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| These are rank-3 temperaments tempering out [[9801/9800]]. Temperaments discussed elsewhere are:
| | {{Technical data page}} |
| * ''[[Jubilee]]'', {50/49, 99/98} → [[Jubilismic family #Jubilee|Jubilismic family]]
| | This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] that [[tempering out|temper out]] the kalisma, [[9801/9800]]. These temperaments always split the octave into halves. |
| * ''[[Fantastic]]'', {225/224, 4375/4356} → [[Marvel family #Fantastic|Marvel family]]
| |
| * ''[[Bisector]]'', {121/120, 245/243} → [[Sensamagic family #Bisector|Sensamagic family]]
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| * ''[[Julius]]'' or ''[[varda]]'', {176/175, 896/891} → [[Diaschismic rank three family #Julius aka varda|Diaschismic rank three family]]
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| * ''[[Hagrid]]'', {243/242, 9801/9800} → [[Cataharry family #Hagrid|Cataharry family]]
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| * ''[[Uniwiz]]'', {385/384, 9801/9800} → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
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| * ''[[Varuna]]'', {441/440, 8019/8000} → [[Werckismic temperaments #Varuna|Werckismic temperaments]]
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| * ''[[Hades]]'', {540/539, 4000/3993} → [[Swetismic temperaments #Hades|Swetismic temperaments]]
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| * ''[[Dimcomp]]'', {1375/1372, 6250/6237} → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]]
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| * ''[[Baldur]]'', {2401/2400, 9801/9800} → [[Breed family #Baldur|Breed family]]
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| * ''[[Thor]]'', {3025/3024, 4375/4374} → [[Ragismic family #Thor|Ragismic family]]
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| * ''[[Semiporwell]]'', {6144/6125, 9801/9800} → [[Porwell family #Semiporwell|Porwell family]]
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| * ''[[Semicanou]]'', {9801/9800, 14641/14580} → [[Canou family #Semicanou|Canou family]]
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| Considered below are odin, loki, van gogh, rishi, hnoss, and gersemi, but we can begin by looking at the rank-4 temperament.
| | Temperaments discussed elsewhere are: |
| | * ''[[Jubilismic]]'' (+50/49) → [[Jubilismic family #Undecimal jubilismic|Jubilismic family]] |
| | * ''[[Fantastic]]'' (+225/224) → [[Marvel family #Fantastic|Marvel family]] |
| | * ''[[Bisector]]'' (+121/120 or 245/243) → [[Sensamagic family #Bisector|Sensamagic family]] |
| | * ''[[Varda]]'' (+176/175) → [[Diaschismic rank-3 family #Varda|Diaschismic rank-3 family]] |
| | * ''[[Hagrid]]'' (+243/242) → [[Cataharry family #Hagrid|Cataharry family]] |
| | * ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]] |
| | * ''[[Varuna]]'' (+441/440) → [[Werckismic temperaments #Varuna|Werckismic temperaments]] |
| | * ''[[Hades]]'' (+540/539) → [[Swetismic temperaments #Hades|Swetismic temperaments]] |
| | * ''[[Dimcomp]]'' (+1375/1372) → [[Dimcomp family #Undecimal dimcomp|Dimcomp family]] |
| | * ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]] |
| | * ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]] |
| | * ''[[Semihemimean]]'' (+3136/3125) → [[Hemimean family #Semihemimean|Hemimean family]] |
| | * ''[[Loki]]'' (+5632/5625) → [[Vishdelismic clan #Loki|Vishdelismic clan]] |
| | * ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]] |
| | * ''[[Semicathart]]'' (+14641/14580) → [[Cathartic family #Semicathart|Cathartic family]] |
| | * ''[[Pessoal]]'' (+131072/130977) → [[Olympic clan #Pessoal|Olympic clan]] |
| | * ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]] |
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| == Kalismic ==
| | Considered below are lycoris, van gogh, sif, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]]. |
| [[Subgroup]]: 2.3.5.7.11 | |
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| [[Comma list]]: 9801/9800 | | == Lycoris == |
| | | Lycoris tempers out the [[parimo]] in addition to the kalisma, and splits the [[syntonic comma]] into three equal parts, one for [[121/120]], and two for [[243/242]]. It is therefore [[support]]ed by third-comma equal temperaments. [[342edo]] shows an excellent example of this, but it can be tuned much more accurate. |
| [[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}] | |
| | |
| Mapping generators: ~99/70, ~3, ~5, ~7
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| {{Val list|legend=1| 8d, 10, 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}
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| == Odin ==
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| {{see also| Landscape family }}
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| [[Subgroup]]: 2.3.5.7.11 | |
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| [[Comma list]]: 9801/9800, 151263/151250 | |
