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]].
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.  
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 64: Line 64:
Comma list: 176/175, 540/539, 5120/5103
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:  
Optimal tunings:  
Line 79: Line 79:
Comma list: 176/175, 351/350, 540/539, 676/675
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:  
Optimal tunings:  
Line 94: Line 94:
Comma list: 176/175, 256/255, 351/350, 442/441, 540/539
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:  
Optimal tunings:  
Line 109: Line 109:
Comma list: 176/175, 256/255, 286/285, 324/323, 351/350, 540/539
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:  
Optimal tunings:  
Line 124: Line 124:
Comma list: 99/98, 385/384, 2200/2187
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:  
Optimal tunings:  
Line 139: Line 139:
Comma list: 99/98, 275/273, 385/384, 572/567
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:  
Optimal tunings:  
Line 149: Line 149:
Badness (Sintel): 1.65
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
[[Subgroup]]: 2.3.5.7
Line 173: Line 196:
Comma list: 540/539, 896/891, 12005/11979
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:  
Optimal tunings:  
Line 188: Line 211:
Comma list: 352/351, 364/363, 540/539, 676/675
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:  
Optimal tunings:  
Line 252: Line 275:
Comma list: 169/168, 225/224, 640/637
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:  
Optimal tunings:  
Line 267: Line 290:
Comma list: 225/224, 385/384, 6655/6561
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:  
Optimal tunings:  
Line 282: Line 305:
Comma list: 169/168, 225/224, 275/273, 385/384
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:  
Optimal tunings:  
Line 297: Line 320:
Comma list: 99/98, 176/175, 51200/50421
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:  
Optimal tunings:  
Line 312: Line 335:
Comma list: 99/98, 169/168, 176/175, 640/637
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:  
Optimal tunings:  
Line 351: Line 374:
Comma list: 126/125, 176/175, 1344/1331
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:  
Optimal tunings:  
Line 366: Line 389:
Comma list: 126/125, 144/143, 176/175, 364/363
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:  
Optimal tunings:  
Line 376: Line 399:
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


Comma list: 126/125, 144/143, 176/175, 221/220, 256/255
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:  
Optimal tunings:  
Line 391: Line 414:
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


Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220
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:  
Optimal tunings:  
Line 406: Line 429:
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


Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
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:  
Optimal tunings:  
Line 421: Line 444:
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


Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230
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:  
Optimal tunings:  
Line 435: Line 458:


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 ==
Line 472: Line 484:
Comma list: 540/539, 1375/1372, 65536/64827
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:  
Optimal tunings:  
Line 487: Line 499:
Comma list: 352/351, 540/539, 676/675, 1375/1372
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:  
Optimal tunings:  
Line 502: Line 514:
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
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:  
Optimal tunings:  
Line 517: Line 529:
Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
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:  
Optimal tunings:  
Line 549: Line 561:
[[Badness]] (Sintel): 4.57
[[Badness]] (Sintel): 4.57


[[Category:Buzzardsmic clan| ]] <!-- main article -->
[[Category:Buzzardsmic| ]] <!-- key article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Buzzardsmic clan| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]
[[Category:Listen]]