User:Eliora/Proposed concept names: Difference between revisions
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== | == Anemoian (name later to be changed) == | ||
384p & 324p, 11-limit. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: | [[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325 | ||
Mapping: | [[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }} | ||
: Mapping generators: ~1375/1296, ~243/200 | |||
Optimal tuning | [[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 }} | |||
= | {{Optimal ET sequence|legend=1| 60, 444, 384 }} | ||
[[Badness]] (Sintel): 21.211 | |||
== 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 | |||
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. | |||
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 == | |||
1125 & 2460, 23-limit. | |||
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 == | |||
Described as the 1178 & 7334 temperament in the 19-limit. | |||
== | == Cadmium == | ||
Described as the 624 & 4320 temperament upwards to the 23-limit. | |||
In the 23-limit, the gen is mapped to [[70/69]]. | |||
== 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 | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245 | |||
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}] | |||
Mapping generators: ~100/99, ~3 | |||
{{Optimal ET sequence|legend=1| 759, 7797 }} | |||
== Rutherfordium == | |||
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit. | |||
== Seaborgium == | |||
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely. | |||
== Kells == | |||
436 & 981 temperament. | |||
== | == Meitnerium == | ||
981 & 3706 temperament. | |||
== Copernicium == | |||
Named after the 112th element. | |||
1904 & 3920 temperament. | |||
== Tenessine == | |||
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma. | |||
== Unpentennium == | |||
Described as the 795 & 3498 temperament and splits the octave into 159. | |||
Latest revision as of 06:59, 10 June 2026
Anemoian (name later to be changed)
384p & 324p, 11-limit.
Subgroup: 2.3.5.7.11
Comma list: 26411/26244, 250047/250000, 2097152/2096325
Mapping: [⟨13 0 92 -355], ⟨0 5 12 14 -16]]
- Mapping generators: ~1375/1296, ~243/200
- WE: ~1375/1296 = 99.997 ¢, ~243/200 = 340.539 ¢
- error map: ⟨-0.006 +0.038 -0.030 -0.013]
- CWE: ~1375/1296 = 100 ¢, ~243/200 = 340.549 ¢
- error map: ⟨0.000, 0.788, 0.269, -1.146, -0.095]
Optimal ET sequence: 60, 444, 384
Badness (Sintel): 21.211
Luminance (tuning)
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.
Increasingly larger luminance values: 2, 3, 5, 7, 10, 12, 22, 24, 31, 41, 53, 87, ...
Natrium
The natrium tempers out the [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
1125 & 2460, 23-limit.
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
Described as the 1178 & 7334 temperament in the 19-limit.
Cadmium
Described as the 624 & 4320 temperament upwards to the 23-limit.
In the 23-limit, the gen is mapped to 70/69.
Thulium
Subgroup: 2.3.5.7.11
Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245
Mapping: [⟨69 0 4316 -2431 8769], ⟨0 1 -38 24 -78]]
Mapping generators: ~100/99, ~3
Optimal ET sequence: 759, 7797
Rutherfordium
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.
Seaborgium
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.
Kells
436 & 981 temperament.
Meitnerium
981 & 3706 temperament.
Copernicium
Named after the 112th element.
1904 & 3920 temperament.
Tenessine
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.
Unpentennium
Described as the 795 & 3498 temperament and splits the octave into 159.