers out~~ [[~~81/80\|81:80~~]] ~~(thus, it is~~ a [[~~meantone~~]] ~~system), and has~~ a [[period]] ~~that is a flattened~~ [[~~3/2\|3:2~~]]~~, four of which make~~ a ~~[[5/1\|pentave]] (5:1), while its~~ [[generator]] ~~is an~~ [[~~octave~~]]. ~~This temperament~~ is very closely related to [[quarter-comma meantone]] (which was the standard for most [[Historical temperaments\|Western classical music]]); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).		'''Angel''' is [[meantone]] that uses a possibly tempered [[3/2\|fifth]] as a [[period]] and an [[octave]] as a [[generator]]. The name was proposed by [[Mason Green]], who thinks it almost seems too good to be true. It is very closely related to [[quarter-comma meantone]] (which was the standard for most [[Historical temperaments\|Western classical music]]); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).

	If the ~~pentaves are~~ required to be ~~exactly 5:1~~, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making ~~this a~~ [[~~31edo\|~~31edo]] ~~temperament~~), the ~~pentaves~~ will be slightly sharp. Both options are perceptually very close to one another.		If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.

	More specifically, the term angel may refer to various [[MOS scale\|~~MOS~~]]~~<nowiki/>es~~ and [[MODMOS scale\|~~MODMOS~~]]~~<nowiki/>es~~ that are derived from this ~~temperament~~. There are ~~MOSes~~ with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[Diatonic, Chromatic, Enharmonic, Subchromatic\|~~pentatonic~~, diatonic, chromatic, and enharmonic]] scales respectively.		More specifically, the term angel may refer to various [[MOS scale\|mosses]] and [[MODMOS scale\|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[Diatonic, Chromatic, Enharmonic, Subchromatic\|pentic, diatonic, chromatic, and enharmonic]] scales respectively.

	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You ~~don't~~ even have to train yourself to hear ~~pentaves~~ as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You do not even have to train yourself to hear the 5th harmonic as [[equivalence\|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

	In particular, the angel ~~MOS~~ with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like [[11/~~8\|11:~~8]] (which is more consonant in compound form). Thus it may actually be beneficial to use a system that ~~doesn't~~ exactly repeat at the octave.		In particular, the angel mos with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like [[11/8]] (which is more consonant in compound form). Thus it may actually be beneficial to use a system that does not exactly repeat at the octave.

	Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in ~~[https://en.wikipedia.org/wiki/All_fifths_tuning~~ all-fifths], since the period is a fifth.		Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in {{w\|All fifths tuning\|all-fifths}}, since the period is a fifth.

	~~<nowiki />* Because this temperament almost seems too good to be true.~~

	~~{{todo\|review}}~~
	[[Category:31edo]]		[[Category:31edo]]
	[[Category:~~meantone~~]]		[[Category:Meantone]]
	[[Category:~~pentave~~]]		[[Category:Pentave]]

BudjarnLambeth: todo

2024-10-02T09:35:44Z

todo

← Older revision		Revision as of 09:35, 2 October 2024
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	<nowiki />* Because this temperament almost seems too good to be true.		<nowiki />* Because this temperament almost seems too good to be true.

			{{todo\|review}}
	[[Category:31edo]]		[[Category:31edo]]
	[[Category:meantone]]		[[Category:meantone]]
	[[Category:pentave]]		[[Category:pentave]]

BudjarnLambeth: Added in-text links

2023-11-17T10:18:33Z

Added in-text links

← Older revision		Revision as of 10:18, 17 November 2023
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	'''Angel''' is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).		'''Angel''' is a name* proposed by Mason Green for the temperament that tempers out [[81/80\|81:80]] (thus, it is a [[meantone]] system), and has a [[period]] that is a flattened [[3/2\|3:2]], four of which make a [[5/1\|pentave]] (5:1), while its [[generator]] is an [[octave]]. This temperament is very closely related to [[quarter-comma meantone]] (which was the standard for most [[Historical temperaments\|Western classical music]]); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).

	If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a [[31edo\|31edo]] temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.		If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a [[31edo\|31edo]] temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.

	More specifically, the term angel may refer to various ~~MOSes~~ and ~~MODMOSes~~ that are derived from this temperament. There are MOSes with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the pentatonic, diatonic, chromatic, and enharmonic scales respectively.		More specifically, the term angel may refer to various [[MOS scale\|MOS]]<nowiki/>es and [[MODMOS scale\|MODMOS]]<nowiki/>es that are derived from this temperament. There are MOSes with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[Diatonic, Chromatic, Enharmonic, Subchromatic\|pentatonic, diatonic, chromatic, and enharmonic]] scales respectively.

	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

	In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.		In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like [[11/8\|11:8]] (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.

	Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.		Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.

FloraC: Undo irrelevant additions

2022-08-05T11:25:02Z

Undo irrelevant additions

← Older revision		Revision as of 11:25, 5 August 2022
Line 7:		Line 7:
	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

	In particular, the ~~[[Angel/Tuning specifications\|~~angel MOS]] with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.		In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.

	Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.		Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.

Moremajorthanmajor at 00:05, 15 July 2022

2022-07-15T00:05:05Z

← Older revision		Revision as of 00:05, 15 July 2022
Line 7:		Line 7:
	Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.		Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

	In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.		In particular, the [[Angel/Tuning specifications\|angel MOS]] with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.

	Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.		Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.

FloraC: Undo irrelevant additions

2022-07-13T11:41:26Z

Undo irrelevant additions

Show changes

Moremajorthanmajor: /* Notation */

2022-07-13T03:35:07Z

Notation

Show changes

Moremajorthanmajor at 02:51, 13 July 2022

2022-07-13T02:51:01Z

Show changes