7L 4s - Revision history

ArrowHead294 at 14:02, 5 May 2025

2025-05-05T14:02:55Z

← Older revision		Revision as of 14:02, 5 May 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	== Scale tree ==		== Scale tree ==

ArrowHead294: /* JI approximation */

2025-04-09T17:55:44Z

JI approximation

← Older revision		Revision as of 17:55, 9 April 2025
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	7L 4s's generator range contains [[17/14]] and [[23/19]].		7L 4s's generator range contains [[17/14]] and [[23/19]].

	In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by ~~[[Wikipedia:Joseph Sauveur~~\|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.		In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by {{w\|Joseph Sauveur}} due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.

	The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup {{nowrap\|47 & 112}} temperament, where it tempers out exactly the same commas as tertiaschis.		The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup {{nowrap\|47 & 112}} temperament, where it tempers out exactly the same commas as tertiaschis.

ArrowHead294 at 14:05, 3 March 2025

2025-03-03T14:05:38Z

← Older revision		Revision as of 14:05, 3 March 2025
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	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==
	7L 4s fails to represent common just intonation intervals and simple temperaments, and it has no clearly discernible harmonic entropy minimum. From a purely computational perspective, 7L 4s's harmonic entropy minimum is [[improper]] and is associated with unusually large step ratios.		7L 4s fails to represent common just intonation intervals and simple temperaments, and it has no clearly discernible harmonic entropy minimum. From a purely computational perspective, 7L 4s's harmonic entropy minimum is [[improper]] and is associated with unusually large step ratios.

	Near the harmonic entropy minimum, the simplest temperament of low-complexity JI supported by 7L 4s is [[amity]] and its variant [[hitchcock]]. It is unconventional to put forward this as the most common approach to this scale, because the large and steps are extremely unequal, being at least of 5:1 step ratio in [[39edo]], the smallest patent val supporting either of the two. However, it is still significant by virtue of it being the only [[5-limit]] [[temperament]] representation of 7L 4s with reasonably low badness.		Near the harmonic entropy minimum, the simplest temperament of low-complexity JI supported by 7L 4s is [[amity]] and its variant [[hitchcock]]. It is unconventional to put forward this as the most common approach to this scale, because the large and steps are extremely unequal, being at least of 5:1 step ratio in [[39edo]], the smallest patent val supporting either of the two. However, it is still significant by virtue of it being the only [[5-limit]] [[temperament]] representation of 7L 4s with reasonably low badness.

	A temperament which spans more of the tuning range is [[sixix]], but it is high in just intonation error relative to its step sizes. Additionally, as sixix shares the mapping for [[3/2]] with amity (-5 generators), the generator is of a similar size, and the most accurate tunings of sixix, [[32edo]] and [[39edo\|39c-edo]], have highly improper 7L 4s scales like with amity.		A temperament which spans more of the tuning range is [[sixix]], but it is high in just intonation error relative to its step sizes. Additionally, as sixix shares the mapping for [[3/2]] with amity (-5 generators), the generator is of a similar size, and the most accurate tunings of sixix, [[32edo]] and [[39edo\|39c-edo]], have highly improper 7L 4s scales like with amity.

	On the soft side of the scale, 7L 4s is a scale of the [[rarity]] temperament, with tunings like [[29edo]], and [[69edo]] which are consistent in the 5-limit. However, the temperament is extremely high [[complexity]] and high [[badness]]. In fact, the third or fifth harmonics do not appear at all in the Rarity[11] 7L 4s scale, and the only common 5-limit intervals which make an appearance are [[16/15]] and [[15/8]]. The comma itself is also quite complex.		On the soft side of the scale, 7L 4s is a scale of the [[rarity]] temperament, with tunings like [[29edo]], and [[69edo]] which are consistent in the 5-limit. However, the temperament is extremely high [[complexity]] and high [[badness]]. In fact, the third or fifth harmonics do not appear at all in the Rarity[11] 7L 4s scale, and the only common 5-limit intervals which make an appearance are [[16/15]] and [[15/8]]. The comma itself is also quite complex.

	[[Subgroup temperaments#Demon temperament\|Demon temperament]] is closer to the center of this MOS's tuning range, but it is in the uncommon subgroup 2.9.11, and like sixix it is moderately inaccurate, compressing [[11/9]] into a supraminor third.		[[Subgroup temperaments#Demon temperament\|Demon temperament]] is closer to the center of this MOS's tuning range, but it is in the uncommon subgroup 2.9.11, and like sixix it is moderately inaccurate, compressing [[11/9]] into a supraminor third.

	7L 4s's generator range contains [[17/14]] and [[23/19]].		7L 4s's generator range contains [[17/14]] and [[23/19]].

	In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur\|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.		In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur\|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.

	The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup 47 & 112 temperament, where it tempers out exactly the same commas as tertiaschis.		The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup {{nowrap\|47 & 112}} temperament, where it tempers out exactly the same commas as tertiaschis.

	== Nomenclature ==		== Nomenclature ==
	The [[TAMNAMS Extension\|extended TAMNAMS]] name for this pattern, as proposed by Eliora, is '''daemotonic'''. The name originates in the term "daemon", an archaic spelling of demon.		The [[TAMNAMS Extension\|extended TAMNAMS]] name for this pattern, as proposed by Eliora, is '''daemotonic'''. The name originates in the term "daemon", an archaic spelling of demon.

