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| == Major Arcana comma == | | == Anemoian (name later to be changed) == |
| 5-limit comma {{Monzo|-193 154 -22}}.
| | 384p & 324p, 11-limit. |
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| == Sekaceauikuk-tritrizo equivalence continuum ==
| | [[Subgroup]]: 2.3.5.7.11 |
| All temperaments are 2.3.7 and satisfy 4760622968832/4747561509943^n ~ 40353607/40310784
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| The just value of n = 2.587611611349098
| | [[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325 |
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| If n = 1: 36 & 400
| | [[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }} |
| | : Mapping generators: ~1375/1296, ~243/200 |
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| if n = 2: 36 & 571
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~1375/1296 = 99.997{{c}}, ~243/200 = 340.539{{c}} |
| | : [[error map]]: {{val| -0.006 +0.038 -0.030 -0.013 }} |
| | * [[CWE]]: ~1375/1296 = 100{{c}}, ~243/200 = 340.549{{c}} |
| | : error map: {{val| 0.000, 0.788, 0.269, -1.146, -0.095 }} |
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| If n = 3: 36 & 706
| | {{Optimal ET sequence|legend=1| 60, 444, 384 }} |
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| If n = 4: 36 & 877
| | [[Badness]] (Sintel): 21.211 |
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| ... | | == 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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| Fractional values of n closer to just:
| | 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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| If n = 2.5: 36 & 1277
| | 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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| == Pseudovishnuzma ==
| | 1125 & 2460, 23-limit. |
| Comma: 6106906624/6103515625
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| Name reasoning: The denominator is the same as for vishnuzma, numerator is close, yet it's different.
| | 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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| Temperaments:
| | Described as the 1178 & 7334 temperament in the 19-limit. |
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| Rank 2: 1261 & 1789 (2.5.7.11.13), 1236 & 764, 1236 & 1084, 1236 & 441, 764 & 1084, 1236 & 87
| | == Cadmium == |
| | Described as the 624 & 4320 temperament upwards to the 23-limit. |
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| == Major Arcana JI scale (detempering of 22edo) ==
| | In the 23-limit, the gen is mapped to [[70/69]]. |
| 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.
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| {| class="wikitable"
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| |+
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| !Step
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| !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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| |-
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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 == | | == Thulium == |
| 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.
| | 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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| == Hafnium ==
| | Subgroup: 2.3.5.7.11 |
| https://sintel.pythonanywhere.com/result?subgroup=17&reduce=on&tenney=on&target=&edos=4320+%26+5544&submit_edo=submit&commas=
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| Period-72 temperament.
| | Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245 |
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| === 17-limit ===
| | Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}] |
| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 9801/9800, 12376/12375, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736
| | Mapping generators: ~100/99, ~3 |
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| Mapping: 72 72 462 876 1302 1193 547, 0 1 -7 -16 -25 -22 -6
| | {{Optimal ET sequence|legend=1| 759, 7797 }} |
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| Mapping generators: ~105/104, ~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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| Vals: 1224, 4320, 5544
| | == Kells == |
| | 436 & 981 temperament. |
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| == Nuclear matter == | | == Meitnerium == |
| 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.
| | 981 & 3706 temperament. |
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| Subgroup: 2.3.5
| | == Copernicium == |
| | Named after the 112th element. |
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| Comma list: [-41, 1, 17⟩
| | 1904 & 3920 temperament. |
| | == Tenessine == |
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| Optimal tuning (CTE): ~5/4
| | Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma. |
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| Vals: 22, 69
| | == Unpentennium == |
| | | Described as the 795 & 3498 temperament and splits the octave into 159. |
| == Berkelium (two varieties) ==
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| 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.
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| === Variety 1: 388 & 2619 ===
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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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| === Variety 2: 388 & 3395 ===
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| ...
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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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| == Triskaififths ==
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| 89 & 289, 11-limit.
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| Gen = 33/32,
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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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