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 & 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.
+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:
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 Badness (Sintel): 1.15
+== 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.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 16875/16807, 65536/64827
+{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
+: mapping generators: ~2, ~15/14
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.2693{{c}}, ~15/14 = 118.8923{{c}}
+: [[error map]]: {{val| -0.731 +0.322 -0.060 +1.543 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 118.9682{{c}}
+: error map: {{val| 0.000 +1.536 +1.545 +3.556 }}
+{{Optimal ET sequence|legend=1| 10, 91cd, 101, 111, 121, 232d }}
+[[Badness]] (Sintel): 3.99
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 1375/1372, 65536/64827
+Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
+Optimal tunings:
+* WE: ~2 = 1199.2891{{c}}, ~15/14 = 118.8978{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9662{{c}}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
+Badness (Sintel): 2.21
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+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:
+* WE: ~2 = 1199.2920{{c}}, ~15/14 = 118.8980{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9666{{c}}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
+Badness (Sintel): 1.31
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+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:
+* WE: ~2 = 1199.2648{{c}}, ~15/14 = 118.8946{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9655{{c}}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232dg }}
+Badness (Sintel): 1.00
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+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 }}
+Optimal tunings:
+* WE: ~2 = 1199.2847{{c}}, ~15/14 = 118.8929{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 118.9644{{c}}
+{{Optimal ET sequence|legend=0| 10, 111, 121, 232dg }}
+Badness (Sintel): 1.09
 == Anthoine ==