Buzzardsmic clan - Revision history

FloraC at 06:42, 7 June 2026

2026-06-07T06:42:07Z

← Older revision		Revision as of 06:42, 7 June 2026
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	Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as {{nowrap\| 53 & 58 }} (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[Mos scale]]s of 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.		Septimal buzzard is not only a naturally motivated extension to 2.3.7 buzzard, but the main extension to [[vulture]] of practical interest, finding prime 7 at only 3 generators down so that the generator is interpreted as a sharp ~[[21/16]], though buzzard is powerful as a full 13-limit system in its own right. It is most naturally described as {{nowrap\| 53 & 58 }} (though [[48edo]] is an interesting higher-damage tuning of it for some purposes). As one might expect, [[111edo]] (111 = 53 + 58) is a great tuning for it. [[Mos scale]]s of 5, 8, 13, 18, 23, 28, 33, 38, 43, 48 or 53 notes are available.

	Its 13-limit [[S-expression]]-based comma list is {[[1728/1715\|S6/S7]], [[5120/5103\|S8/S9]], [[847/845\|S11/S13]], [[676/675\|S13/S15]]}, with the structure of its 7-limit implied by the first two equivalences combined with the nontrivial [[JI]] equivalence [[36/35\|S6]] = [[64/63\|S8]] × [[81/80\|S9]]. [[~~Hemifamity~~]] leverages it by splitting [[36/35]] into two syntonic~septimal commas, so buzzard naturally finds an interval between [[6/5]] and [[7/6]] which in the 7-limit is [[32/27]] and in the 13-limit is [[13/11]]. Then the vanishing of the orwellisma implies [[49/48]], the large septimal diesis, is equated with 36/35, so 49/48 is also split into two so that the system also finds an interval between 7/6 and 8/7 which in the 7-limit is 7/6 inflected down by a comma or 8/7 inflected up by a comma, and in the 13-limit is [[15/13]], so that it is clear this system naturally wants to be extended to and interpreted in the full 13-limit.		Its 13-limit [[S-expression]]-based comma list is {[[1728/1715\|S6/S7]], [[5120/5103\|S8/S9]], [[847/845\|S11/S13]], [[676/675\|S13/S15]]}, with the structure of its 7-limit implied by the first two equivalences combined with the nontrivial [[JI]] equivalence [[36/35\|S6]] = [[64/63\|S8]] × [[81/80\|S9]]. [[Aberschismic]] leverages it by splitting [[36/35]] into two syntonic~septimal commas, so buzzard naturally finds an interval between [[6/5]] and [[7/6]] which in the 7-limit is [[32/27]] and in the 13-limit is [[13/11]]. Then the vanishing of the orwellisma implies [[49/48]], the large septimal diesis, is equated with 36/35, so 49/48 is also split into two so that the system also finds an interval between 7/6 and 8/7 which in the 7-limit is 7/6 inflected down by a comma or 8/7 inflected up by a comma, and in the 13-limit is [[15/13]], so that it is clear this system naturally wants to be extended to and interpreted in the full 13-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Subsedia ==		== Subsedia ==
	Named by [[Xenllium]] in 2022, subsedia tempers out the [[~~mirkwai~~ comma]] and may be described as the {{nowrap\| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.		Named by [[Xenllium]] in 2022, subsedia tempers out the [[canopic comma]] and may be described as the {{nowrap\| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

VectorGraphics at 21:43, 1 June 2026

2026-06-01T21:43:08Z

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	Badness (Sintel): 0.944		Badness (Sintel): 0.944

	=== 17-limit ===		==== 17-limit ====
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

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	Badness (Sintel): 1.14		Badness (Sintel): 1.14

	=== 19-limit ===		==== 19-limit ====
	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

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	Badness (Sintel): 1.15		Badness (Sintel): 1.15

	=== 23-limit ===		==== 23-limit ====
	Subgroup: 2.3.5.7.11.13.17.19.23		Subgroup: 2.3.5.7.11.13.17.19.23

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	Badness (Sintel): 1.19		Badness (Sintel): 1.19

	=== 29-limit ===		==== 29-limit ====
	Subgroup: 2.3.5.7.11.13.17.19.23.29		Subgroup: 2.3.5.7.11.13.17.19.23.29

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	Badness (Sintel): 1.15		Badness (Sintel): 1.15

			=== Antemka ===
			This temperament has the opposite mappings of 5 and 13 to [[emka]].