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| [[Mapping]]: [{{val| 6 0 0 8 17 }}, {{val| 0 1 0 -2 -4 }}, {{val| 0 0 1 2 3 }}] | |
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| Mapping generators: ~55/49, ~3, ~5
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| {{Val list|legend=1| 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e }}
| | It was named by [[Flora Canou]] in 2023 after the flower associated with afterlife in Japanese culture, under the impression that a temperament with such intricacy will never be fully explored in a lifetime. |
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| [[Badness]]: 0.116 × 10<sup>-3</sup>
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| == Lycoris ==
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| [[Subgroup]]: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 9801/9800, 1771561/1771470 | | [[Comma list]]: 9801/9800, 1771561/1771470 |
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| [[Mapping]]: [{{val| 2 0 4 -6 1 }}, {{val| 0 1 1 3 2 }}, {{val| 0 0 -6 5 -1 }}]
| | {{Mapping|legend=1| 2 0 -2 1 0 | 0 1 1 3 2 | 0 0 6 -5 1 }} |
| | : mapping generators: ~99/70, ~3, ~11/9 |
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| Mapping generators: ~99/70, ~3, ~81/70
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~99/70 = 600.0018{{c}}, ~3/2 = 701.9411{{c}}, ~11/9 = 347.3976{{c}} |
| | : [[error map]]: {{val| +0.004 -0.010 +0.013 -0.018 -0.031 }} |
| | * [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9414{{c}}, ~11/9 = 347.3969{{c}} |
| | : error map: {{val| 0.000 -0.014 +0.009 +0.014 -0.038 }} |
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| [[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 701.9439, ~81/70 = 252.6028
| | {{Optimal ET sequence|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }} |
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| {{Val list|legend=1| 152, 328, 342, 836, 1178, 1354, 1506, 1848, 2684, 4038, 4190, 4532, 11254, 15786e }}
| | [[Badness]] (Sintel): 0.299 |
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| [[Badness]]: 0.249 × 10<sup>-3</sup> | |
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| === Higanbana === | | === Higanbana === |
| Subgroup: 2.3.5.7.11.13 | | Subgroup: 2.3.5.7.11.13 |
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| Comma list: 9801/9800, 10648/10647, 1574640/1574573 | | Comma list: 9801/9800, 10648/10647, 1399680/1399489 |
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| Mapping: [{{val| 2 1 5 -3 3 8 }}, {{val| 0 2 2 6 4 1 }}, {{val| 0 0 -6 5 -1 4 }}]
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| Mapping generators: ~99/70, ~1458/1001, ~81/70 | | Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }} |
| | : mapping generators: ~99/70, ~1458/1001, ~81/70 |
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| Optimal tuning (CTE): ~99/70 = 1\2, ~1458/1001 = 650.9715, ~81/70 = 252.6037 | | Optimal tunings: |
| | * WE: ~99/70 = 599.9996{{c}}, ~1458/1001 = 650.9717{{c}}, ~11/9 = 347.3963{{c}} |
| | * CWE: ~99/70 = 600.0000{{c}}, ~1458/1001 = 650.9718{{c}}, ~11/9 = 347.3964{{c}} |
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| Optimal GPV sequence: {{Val list| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }} | | {{Optimal ET sequence|legend=0| 166, 190, 304d, 328, 494, 684, 1012, 1178, 1506, 2190, 2684, 4190, 6380, 9064, 15938 }} |
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| Badness: 0.416 × 10<sup>-3</sup> | | Badness (Sintel): 0.389 |
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| == Van Gogh == | | == Van gogh == |
| [[Subgroup]]: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 9801/9800, 199297406/199290375 | | [[Comma list]]: 9801/9800, 199297406/199290375 |
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| [[Mapping]]: [{{val| 2 0 8 0 11 }}, {{val| 0 1 1 2 1 }}, {{val| 0 0 -9 -1 -10 }}]
| | {{Mapping|legend=1| 2 0 8 0 11 | 0 1 1 2 1 | 0 0 -9 -1 -10 }} |
| | : mapping generators: ~99/70, ~3, ~11/10 |
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| Mapping generators: ~99/70, ~3, ~9/7
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~99/70 = 600.0022{{c}}, ~3/2 = 701.9464{{c}}, ~11/9 = 164.9319{{c}} |
| | : [[error map]]: {{val| +0.004 -0.004 +0.022 +0.005 -0.046 }} |
| | * [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9469{{c}}, ~11/9 = 164.9316{{c}} |
| | : error map: {{val| 0.000 -0.008 +0.018 -0.000 -0.055 }} |
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| {{Val list|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }} | | {{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 204cde, 226ce, 240d, 262d, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }} |
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| [[Badness]]: 0.297 × 10<sup>-3</sup> | | [[Badness]] (Sintel): 0.358 |
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| == Hnoss == | | == Sif == |
| To the wizma {{monzo| -6 -8 2 5 }} = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]].
