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| == Minutes == | | == Luminance (tuning) == |
| Defined as the 2460 & 4320 temperament, and named "minutes" for period-60, since there's 60 minutes in an hour. In the limits below 13, it's a contorted atomic temperament.
| | 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: 2.3.5.7.11.13
| | 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: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125
| | 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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| Mapping: 60 60 385 730 1085 573, 0 1 7 -16 -25 -10
| | 1125 & 2460, 23-limit. |
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| Mapping generators: ~2704/2673, ~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 = 701.948
| | Described as the 1178 & 7334 temperament in the 19-limit. |
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| === 17-limit === | | == Cadmium == |
| Subgroup: 2.3.5.7.11.13.17
| | Described as the 624 & 4320 temperament upwards to the 23-limit. |
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| Comma list: 9801/9800, 12376/12375, 28561/28560, 250047/250000, 253755392/253746675
| | In the 23-limit, the gen is mapped to [[70/69]]. |
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| Mapping: 60 60 385 730 1085 573 877, 0 1 7 -16 -25 -10 -18
| | == 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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| Mapping generators: ~3520/3213, ~3/2
| | Subgroup: 2.3.5.7.11 |
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| Optimal tuning (CTE): ~3/2 = 701.948
| | Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245 |
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| === 19-limit ===
| | Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}] |
| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: ''to be filled in''
| | Mapping generators: ~100/99, ~3 |
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| Mapping: ''to be filled in''
| | {{Optimal ET sequence|legend=1| 759, 7797 }} |
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| Mapping generators: ~3520/3213, ~3/2
| | == Rutherfordium == |
| | Rutherfordium is described as the 624 & 4472 temperament in the 23-limit. |
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| Optimal tuning (CTE): ~3/2 = 701.948
| | == Seaborgium == |
| | Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely. |
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| == Nuclear matter == | | == Kells == |
| Defined as the 22 & 69 temperament, and the comma in the 5-limit is [-41, 1, 17⟩. The name comes from the fact that nuclear matter density is 4.1 * 10^17 kg/m^3.
| | 436 & 981 temperament. |
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| Subgroup: 2.3.5
| | == Meitnerium == |
| | 981 & 3706 temperament. |
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| Comma list: [-41, 1, 17⟩
| | == Copernicium == |
| | Named after the 112th element. |
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| Optimal tuning (CTE): ~5/4
| | 1904 & 3920 temperament. |
| | == Tenessine == |
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| Vals: 22, 69
| | Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma. |
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| == Berkelium == | | == Unpentennium == |
| A remarkable high-limit temperament, extended as high as the 29-limit owing to the fact that both 388edo and 2619edo are consistent that high. Named after the 97th element.
| | Described as the 795 & 3498 temperament and splits the octave into 159. |
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| Subgroup: 2.3.5.7.11.13
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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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| == 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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| == Mabon ==
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| Named after the celebration of the autumn equinox, and defined as the 11 & 62 temperament in the 2.9.7, since the 11/62 solar calendar leap rule representes the autumn equinox. Three below 600c generators amount to 16/9.
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| Subgroup: 2.9.7
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| Comma list: 44957696/43046721
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| Sval mapping: [1 1 -3], [0 3 8]
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| Optimal tuning (CTE): ~729/448 = 870.792
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| Vals: 11, 29, 40, 51, 62, ...
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| === 11-limit ===
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| In the 11-limit, the 11th harmonic plus an octave is reached by stacking two 16/11.
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| Subgroup: 2.9.7.11
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| Comma list: 896/891, 1331/1296
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| Sval mapping: [1 1 -3 2], [0 3 8 2]
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| Optimal tuning (CTE): ~18/11
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| == Leaves ==
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| Defined as the 323 & 2023 temperament, and also as the no-11s temperament, because both 323edo and 2023edo have a bad 11th harmonic.
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| Subgroup: 2.3.5.7
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| Comma list: -21 11 10 -7, 31 28 -24 -7
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| Mapping: 17 10 31 9, 0 14 7 32
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| Mapping generators: ~25/24, ~6125/5832
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| Optimal tuning (CTE): ~6125/5832 = 85.427
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| Vals: 323, 1700, 2023
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| === 2.3.5.7.13 subgroup ===
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| Subgroup: 2.3.5.7.13
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| Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096
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| Sval mapping:
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| Sval maping generators: ~25/24, ~1024/975
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| Optimal tuning (CTE): ~1024/975 = ...
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| === 2.3.5.7.13.17 subgroup ===
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| 9 periods and 2 generators correspond to 17/13.
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| Subgroup:
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| Comma list: 57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000
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| Sval mapping: 17 10 31 9 98 107, 0 14 7 32 -29 -31
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| Sval mapping generators: ~25/24, ~765/728
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| Optimal tuning (CTE): ~765/728 = 85.424
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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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