Buzzardsmic clan: Difference between revisions

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The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. [[Tempering out]] this comma implies a sharpened [[7/1|7th]] [[harmonic]], and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].

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.

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]]); mazzard ({{nowrap| 5 & 43 }}), which tempers out [[81/80]]; redtail ({{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 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:

* [[Blackwood]] (+28/27) → [[~~Limmic temperaments~~ #Blackwood|~~Limmic temperaments~~]]

* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]

* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]

* ''[[Hemikleismic]] (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]

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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.

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

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Comma list: 176/175, 540/539, 5120/5103

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 -12 | 0 4 21 -3 39 }}

Optimal tunings:

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Comma list: 176/175, 351/350, 540/539, 676/675

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}

Optimal tunings:

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Comma list: 176/175, 256/255, 351/350, 442/441, 540/539

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}

Optimal tunings:

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Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}

{{Mapping|legend=0| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}

Optimal tunings:

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Comma list: 99/98, 385/384, 2200/2187

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 9 | 0 4 21 -3 -14 }}

Optimal tunings:

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Comma list: 99/98, 275/273, 385/384, 572/567

~~Mapping:~~ {{~~mapping~~| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}

Optimal tunings:

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Badness (Sintel): 1.65

== ~~Subfourth~~ ==

== Mazzard ==

~~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.

Mazzard tempers out 81/80, the [[syntonic comma]], and finds the [[5/1|5th harmonic]] as a diatonic major third, 16 generator steps away. [[43edo]] gives a nearly perfect tuning for it, though [[38edo]] and [[48edo]] in the 48c [[val]] are among the alternatives.

Mazzard was described as "meantone buzzard" and known to many before the adoption of the name, first suggested by {{u|VIxen}}, in 2026.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 81/80, 12288/12005

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.4221{{c}}, ~21/16 = 474.2178{{c}}

: [[error map]]: {{val| -0.578 -5.084 +3.482 +6.209 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/16 = 474.4228{{c}}

: error map: {{val| 0.000 -4.264 +4.451 +7.906 }}

[[Badness]] (Sintel): 2.73

== Redtail ==

Redtail tempers out 10976/10935, the [[hemimage comma]], 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.

Redtail was previously named ''subfourth'' but was renamed in 2026 to avoid confusion with the [[interval region]] and to increase distinctiveness in the clan. The name ''redtail'' was coined by {{u|Frostburn}}, named after the red-tailed hawk.

[[Subgroup]]: 2.3.5.7

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Comma list: 540/539, 896/891, 12005/11979

~~Mapping:~~ {{~~mapping~~| 1 0 17 4 11 | 0 4 -37 -3 -19 }}

Optimal tunings:

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Comma list: 352/351, 364/363, 540/539, 676/675

~~Mapping:~~ {{~~mapping~~| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}

Optimal tunings:

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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.

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

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Comma list: 169/168, 225/224, 640/637

~~Mapping:~~ {{~~mapping~~| 1 -4 10 7 3 | 0 8 -11 -6 1 }}

Optimal tunings:

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Comma list: 225/224, 385/384, 6655/6561

~~Mapping:~~ {{~~mapping~~| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}

Optimal tunings:

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Comma list: 169/168, 225/224, 275/273, 385/384

~~Mapping:~~ {{~~mapping~~| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}

Optimal tunings:

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Comma list: 99/98, 176/175, 51200/50421

~~Mapping:~~ {{~~mapping~~| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}

Optimal tunings:

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Comma list: 99/98, 169/168, 176/175, 640/637

~~Mapping:~~ {{~~mapping~~| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}

Optimal tunings:

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Comma list: 126/125, 176/175, 1344/1331

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 | 0 12 5 -9 1 }}

Optimal tunings:

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Comma list: 126/125, 144/143, 176/175, 364/363

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}

Optimal tunings:

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Comma list: 126/125, 144/143, 176/175, 221/220, 256/255

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}

Optimal tunings:

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Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}

Optimal tunings:

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Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}

{{Mapping|legend=0| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}

Optimal tunings:

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Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230

~~Mapping:~~ {{~~mapping~~| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}

{{Mapping|legend=0| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}

Optimal tunings:

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== 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 [[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

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Comma list: 540/539, 1375/1372, 65536/64827

~~Mapping:~~ {{~~mapping~~| 1 0 5 4 -1 | 0 16 -27 -12 45 }}

Optimal tunings:

