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| == Berkelium == | | == Luminance (tuning) == |
| A remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings. Since it was conceived in this specific subgroup, it makes no sense to name it for smaller subgroups.
| | https://www.wolframalpha.com/input?i=plot+sqrt%28%28RiemannSiegelZ%5B%282*pi*x%2Fln%282%29%29%5D%29%5E2%2B%28%28DivisorSum%5Bx%2C+%23+%26%5D-x%29%2Fx%29%5E2%29%2C+x+from+1+to+100 |
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| Subgroup: 2.3.5.13.17.23.29.31
| | Luminance is a measure of an equal temperament based on both is [[abundancy index]] and [[zeta peak integer edo]] position. It is equal to sqrt(Z^2+A^2), where Z is the zeta value while A is the abundancy index. |
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| Comma list: 10881/10880, 13312/13311, 86411/86400, 96876/96875, 4784000/4782969, 223171875/223135744
| | Increasingly larger luminance values: {{EDOs|2, 3, 5, 7, 10, 12, 22, 24, 31, 41, 53, 87, ...}} |
| | == Natrium == |
| | The natrium tempers out the {{monzo|403 -77 -121}} comma in the 5-limit, not only splitting the octave in 11, but using [[1125/1024]] as a generator, eleven of which plus one step of [[11edo]] make [[3/1]]. |
| | == Phosphorus == |
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| Sval mapping: [{{val|97 97 55 -95 283 609 301 821}}, {{val|0 1 3 8 2 -3 3 -6}}]
| | 1125 & 2460, 23-limit. |
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| Sval mapping generators: ~6075/6032, ~3/2
| | 1125 patent val branching tempers out the [[flashma]] and therefore is to be named white phosphorus, and 1125g val branching is to be named red phosphorus. |
| | == Strontium == |
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| Optimal tuning (CTE): ~3/2 = 701.9...
| | Described as the 1178 & 7334 temperament in the 19-limit. |
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| Vals: 388, 2619, 3395...
| | == Cadmium == |
| | Described as the 624 & 4320 temperament upwards to the 23-limit. |
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| === Berkelium-248 ===
| | In the 23-limit, the gen is mapped to [[70/69]]. |
| The temperament with higher TE error of the two branchings, therefore named after the second most stable berkelium isotope.
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| Subgroup: 2.3.5.7.11.13
| | == Thulium == |
| | https://sintel.pythonanywhere.com/result?subgroup=11&reduce=on&tenney=on&target=&edos=&commas=%5B-4%2C+2%2C+-11%2C+2%2C+6%3E%0D%0A%5B-21%2C+-14%2C+8%2C+10%2C+-1%3E%0D%0A%5B-25%2C+-12%2C+-3%2C+12%2C+5%3E%0D%0A%5B-17%2C+-16%2C+19%2C+8%2C+-7%3E%0D%0A%5B-29%2C+-10%2C+-14%2C+14%2C+11%3E%0D%0A%5B55%2C+-50%2C+-1%2C+7%2C+2%3E&submit_comma=submit |
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| Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
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| Mapping generators: ~144/143, ~3/2
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| Optimal tuning (CTE): ~3/2 = 701.945
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| EDOs: 388, 2619, ...
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| === Berkelium-247 ===
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| The temperament with lower TE error of the two branchings, therefore named after the most stable berkelium isotope.
