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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Line 275:

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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Line 290:

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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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 }}

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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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 }}

Optimal tunings:

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Line 374:

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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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 }}

Optimal tunings:

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Badness (Sintel): 0.944

==== 17-limit ====

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

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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Line 414:

Badness (Sintel): 1.14

==== 19-limit ====

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

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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Badness (Sintel): 1.15

==== 23-limit ====

=== 23-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23

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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Badness (Sintel): 1.19

==== 29-limit ====

=== 29-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23.29

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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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 ==

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

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Line 484:

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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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 }}

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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[[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 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 376: / Line 399: @@
 Badness (Sintel): 0.944
-==== 17-limit ====
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
 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 391: / Line 414: @@
 Badness (Sintel): 1.14
-==== 19-limit ====
+=== 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
 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 406: / Line 429: @@
 Badness (Sintel): 1.15
-==== 23-limit ====
+=== 23-limit ===
 Subgroup: 2.3.5.7.11.13.17.19.23
 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 421: / Line 444: @@
 Badness (Sintel): 1.19
-==== 29-limit ====
+=== 29-limit ===
 Subgroup: 2.3.5.7.11.13.17.19.23.29
 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 435: / Line 458: @@
 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 ==
-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
@@ Line 472: / 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 487: / 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 502: / 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 517: / 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 549: / 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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