			Comma list: 105/104, 126/125, 66/65, 1024/1001

			Edo join: 15 & 28

			Mapping: {{mapping\| 1 8 5 -2 4 8\|0 -12 -5 9 -1 -8}}

			Optimal tuning (CWE): ~2 = 1200.0000{{c}}, ~16/11 = 641.492{{c}}

	== Subsedia ==		== Subsedia ==

FloraC: Complete source of names

2026-05-01T11:56:14Z

Complete source of names

← Older revision		Revision as of 11:56, 1 May 2026
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	== Lemongrass ==		== Lemongrass ==
	~~Lemongrass~~ tempers out [[245/243]] and may be described as the {{nowrap\| 63 & 68 }} temperament. Characterized by a sharper generator than septimal buzzard, lemongrass compresses the septimal comma so much that the syntonic comma is no longer equated with it but with twice of it, or the large septimal diesis. [[68edo]] itself is a great tuning for this, though [[63edo]] and [[73edo]] are also possible.		Named by [[Lériendil]] in 2025, lemongrass tempers out [[245/243]] and may be described as the {{nowrap\| 63 & 68 }} temperament. Characterized by a sharper generator than septimal buzzard, lemongrass compresses the septimal comma so much that the syntonic comma is no longer equated with it but with twice of it, or the large septimal diesis. [[68edo]] itself is a great tuning for this, though [[63edo]] and [[73edo]] are also possible.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Subsedia ==		== Subsedia ==
	~~Subsedia~~ tempers out the [[mirkwai comma]] and may be described as the {{nowrap\| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.		Named by [[Xenllium]] in 2022, subsedia tempers out the [[mirkwai comma]] and may be described as the {{nowrap\| 111 & 121 }} temperament. The generator for subsedia is 0.5 cents flat of [[15/14]]-wide semitone. In this temperament, three generators make ~[[16/13]], five make ~[[24/17]], twelve make ~[[16/7]], sixteen make ~[[3/1]], and 45 make ~22/1.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Anthoine]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Anthoine]].''

	~~Anthoine~~ is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator is found at 5 generators up. It is most notable as the {{nowrap\| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo. Its ploidacot is 13-sheared-20-cot.		Named by [[Lériendil]] in 2025, anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator is found at 5 generators up. It is most notable as the {{nowrap\| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo. Its ploidacot is 13-sheared-20-cot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Move subsedia here

2026-05-01T10:59:48Z

Move subsedia here

@@ Line 4: / Line 4: @@
 Extensions of buzzard to incorporate [[prime interval|prime]] [[5/1|5]] along its chain of generators (and therefore the full [[7-limit]]) include septimal buzzard ({{nowrap| 53 & 58 }}), which tempers out [[1728/1715]] (and [[5120/5103]]); subfourth ({{nowrap| 58 & 63 }}), which tempers out [[10976/10935]]; and lemongrass ({{nowrap| 63 & 68 }}), which tempers out [[245/243]]. All are considered below.
-Weak extensions include submajor ({{nowrap| 10 & 53 }}), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; and thuja ({{nowrap| 15 & 43 }}), which tempers out [[126/125]] and splits [[21/8]] into three.
+Weak extensions include demibuzzard ({{nowrap| 10 & 53 }}), which tempers out [[225/224]] and splits [[32/21]] (the superfifth) in two; thuja ({{nowrap| 15 & 43 }}), which tempers out [[126/125]] and splits [[21/8]] into three; subsedia ({{nowrap| 10 & 111 }}), which tempers out [[16875/16807]] and splits [[21/16]] in four; and anthoine ({{nowrap| 25 & 53 }}), which tempers out [[3125/3087]] and splits [[21/2]] in five.
 Full 7-limit temperaments discussed elsewhere are:
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 Badness (Sintel): 1.15
 == Anthoine ==