| | Sif tempers out 2097152/2096325, and extends to a strong [[13-limit]] temperament by virtue of the identity 2097152/2096325 = ([[4096/4095]])⋅([[6656/6655]]). It was named by [[Flora Canou]] in 2023 as a sharp-tending counterpart of [[thor]]. |
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| [[Subgroup]]: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 9801/9800, 41503/41472 | | [[Comma list]]: 9801/9800, 2097152/2096325 |
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| [[Mapping]]: [{{val| 2 0 1 2 6 }}, {{val| 0 1 4 0 2 }}, {{val| 0 0 -5 2 -3 }}]
| | {{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }} |
| | : mapping generators: ~99/70, ~3 |
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| Mapping generators: ~99/70, ~3, ~144/77
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~99/70 = 599.9863{{c}}, ~3/2 = 701.9658{{c}}, ~48/35 = 546.5930{{c}} |
| | : [[error map]]: {{val| -0.027 -0.017 +0.045 +0.052 +0.000 }} |
| | * [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9755{{c}}, ~48/35 = 546.6052{{c}} |
| | : error map: {{val| 0.000 +0.021 +0.107 +0.124 +0.101 }} |
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| {{Val list|legend=1| 22, 50, 72, 166, 176, 198, 248, 270, 342, 612, 954, 1566, 4086dee, 5652cddeee }} | | {{Optimal ET sequence|legend=1| 22, 46, 68, 114, 134, 156, 178, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2742, 3236, 3506, 4742d, 10990ccdde, 15732ccdddee }} |
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| [[Badness]]: 0.368 × 10<sup>-3</sup> | | [[Badness]] (Sintel): 0.508 |
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| === 13-limit === | | === 13-limit === |
| Subgroup: 2.3.5.7.11.13 | | Subgroup: 2.3.5.7.11.13 |
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| Comma list: 1716/1715, 2080/2079, 17303/17280 | | Comma list: 4096/4095, 6656/6655, 9801/9800 |
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| Mapping: [{{val| 2 0 1 2 6 -3 }}, {{val| 0 1 4 0 2 1 }}, {{val| 0 0 -5 2 -3 4 }}]
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| Optimal GPV sequence: {{Val list| 22f, 32cf, 54cff, 72, 166, 198, 270, 634, 904, 1174, 1880ef }}
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| Badness: 0.867 × 10<sup>-3</sup>
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 715/714, 1089/1088, 1225/1224, 2025/2023
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| Mapping: [{{val| 2 0 1 2 6 -3 0 }}, {{val| 0 1 4 0 2 1 6 }}, {{val| 0 0 -5 2 -3 4 -6 }}]
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| Optimal GPV sequence: {{Val list| 22f, 54cffgg, 72, 166g, 198g, 270, 364, 436, 634g, 706f }}
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| Badness: 0.862 × 10<sup>-3</sup>
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| ==== 19-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 4200/4199
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| Mapping: [{{val| 2 0 1 2 6 -3 0 13 }}, {{val| 0 1 4 0 2 1 6 2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 }}]
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| Optimal GPV sequence: {{Val list| 72, 94, 166g, 198g, 270, 436, 634g, 706f }}
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| Badness: 0.901 × 10<sup>-3</sup>
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| ==== 23-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19.23
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| Comma list: 715/714, 1225/1224, 1540/1539, 2080/2079, 2530/2527, 2737/2736
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| Mapping: [{{val| 2 0 1 2 6 -3 0 13 19 }}, {{val| 0 1 4 0 2 1 6 2 -2 }}, {{val| 0 0 -5 2 -3 4 -6 -6 -2 }}]
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| Optimal GPV sequence: {{Val list| 72, 94, 166g, 270, 342f, 436, 706fi }}
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| Badness: 1.14 × 10<sup>-3</sup>
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| === Gersemi ===
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| The extension to 13-limit with [[4225/4224]] is weak but facilitates the use of 18/7 as the equave. Fokker blocks of 128 notes are available for the latter, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)<sup>3</sup> ~ 17/1 via the [[5832/5831|chlorisma]]. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings.
