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| == Pseudovishnuzma == | | == Anemoian (name later to be changed) == |
| Comma: 6106906624/6103515625
| | 384p & 324p, 11-limit. |
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| Name reasoning: The denominator is the same as for vishnuzma, numerator is close, yet it's different.
| | [[Subgroup]]: 2.3.5.7.11 |
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| Temperaments:
| | [[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325 |
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| Rank 2: 1261 & 1789 (2.5.7.11.13), 1236 & 764, 1236 & 1084, 1236 & 441, 764 & 1084, 1236 & 87
| | [[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }} |
| | : Mapping generators: ~1375/1296, ~243/200 |
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| == Major Arcana JI scale (detempering of 22edo) == | | [[Optimal tuning]]s: |
| A Factor 9-Grid style detempering, where in the first octave which goes from A = 432 Hz to A = 864 Hz all frequency values are integers.
| | * [[WE]]: ~1375/1296 = 99.997{{c}}, ~243/200 = 340.539{{c}} |
| {| class="wikitable" | | : [[error map]]: {{val| -0.006 +0.038 -0.030 -0.013 }} |
| |+
| | * [[CWE]]: ~1375/1296 = 100{{c}}, ~243/200 = 340.549{{c}} |
| !Step
| | : error map: {{val| 0.000, 0.788, 0.269, -1.146, -0.095 }} |
| !Card
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| !Frequency
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| !JI ratio
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| |-
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| |0
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| |The Fool
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| |432
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| |1/1
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| |-
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| |1
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| |448
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| |-
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| |2
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| |464
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| |-
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| |3
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| |486
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| |-
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| |4
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| |495
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| |-
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| |5
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| |504
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| |7/6
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| |-
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| |6
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| |513
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| |19/16
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| |- | |
| |7
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| |540
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| |-
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| |8
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| |558
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| |-
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| |9
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| |576
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| |-
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| |10
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| |594
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| |-
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| |11
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| |612
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| |-
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| |12
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| |630
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| |-
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| |13
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| |648
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| |-
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| |14
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| |672
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| |-
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| |15
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| |696
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| |-
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| |16
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| |720
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| |-
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| |17
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| |744
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| |-
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| |18
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| |768
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| |-
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| |19
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| |792
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| |-
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| |20
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| |816
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| |-
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| |21
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| |840
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| |-
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| |22
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| |864
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| |2/1
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| |}
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| == Thulium == | | {{Optimal ET sequence|legend=1| 60, 444, 384 }} |
| 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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| == Nuclear matter ==
| | [[Badness]] (Sintel): 21.211 |
| 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.
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| Subgroup: 2.3.5
| | == Luminance (tuning) == |
| | 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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| Comma list: [-41, 1, 17⟩
| | 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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| Optimal tuning (CTE): ~5/4
| | 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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| Vals: 22, 69
| | 1125 & 2460, 23-limit. |
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| == Berkelium (two varieties) == | | 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. |
| 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.
| | == Strontium == |
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| === Variety 1: 388 & 2619 ===
| | Described as the 1178 & 7334 temperament in the 19-limit. |
| Subgroup: 2.3.5.7.11.13
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| Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
| | == Cadmium == |
| | Described as the 624 & 4320 temperament upwards to the 23-limit. |
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| Mapping generators: ~144/143, ~3/2
| | In the 23-limit, the gen is mapped to [[70/69]]. |
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| Optimal tuning (CTE): ~3/2 = 701.945
| | == 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 |
| EDOs: 388, 2619, ...
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| === Variety 2: 388 & 3395 ===
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| ...
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| == Point Zero Seven == | |
| 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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| == Leaves == | |
| Defined as the 323 & 2023 temperament in the 17-limit. Originally intended to be no-11, Eliora later included the 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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| === 13-limit ===
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| 10 generators map to 13/11.
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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: 17 10 31 9 106 98, 0 14 7 32 -39 -29
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| Sval maping generators: ~25/24, ~1024/975
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| Optimal tuning (CTE): ~1024/975 = ...
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| === 17-limit ===
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| 2 generators correspond to 17/13.
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| Subgroup: | | Subgroup: 2.3.5.7.11 |
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| Comma list: | | Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245 |
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| Sval mapping: 17 10 31 9 106 98 107, 0 14 7 32 -39 -29 -31
| | Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}] |
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| Sval mapping generators: ~25/24, ~765/728
| | Mapping generators: ~100/99, ~3 |
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| Optimal tuning (CTE): ~765/728 = 85.424 | | {{Optimal ET sequence|legend=1| 759, 7797 }} |
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| == Lamina == | | == Rutherfordium == |
| 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]].
| | Rutherfordium is described as the 624 & 4472 temperament in the 23-limit. |
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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.
| | == Seaborgium == |
| | Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely. |
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| === Grand lamina === | | == Kells == |
| 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.
| | 436 & 981 temperament. |
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| == Triskaififths == | | == Meitnerium == |
| 89 & 289, 11-limit.
| | 981 & 3706 temperament. |
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| Gen = 33/32,
| | == Copernicium == |
| | Named after the 112th element. |
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| == Tritonopod == | | 1904 & 3920 temperament. |
| ''Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.''
| | == Tenessine == |
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| ''Possibly rank-3?''
| | Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma. |
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| == Playing cards == | | == Unpentennium == |
| ''Work in progress''
| | Described as the 795 & 3498 temperament and splits the octave into 159. |