FloraC: /* Demibuzzard */

2026-02-09T11:46:29Z

Demibuzzard

← Older revision		Revision as of 11:46, 9 February 2026
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	= Weak extensions =		= Weak extensions =
	== Demibuzzard ==		== Demibuzzard ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Demibuzzard]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Demibuzzard]].''
	Demibuzzard may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.
			Demibuzzard may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The [[ploidacot]] for this temperament is epsilon-octacot.

	This temperament naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].		This temperament naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].

	It diverges into two extensions for prime 11: submajor ({{nowrap\| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].		It diverges into two extensions for prime 11: submajor ({{nowrap\| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]]. Note that ''submajor'' (referring to the submajor third, not the supraminor sixth) used to be the name for the 7-limit temperament.

	=== 7-limit ===		=== 7-limit ===

Lériendil: /* Demibuzzard */

2026-02-08T16:05:29Z

Demibuzzard

← Older revision		Revision as of 16:05, 8 February 2026
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	= Weak extensions =		= Weak extensions =
	== Demibuzzard ==		== Demibuzzard ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#~~Submajor~~]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Demibuzzard]].''
	Demibuzzard may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.		Demibuzzard may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.

Lériendil: 2.3.5.7.13 submajor -> demibuzzard

2026-02-08T16:05:19Z

2.3.5.7.13 submajor -> demibuzzard

← Older revision		Revision as of 16:05, 8 February 2026
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	= Weak extensions =		= Weak extensions =
	== ~~Submajor~~ ==		== Demibuzzard ==
	: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Submajor]].''		: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Submajor]].''
	~~Submajor~~ may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third~~, hence the name~~; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.		Demibuzzard may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.

	~~Submajor~~ naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].		This temperament naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].

	It diverges into two extensions for prime 11: ~~the canonical one~~ ({{nowrap\| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].		It diverges into two extensions for prime 11: submajor ({{nowrap\| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].

	=== 7-limit ===		=== 7-limit ===
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	Badness (Sintel): 0.847		Badness (Sintel): 0.847

	=== ~~11-limit~~ ===		=== Submajor ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Xenllium at 22:16, 21 January 2026

2026-01-21T22:16:34Z

← Older revision		Revision as of 22:16, 21 January 2026
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	== Anthoine ==		== Anthoine ==
			: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Anthoine]].''

	Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator is found at 5 generators up. It is most notable as the {{nowrap\| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo. Its ploidacot is 13-sheared-20-cot.		Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma; note that the data below shows the octave complement generator, ~8/5, so that buzzard's generator is found at 5 generators up. It is most notable as the {{nowrap\| 25 & 28 }} temperament and as the chain of 5/4's present in 53edo. Its ploidacot is 13-sheared-20-cot.

Overthink: /* Submajor */ link to 5-limit

2025-12-28T00:31:34Z

Submajor: link to 5-limit

← Older revision		Revision as of 00:31, 28 December 2025
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	= Weak extensions =		= Weak extensions =
	== Submajor ==		== Submajor ==
			: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Submajor]].''
	Submajor may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third, hence the name; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.		Submajor may be described as the {{nowrap\| 10 & 53 }} temperament. It is generated by a submajor third, hence the name; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.

Overthink: /* Weak extensions */ fix typo

2025-12-28T00:28:48Z

Weak extensions: fix typo

← Older revision		Revision as of 00:28, 28 December 2025
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	Submajor naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].		Submajor naturally comes about from a structure in edos like [[43edo\|43-]], [[53edo\|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].

	It diverges into two extensions for prime 11: the canonical one ({{nowrap\| 53 & 63 }} favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].		It diverges into two extensions for prime 11: the canonical one ({{nowrap\| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap\| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].

	=== 7-limit ===		=== 7-limit ===