Buzzardsmic clan: Difference between revisions

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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 & 43 }}), 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 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.

Full 7-limit temperaments discussed elsewhere are:

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== Subfourth ==

Subfourth tempers out [[10976/10935]] and may be described as the {{nowrap| 58 & 63 }} temperament, more notable in the higher limits than the lower as it supplies a lot of essentially tempered chords there, including everything from [[parapyth]]. Among the good tunings are [[121edo]] and [[179edo]] using the 179ef val in the 13-limit.

[[Subgroup]]: 2.3.5.7

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== 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.

[[Subgroup]]: 2.3.5.7

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= Weak extensions =

== 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 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]].

=== 7-limit ===

[[Subgroup]]: 2.3.5.7

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==== 2.3.5.7.13 subgroup ====

This temperament naturally comes about from a structure in edos like [[43edo|43]] and [[53edo|53]] 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]].

Subgroup: 2.3.5.7.13

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=== 11-limit ===

~~Submajor diverges into two extensions to prime 11: this one favoring sharp fifths, and interpental, favoring flat fifths; the two mappings meet at [[53edo]].~~

Subgroup: 2.3.5.7.11

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== Thuja ==

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

Thuja tempers out 126/125 and may be described as the {{nowrap| 15 & 43 }} temperament. The generator is a somewhat sharp fourth, which may be taken as a ~11/8 in the 11-limit, and three minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-dodecacot.

Thuja can be extended up to the 29-limit, with a simple and accurate approximation to 29, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.

[[Subgroup]]: 2.3.5.7

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=== 29-limit ===

~~The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.~~

Subgroup: 2.3.5.7.11.13.17.19.23.29

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== Anthoine ==

Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that ~~32/21~~ 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.

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

@@ 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 & 43 }}), 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 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.
 Full 7-limit temperaments discussed elsewhere are:
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 == Subfourth ==
+Subfourth tempers out [[10976/10935]] and may be described as the {{nowrap| 58 & 63 }} temperament, more notable in the higher limits than the lower as it supplies a lot of essentially tempered chords there, including everything from [[parapyth]]. Among the good tunings are [[121edo]] and [[179edo]] using the 179ef val in the 13-limit.
 [[Subgroup]]: 2.3.5.7
@@ Line 197: / Line 199: @@
 == 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.
 [[Subgroup]]: 2.3.5.7
@@ Line 215: / Line 219: @@
 = Weak extensions =
 == 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 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]].
 === 7-limit ===
 [[Subgroup]]: 2.3.5.7
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 ==== 2.3.5.7.13 subgroup ====
 {{See also| Greater tendoneutralic }}
-This temperament naturally comes about from a structure in edos like [[43edo|43]] and [[53edo|53]] 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]].
 Subgroup: 2.3.5.7.13
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 === 11-limit ===
-Submajor diverges into two extensions to prime 11: this one favoring sharp fifths, and interpental, favoring flat fifths; the two mappings meet at [[53edo]].
 Subgroup: 2.3.5.7.11
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 == Thuja ==
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Thuja]].''
+Thuja tempers out 126/125 and may be described as the {{nowrap| 15 & 43 }} temperament. The generator is a somewhat sharp fourth, which may be taken as a ~11/8 in the 11-limit, and three minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-dodecacot.
+Thuja can be extended up to the 29-limit, with a simple and accurate approximation to 29, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.
 [[Subgroup]]: 2.3.5.7
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 === 29-limit ===
-The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.
 Subgroup: 2.3.5.7.11.13.17.19.23.29
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 == Anthoine ==
-Anthoine is generated by [[5/4]] and tempers out [[3125/3087]] in addition to the buzzardsma, so that 32/21 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.
+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