	The name is prescribed to 7L 4s due to the fact that among relatively simple scales it has lowest degree of adherence to regular temperament theory and just intonation (see above). In addition, ''daemon'' in ancient times didn't necessarily mean an evil entity, but it could be any kind of spirit, encapsulating that 7L 4s can be found as a useful scale by composers who do not adhere to common regular temperament or consonance-based approaches. A coincidence in the cent measuring system is that two basic (L:s = 2:1) generators stacked together are equal to 666.6666… cents.		The name is prescribed to 7L 4s due to the fact that among relatively simple scales it has lowest degree of adherence to regular temperament theory and just intonation (see above). In addition, ''daemon'' in ancient times didn't necessarily mean an evil entity, but it could be any kind of spirit, encapsulating that 7L 4s can be found as a useful scale by composers who do not adhere to common regular temperament or consonance-based approaches. A coincidence in the cent measuring system is that two basic ({{nowrap\|L:s {{=}} 2:1}}) generators stacked together are equal to 666.6666… cents.

	From traditional TAMNAMS perspective, the scale may be called '''m-chro smitonic'''. Another name, which is deprecated but proposed for reinstation by [[User:Ganaram inukshuk\|Ganaram inukshuk]], is '''suprasmitonic'''.		From traditional TAMNAMS perspective, the scale may be called '''m-chro smitonic'''. Another name, which is deprecated but proposed for reinstation by [[User:Ganaram inukshuk\|Ganaram inukshuk]], is '''suprasmitonic'''.

	== ~~Modes~~ ==		== Scale properties ==
	{{~~MOS mode degrees~~}}		{{TAMNAMS use}}
			{{MOS data}}
	~~== Intervals ==~~
	{{MOS ~~intervals~~}}

	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~Comments=~~		{{MOS tuning spectrum
	6/5: [[Mabon]];		\| 6/5 = [[Mabon]]
	7/5: [[Rarity]];		\| 7/5 = [[Rarity]]
	13/8: Unnamed golden tuning;		\| 13/8 = Unnamed golden tuning
	13/5: [[Cohemimabila]], unnamed golden tuning;		\| 13/5 = [[Cohemimabila]], unnamed golden tuning
	4/1: [[Sixix]];		\| 4/1 = [[Sixix]]
	6/1:↓ [[Amity]] / [[hitchcock]];		\| 6/1 = ↓ [[Amity]] / [[hitchcock]]
	}}		}}

FloraC: Oops, accidentally removed the infobox

2024-12-18T10:54:23Z

Oops, accidentally removed the infobox

← Older revision		Revision as of 10:54, 18 December 2024
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			{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==

FloraC: Reviewed scale tree

2024-12-18T10:53:42Z

Reviewed scale tree

← Older revision		Revision as of 10:53, 18 December 2024
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	~~{{Todo\|review\|inline=1\|text=Review entries (entries from past revisions of page have not been copied to the scale tree yet)}}{{Infobox MOS}}~~
	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==

FloraC: /* Scale tree */ restore contents

2024-12-18T10:53:17Z

Scale tree: restore contents

← Older revision		Revision as of 10:53, 18 December 2024
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	== Scale tree ==		== Scale tree ==
	{{Scale tree}}		{{Scale tree\|Comments=
			6/5: [[Mabon]];
			7/5: [[Rarity]];
			13/8: Unnamed golden tuning;
			13/5: [[Cohemimabila]], unnamed golden tuning;
			4/1: [[Sixix]];
			6/1:↓ [[Amity]] / [[hitchcock]];
			}}

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-16T01:43:05Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 01:43, 16 December 2024
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	== Modes ==		== Modes ==
	{{MOS mode degrees}}		{{MOS mode degrees}}

			== Intervals ==
			{{MOS intervals}}

	== Scale tree ==		== Scale tree ==
	{{Scale tree}}		{{Scale tree}}

Ganaram inukshuk: There were entries that preceded the scale tree being added; they just haven't been copied yet

2024-11-15T02:21:30Z

There were entries that preceded the scale tree being added; they just haven't been copied yet

← Older revision		Revision as of 02:21, 15 November 2024
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	{{Todo\|review\|inline=1\|text=Review entries}}{{Infobox MOS}}		{{Todo\|review\|inline=1\|text=Review entries (entries from past revisions of page have not been copied to the scale tree yet)}}{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==

Ganaram inukshuk: Undo revision 165345 by Eliora (talk)

2024-11-15T02:20:40Z

Undo revision 165345 by Eliora (talk)

← Older revision		Revision as of 02:20, 15 November 2024
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	{{Infobox MOS}}		{{Todo\|review\|inline=1\|text=Review entries}}{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==

Eliora: if the "entries" refers to the entries in the scale tree, then that is redundant as the official template has been adopted.

2024-11-15T01:39:40Z

if the "entries" refers to the entries in the scale tree, then that is redundant as the official template has been adopted.

← Older revision		Revision as of 01:39, 15 November 2024
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	~~{{Todo\|review\|inline=1\|text=Review entries}}~~{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}
	== JI approximation ==		== JI approximation ==