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Comma list: 352/351, 540/539, 676/675, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}

Optimal tunings:

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Comma list: 256/255, 352/351, 442/441, 540/539, 715/714

~~Mapping:~~ {{~~mapping~~| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}

Optimal tunings:

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Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714

~~Mapping:~~ {{~~mapping~~| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}

{{Mapping|legend=0| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}

Optimal tunings:

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: ''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

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[[Badness]] (Sintel): 4.57

[[Category:Buzzardsmic clan| ]]

[[Category:Buzzardsmic| ]]

[[Category:Temperament clans]]

[[Category:~~Buzzardsmic clan| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

~~[[Category:Listen~~]]

@@ Line 2: / Line 2: @@
 The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''buzzardsmic clan''' is the buzzardsma, [[65536/64827]], with [[monzo]] {{monzo| 16 -3 0 -4 }}, which implies that the tritave, [[3/1]], is divided into four intervals each representing a [[21/16]] subfourth. [[Tempering out]] this comma implies a sharpened [[7/1|7th]] [[harmonic]], and especially a sharpened [[~]]21/16 generator, which approaches the 480{{c}} fourth of [[5edo]].
-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.
+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]]); mazzard ({{nowrap| 5 & 43 }}), which tempers out [[81/80]]; redtail ({{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 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:
-* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
+* [[Blackwood]] (+28/27) → [[Blackwood family #Blackwood|Blackwood family]]
 * ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
 * ''[[Hemikleismic]] (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
@@ Line 41: / Line 41: @@
 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
@@ Line 64: / Line 64: @@
 Comma list: 176/175, 540/539, 5120/5103
-Mapping: {{mapping| 1 0 -6 4 -12 | 0 4 21 -3 39 }}
+{{Mapping|legend=0| 1 0 -6 4 -12 | 0 4 21 -3 39 }}
 Optimal tunings:
@@ Line 79: / Line 79: @@
 Comma list: 176/175, 351/350, 540/539, 676/675
-Mapping: {{mapping| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}
+{{Mapping|legend=0| 1 0 -6 4 -12 -7 | 0 4 21 -3 39 27 }}
 Optimal tunings:
@@ Line 94: / Line 94: @@
 Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
-Mapping: {{mapping| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}
+{{Mapping|legend=0| 1 0 -6 4 -12 -7 14 | 0 4 21 -3 39 27 -25 }}
 Optimal tunings:
@@ Line 109: / Line 109: @@
 Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
-Mapping: {{mapping| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}
+{{Mapping|legend=0| 1 0 -6 4 -12 -7 14 -12 | 0 4 21 -3 39 27 -25 41 }}
 Optimal tunings:
@@ Line 124: / Line 124: @@
 Comma list: 99/98, 385/384, 2200/2187
-Mapping: {{mapping| 1 0 -6 4 9 | 0 4 21 -3 -14 }}
+{{Mapping|legend=0| 1 0 -6 4 9 | 0 4 21 -3 -14 }}
 Optimal tunings:
@@ Line 139: / Line 139: @@
 Comma list: 99/98, 275/273, 385/384, 572/567
-Mapping: {{mapping| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}
+{{Mapping|legend=0| 1 0 -6 4 9 -7 | 0 4 21 -3 -14 27 }}
 Optimal tunings:
@@ Line 149: / Line 149: @@
 Badness (Sintel): 1.65
-== Subfourth ==
+== Mazzard ==
-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.
+Mazzard tempers out 81/80, the [[syntonic comma]], and finds the [[5/1|5th harmonic]] as a diatonic major third, 16 generator steps away. [[43edo]] gives a nearly perfect tuning for it, though [[38edo]] and [[48edo]] in the 48c [[val]] are among the alternatives.
+Mazzard was described as "meantone buzzard" and known to many before the adoption of the name, first suggested by {{u|VIxen}}, in 2026.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 81/80, 12288/12005
+{{Mapping|legend=1| 1 0 -4 4 | 0 4 16 -3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4221{{c}}, ~21/16 = 474.2178{{c}}
+: [[error map]]: {{val| -0.578 -5.084 +3.482 +6.209 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/16 = 474.4228{{c}}
+: error map: {{val| 0.000 -4.264 +4.451 +7.906 }}
+{{Optimal ET sequence|legend=1| 5, 38, 43 }}
+[[Badness]] (Sintel): 2.73
+== Redtail ==