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 4225/4224, 9801/9800, 41503/41472
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| Mapping: [{{val| 2 0 1 2 6 9 }}, {{val| 0 1 9 -2 5 -6 }}, {{val| 0 0 -10 4 -6 7 }}] | | Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }} |
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| Mapping generators: ~99/70, ~3, ~154/65
| | Optimal tunings: |
| | * WE: ~99/70 = 599.9857{{c}}, ~3/2 = 701.9705{{c}}, ~48/35 = 546.5927{{c}} |
| | * CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9877{{c}}, ~48/35 = 546.6058{{c}} |
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| Optimal GPV sequence: {{Val list| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }} | | {{Optimal ET sequence|legend=0| 22, 46, 156f, 178, 202f, 224, 270, 494, 764, 1012, 1236, 1506, 3236, 3506, 4742df, 6248cdf, 8248cdef, 12990ccddeff, 14496ccdddeeff }} |
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| Badness: 1.06 × 10<sup>-3</sup> | | Badness (Sintel): 0.317 |
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| ==== 17-limit ==== | | == Linus == |
| Subgroup: 2.3.5.7.11.13.17
| | {{Main| Linus }} |
| | : ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Linus]].'' |
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| Comma list: 1089/1088, 1225/1224, 2025/2023, 4225/4224
| | Linus [[tempering out|tempers out]] the [[linus comma]], {{monzo| 11 -10 -10 10 }} in the 7-limit and can be described as the {{nowrap| 80 & 130 & 270 }} temperament. It tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99. |
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| Mapping: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}]
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| Optimal GPV sequence: {{Val list| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }}
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| Badness: 1.46 × 10<sup>-3</sup>
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| ==== 19-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757
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| Mapping: [{{val| 2 0 1 2 6 9 0 1 }}, {{val| 0 1 9 -2 5 -6 12 11 }}, {{val| 0 0 -10 4 -6 7 -12 -11 }}]
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| Mapping generators: ~99/70, ~3, ~45/19
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| Optimal GPV sequence: {{Val list| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }}
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| Badness: 1.11 × 10<sup>-3</sup>
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| ==== 23-limit ====
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| Subgroup: 2.3.5.7.11.13.17.19.23
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| Comma list: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925
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| Mapping: [{{val| 2 0 1 2 6 9 0 1 7 }}, {{val| 0 1 9 -2 5 -6 12 11 3 }}, {{val| 0 0 -10 4 -6 7 -12 -11 -3 }}]
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| Optimal GPV sequence: {{Val list| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }}
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| Badness: 1.23 × 10<sup>-3</sup>
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| == Loki ==
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 5632/5625, 9801/9800
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| [[Mapping]]: [{{val| 2 0 0 -21 -18 }}, {{val| 0 1 0 4 2 }}, {{val| 0 0 1 3 4 }}]
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| Mapping generators: ~99/70, ~3, ~5
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| {{Val list|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
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| [[Badness]]: 0.493 × 10<sup>-3</sup>
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| == Pessoal ==
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| {{See also| Pessoalisma }}
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| [[Subgroup]]: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 9801/9800, 131072/130977 | | [[Comma list]]: 9801/9800, 391314/390625 |
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| [[Mapping]]: [{{val| 2 0 1 10 14 }}, {{val| 0 1 0 -1 -3 }}, {{val| 0 0 3 -1 2 }}]
| | {{Mapping|legend=1| 10 0 0 -11 4 | 0 1 0 1 -1 | 0 0 1 1 2 }} |
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| Mapping generators: ~99/70, ~3, ~32/21
