Avicennmic temperaments: Difference between revisions

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+{{Technical data page}}
-These temper out the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.
+This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis.
-== Roman ==
+Tempereaments discussed elsewhere are:
-Commas: 525/512, 4000/3969
+* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
+* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Pelogic|Mavila family]]
+* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
+* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
+* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
+* [[Muggles]] (+126/125) → [[Magic family #Muggles|Magic family]]
+* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]]
+* ''[[Pycnic]]'' (+245/243) → [[Sensamagic clan #Pycnic|Sensamagic clan]]
+* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
+* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]]
-[[POTE_tuning|POTE generator]]: ~63/50 = 414.552
+Considered below is submerged.
-Map: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
+== Submerged ==
+{{Main| Submerged }}
-Wedgie: &lt;&lt;7 2 -11 -13 -37 -31||
+Named by [[Fitzgerald Lee]] in 2025, submerged tempers out 3125/3087, the [[gariboh comma]]. It may be described as the {{nowrap| 16 & 29 }} temperament, generated by a sharply tuned ~8/5, eleven of which minus seven octaves make a perfect fifth; its [[ploidacot]] is therefore zeta-hendecacot. [[45edo]] makes for an excellent tuning.
-EDOs: [[23edo|23]], [[26edo|26]], [[29edo|29]], [[55edo|55c]]
+[[Subgroup]]: 2.3.5.7
-Badness: 0.1134
+[[Comma list]]: 525/512, 3125/3087
-=== 11-limit ===
+{{Mapping|legend=1| 1 -6 3 9 | 0 11 -1 -9 }}
-Commas: 100/99, 245/242, 1375/1344
+: mapping generators: ~2, ~8/5
-[[POTE_tuning|POTE generator]]: ~14/11 = 414.471
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1203.3342{{c}}, ~8/5 = 829.2070{{c}}
+: [[error map]]: {{val| +3.334 -0.683 -5.518 -1.681 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 826.9483{{c}}
+: error map: {{val| 0.000 -5.523 -13.262 -11.361 }}
-Map: [&lt;1 4 3 -1 0|, &lt;0 -7 -2 11 10|]
+{{Optimal ET sequence|legend=1| 16, 29, 45, 74cd, 119bccdd }}
-EDOs: 23, 26, 29, 55c
+[[Badness]] (Sintel): 3.98
-Badness: 0.0528
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-=== 13-limit ===
-Commas: 65/64, 100/99, 105/104, 245/243
-[[POTE_tuning|POTE generator]]: ~14/11 = 414.472
-Map: [&lt;1 4 3 -1 0 3|, &lt;0 -7 -2 11 10 2|]
-EDOs: 23, 26, 29, 55
-Badness: 0.0300
+Comma list: 121/120, 441/440, 525/512
-=== 17-limit ===
+Mapping: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}
-Commas: 35/34, 52/51, 100/99, 169/168, 275/273
-[[POTE_tuning|POTE generator]]: ~14/11 = 414.164
+Optimal tunings:
+* WE: ~2 = 1203.6231{{c}}, ~8/5 = 829.4195{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9730{{c}}
-Map: [&lt;1 4 3 -1 0 3 1|, &lt;0 -7 -2 11 10 2 9|]
+{{Optimal ET sequence|legend=0| 16, 29, 45e, 74cde, 119bccddeee }}
-EDOs: 26, 29, [[84edo|84]], [[113edo|113]]
+Badness (Sintel): 1.93
-Badness: 0.0416
-=== 19-limit ===
-Commas: 35/34, 52/51, 100/99, 121/119, 133/132, 169/168
-[[POTE_tuning|POTE generator]]: ~14/11 = 414.130
-Map: [&lt;1 4 3 -1 0 3 1 7|, &lt;0 -7 -2 11 10 2 9 -8|]
-EDOs: 26g, 29
-Badness: 0.0337
-== Secund ==
-Commas: 405/392, 525/512
-POTE generator: ~16/15 = 137.958
-Map: [&lt;1 1 3 2|, &lt;0 5 -6 7|]
-Wedgie: &lt;&lt;5 -6 7 -21 -3 33||
-EDOs: [[9edo|9]], [[17edo|17]], 26, [[61edo|61bc]], [[87edo|87bc]]
-Badness: 0.0898
-=== 11-limit ===
-Commas: 45/44, 99/98, 385/384
-POTE generator: ~12/11 = 137.900
-Map: [&lt;1 1 3 2 3|, &lt;0 5 -6 7 4|]
-EDOs: 9, 17, 26, 61bc, 87bc
-Badness: 0.0426
 === 13-limit ===
-Commas: 27/26, 45/44, 99/98, 385/384
+Subgroup: 2.3.5.7.11.13
-POTE generator: ~12/11 = 136.937
-Map: [&lt;1 1 3 2 3 2|, &lt;0 5 -6 7 4 15|]
-EDOs: 9, 26f, [[35edo|35]]
-Badness: 0.0497
-=== Secundly ===
+Comma list: 65/64, 105/104, 121/120, 441/440
-Commas: 45/44, 78/77, 81/80, 640/637
-POTE generator: ~12/11 = 137.917
+Mapping: {{mapping| 1 -6 3 9 0 3 | 0 11 -1 -9 5 1 }}
-Map: [&lt;1 1 3 2 3 3|, &lt;0 5 -6 7 4 6|]
+Optimal tunings:
+* WE: ~2 = 1203.6316{{c}}, ~8/5 = 829.4249{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9677{{c}}
-EDOs: 9, 17, 26, 61bcf, 87bcf
+{{Optimal ET sequence|legend=0| 16, 29, 45ef, 74cdef, 119bccddeeeff }}
-Badness: 0.0262
+Badness (Sintel): 1.35
-[[Category:Theory]]
+[[Category:Temperament collections]]
-[[Category:Temperament]]
+[[Category:Avicennmic temperaments| ]] <!-- main article -->
-[[Category:Avicennmic]]
 [[Category:Rank 2]]