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| Subgroup: 2.3.5.7
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| Comma list: 12824703626379264/12822723388671875, {{monzo|56 -57 16 -1}}
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| Mapping: [{{val|97 97 55 783}}, {{val|0 1 3 -9}}]
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| Mapping generators: ~13839047287569/13743895347200 = 1\97, ~3/2 = 701.973
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| Optimal tuning (CTE):~ 3/2 = 701.973
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11 | | Subgroup: 2.3.5.7.11 |
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| Comma list: 21437500/21434787, 44660948992/44659644435, 1573159698432/1572763671875 | | Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245 |
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| Mapping: [{{val|97 97 55 783 903}}, {{val|0 1 3 -9 -10}}]
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| Mapping generators: ~4125/4096 = 1\97, ~3/2 = 701.976
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| Optimal tuning (CTE):~ 3/2 = 701.976
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 1990656/1990625, 1146880/1146717, 492128/492075, 2662250409/2662000000
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| Mapping: [{{val|97 97 55 783 903 -95}}, {{val|0 1 3 -9 -10 8}}]
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| Mapping generators: ~16038/15925, ~3/2
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| Optimal tuning (CTE): ~3/2 = 701.976
| | Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}] |
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| ==== 17-limit ====
| | Mapping generators: ~100/99, ~3 |
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| Subgroup: 2.3.5.7.11.13.17
| | {{Optimal ET sequence|legend=1| 759, 7797 }} |
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| Comma list: 12376/12375, 37180/37179, 1990656/1990625, 1146880/1146717, 263299491/263296000
| | == Rutherfordium == |
| | Rutherfordium is described as the 624 & 4472 temperament in the 23-limit. |
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| Mapping: [{{val|97 97 55 783 903 -95 283}}, {{val|0 1 3 -9 -10 8 2}}]
| | == Seaborgium == |
| | Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely. |
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| Mapping generators: ~1547/1536, ~3/2
| | == Kells == |
| | 436 & 981 temperament. |
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| Optimal tuning (CTE): ~3/2 = 701.976
| | == Meitnerium == |
| | 981 & 3706 temperament. |
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| ==== 19-limit ==== | | == Copernicium == |
| | Named after the 112th element. |
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| Subgroup: 2.3.5.7.11.13
| | 1904 & 3920 temperament. |
| | == Tenessine == |
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| Comma list: 12376/12375, 13377/13376, 14080/14079, 27456/27455, 37180/37179, 165376/165375, 722007/722000
| | Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma. |
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| Mapping: [{{val|97 97 55 783 903 -95 283}}, {{val|0 1 3 -9 -10 8 2}}]
| | == Unpentennium == |
| | | Described as the 795 & 3498 temperament and splits the octave into 159. |
| Mapping generators: ~16038/15925, ~3/2
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| Optimal tuning (CTE): ~3/2 = 701.976
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| == Point Zero Seven ==
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| A meantone version of sextilififths that's quite bad at JI. Named because the generator is 7\100, and since the name sounds like an alcohol percentage, it corresponds to the "drunken and imprecise feel" of the badness of JI of the scale.
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| Subgroup: 2.3.5.7
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| Comma list: 81/80, 121500/117649
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| Mapping: [1 2 4 4], [0 -6 -24 -17]
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| Optimal tuning (CTE): ~21/20 = 83.888
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| Vals: 14, 43, 100
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| == Lamina == | |
| Leaves temperament in the 51L 1s 1|1 scale has a meantone fifth which is flat of 17edo fifth by a leaves' reduced generator. Lamina takes the said fifth and uses it as a generator. Name comes from the flat surface that makes up the texture of a leaf. Defined as 33 & 323 in the 17-limit, and with step size difference of around JND it can be treated as a barely noticeable well temperament for [[33edo]].
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| The fifth reaches 13/11 in 10 steps, just as generator of lamina does. In addition, 21/16 is reached in 8 steps, 7/5 is reached in 13 steps, 16/15 is reached in 21 steps.
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| === Grand lamina ===
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| Grand lamina is defined as 257 & 2023, and it is a metatemperament for lamina, with both having the same relationships in the 33-note MOS.
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| == Tritonopod ==
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| ''Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.''
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| ''Possibly rank-3?''
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| == Playing cards ==
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| ''Work in progress''
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| == Titanium II ==
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| https://sintel.pythonanywhere.com/result?subgroup=13&reduce=on&tenney=on&target=&edos=198+%26+1012&submit_edo=submit&commas=
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| 198 & 1012 temperament.
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| == Thulium ==
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| Period-69 temperament conceptualized as having a period of 100/99 and a generator of 3/2. Conceptualized as the 759(some kind of val) & 7797 temperament
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