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.

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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 [[Frostburn]], named after the red-tailed hawk.

[[Subgroup]]: 2.3.5.7

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[[Category:Buzzardsmic clan| ]]

[[Category:Buzzardsmic| ]]

[[Category:Temperament clans]]

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

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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.
@@ 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 [[Frostburn]], named after the red-tailed hawk.
 [[Subgroup]]: 2.3.5.7
@@ Line 539: / Line 562: @@
 [[Category:Buzzardsmic clan| ]] <!-- main article -->
+[[Category:Buzzardsmic| ]] <!-- key article -->
 [[Category:Temperament clans]]
 [[Category:Catalogs of rank-2 temperaments]]