+Redtail tempers out 10976/10935, the [[hemimage comma]], 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.
+Redtail was previously named ''subfourth'' but was renamed in 2026 to avoid confusion with the [[interval region]] and to increase distinctiveness in the clan. The name ''redtail'' was coined by {{u|Frostburn}}, named after the red-tailed hawk.
 [[Subgroup]]: 2.3.5.7
@@ Line 173: / Line 196: @@
 Comma list: 540/539, 896/891, 12005/11979
-Mapping: {{mapping| 1 0 17 4 11 | 0 4 -37 -3 -19 }}
+{{Mapping|legend=0| 1 0 17 4 11 | 0 4 -37 -3 -19 }}
 Optimal tunings:
@@ Line 188: / Line 211: @@
 Comma list: 352/351, 364/363, 540/539, 676/675
-Mapping: {{mapping| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}
+{{Mapping|legend=0| 1 0 17 4 11 16 | 0 4 -37 -3 -19 -31 }}
 Optimal tunings:
@@ Line 199: / Line 222: @@
 == 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
@@ Line 252: / Line 275: @@
 Comma list: 169/168, 225/224, 640/637
-Mapping: {{mapping| 1 -4 10 7 3 | 0 8 -11 -6 1 }}
+{{Mapping|legend=0| 1 -4 10 7 3 | 0 8 -11 -6 1 }}
 Optimal tunings:
@@ Line 267: / Line 290: @@
 Comma list: 225/224, 385/384, 6655/6561
-Mapping: {{mapping| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}
+{{Mapping|legend=0| 1 -4 10 7 -14 | 0 8 -11 -6 25 }}
 Optimal tunings:
@@ Line 282: / Line 305: @@
 Comma list: 169/168, 225/224, 275/273, 385/384
-Mapping: {{mapping| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}
+{{Mapping|legend=0| 1 -4 10 7 -14 3 | 0 8 -11 -6 25 1 }}
 Optimal tunings:
@@ Line 297: / Line 320: @@
 Comma list: 99/98, 176/175, 51200/50421
-Mapping: {{mapping| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}
+{{Mapping|legend=0| 1 -4 10 7 23 | 0 8 -11 -6 -28 }}
 Optimal tunings:
@@ Line 312: / Line 335: @@
 Comma list: 99/98, 169/168, 176/175, 640/637
-Mapping: {{mapping| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}
+{{Mapping|legend=0| 1 -4 10 7 23 3 | 0 8 -11 -6 -28 1 }}
 Optimal tunings:
@@ Line 351: / Line 374: @@
 Comma list: 126/125, 176/175, 1344/1331
-Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}
+{{Mapping|legend=0| 1 -4 0 7 3 | 0 12 5 -9 1 }}
 Optimal tunings:
@@ Line 366: / Line 389: @@
 Comma list: 126/125, 144/143, 176/175, 364/363
-Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}
+{{Mapping|legend=0| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}
 Optimal tunings:
@@ Line 381: / Line 404: @@
 Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}
+{{Mapping|legend=0| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}
 Optimal tunings:
@@ Line 396: / Line 419: @@
 Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}
+{{Mapping|legend=0| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}
 Optimal tunings:
@@ Line 411: / Line 434: @@
 Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}
+{{Mapping|legend=0| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}
 Optimal tunings:
@@ Line 426: / Line 449: @@
 Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
-Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}
+{{Mapping|legend=0| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}
 Optimal tunings:
@@ Line 437: / Line 460: @@
 == 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 [[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
@@ Line 461: / Line 484: @@
 Comma list: 540/539, 1375/1372, 65536/64827
-Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
+{{Mapping|legend=0| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
 Optimal tunings:
@@ Line 476: / Line 499: @@
 Comma list: 352/351, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
+{{Mapping|legend=0| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
 Optimal tunings:
@@ Line 491: / Line 514: @@
 Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
+{{Mapping|legend=0| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
 Optimal tunings:
@@ Line 506: / Line 529: @@
 Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
+{{Mapping|legend=0| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
 Optimal tunings:
@@ Line 519: / Line 542: @@
 : ''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
@@ Line 538: / Line 561: @@
 [[Badness]] (Sintel): 4.57
+[[Category:Buzzardsmic clan| ]] <!-- main article -->
+[[Category:Buzzardsmic| ]] <!-- key article -->
 [[Category:Temperament clans]]
-[[Category:Buzzardsmic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]
-[[Category:Listen]]

Buzzardsmic clan: Difference between revisions

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