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~15/14 = 119.9975{{c}}, ~3/2 = 702.0188{{c}}, ~5/4 = 386.6399{{c}} |
| | : [[error map]]: {{val| -0.025 +0.039 +0.276 -0.215 -0.143 }} |
| | * [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 702.0181{{c}}, ~5/4 = 386.6218{{c}} |
| | : error map: {{val| 0.000 +0.063 +0.308 -0.186 -0.092 }} |
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| [[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 702.0759, ~32/21 = 728.7910
| | {{Optimal ET sequence|legend=1| 50, 60e, 80, 130, 190, 270, 670, 940, 1130, 1400, 1800c, 2070c, 2340c }} |
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| {{Val list|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
| | [[Badness]] (Sintel): 1.34 |
| | |
| [[Badness]]: 0.499 × 10<sup>-3</sup> | |
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| === 13-limit === | | === 13-limit === |
| Subgroup: 2.3.5.7.11.13 | | Subgroup: 2.3.5.7.11.13 |
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| Comma list: 1716/1715, 2080/2079, 4096/4095 | | Comma list: 1001/1000, 4225/4224, 4459/4455 |
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| Mapping: [{{val| 2 0 1 10 14 13 }}, {{val| 0 1 0 -1 -3 -1 }}, {{val| 0 0 3 -1 2 -2 }}] | | Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }} |
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| Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.0637, ~32/21 = 728.7786 | | Optimal tunings: |
| | * WE: ~15/14 = 120.0054{{c}}, ~3/2 = 701.9625{{c}}, ~5/4 = 386.4910{{c}} |
| | * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 701.9533{{c}}, ~5/4 = 386.5119{{c}} |
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| Optimal GPV sequence: {{Val list| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }} | | {{Optimal ET sequence|legend=0| 50, 60e, 80, 130, 190, 270, 590, 730, 860, 1130, 1590df, 1860def }} |
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| Badness: 0.391 × 10<sup>-3</sup> | | Badness (Sintel): 0.721 |
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| == Rishi ==
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| The 7-limit comma {{monzo| 65 -84 10 16 }} ~ 0.13¢ has the ratio of the exponents of 3 and 2 that is close to the one in 81/8. The square root of the latter is close to 35/11. This suggests tempering out (81/8)(35/11)<sup>-2</sup>, which is the kalisma.
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| Apart from 35/11, 35/33, and the equivalents of their squares, 81/8 and 9/8, another equave that comes to mind is 3/2, especially after tempering out the [[chalmersia]]. When 3/2 is chosen as the equave, Fokker blocks of 34 notes can be used that are close to [[34edf]] and 58edo.
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| [[Subgroup]]: 2.3.5.7.11
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| [[Comma list]]: 9801/9800, 572145834917888/571919811374025
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| [[Mapping]]: [{{val| 2 0 3 -10 -4 }}, {{val| 0 1 2 4 4 }}, {{val| 0 0 8 -5 3 }}]
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| Mapping generators: ~99/70, ~3, ~17364375/14172488
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| {{Val list|legend=1| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 7414, 9874, 12828e }}
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| [[Badness]]: 2.10 × 10<sup>-3</sup>
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 9801/9800, 10648/10647, 371293/371250
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| Mapping: [{{val| 2 0 3 -10 -4 2 }}, {{val| 0 1 2 4 4 3 }}, {{val| 0 0 8 -5 3 7 }}]
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| Mapping generators: ~99/70, ~3, ~364/297
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| Optimal GPV sequence: {{Val list| 24, 34d, 58, …, 436, 460, 494, 954, 1448, 1506, 2460, 2954, 5414, 6920, 7414, 9874, 12828e }}
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| [[Badness]]: 0.505 × 10<sup>-3</sup>
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| | [[Category:Kalismic temperaments| ]] <!-- main article --> |
| [[Category:Temperament collections]] | | [[Category:Temperament collections]] |
| [[Category:Kalismic temperaments| ]] <!-- main article --> | | [[Category:Catalogs of rank-3 temperaments]] |
| [[Category:Rank 3]]
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