User:Eliora/Proposed concept names: Difference between revisions

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== Anemoian (name later to be changed) ==
384p & 324p, 11-limit.


== Dzelic ==
[[Subgroup]]: 2.3.5.7.11
Named after the Slavic letter for 7, because it takes 7 generators to reach 3/2, and the period is 1/37th of the octave. Described as the 296 & 1665 temperament.


== Berkelium ==
[[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325
A remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings.


Subgroup: 2.3.5.13.17.23.29.31
[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}
: Mapping generators: ~1375/1296, ~243/200


Comma list: 10881/10880, 13312/13311, 86411/86400, 96876/96875, 4784000/4782969, 223171875/223135744
[[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 }}


Sval mapping: 97 97 55 -95 283 609 301 821, 0 1 3 8 2 -3 3 -6
{{Optimal ET sequence|legend=1| 60, 444, 384 }}


Sval mapping generators: ~6075/6032, ~3/2
[[Badness]] (Sintel): 21.211


Optimal tuning (CTE): ~3/2 = 701.9...
== 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


Vals: 388, 2619, 3395...
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.


=== Variety 1: 388 & 2619 ===
Increasingly larger luminance values: {{EDOs|2, 3, 5, 7, 10, 12, 22, 24, 31, 41, 53, 87, ...}}
Subgroup: 2.3.5.7.11.13
== 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 ==


Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
1125 & 2460, 23-limit.


Mapping generators: ~144/143, ~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 ==


Optimal tuning (CTE): ~3/2 = 701.945
Described as the 1178 & 7334 temperament in the 19-limit.


EDOs: 388, 2619, ...
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


=== Variety 2: 388 & 3395 ===
In the 23-limit, the gen is mapped to [[70/69]].
Subgroup: 2.3.5.7.11.13


Comma list: 1990656/1990625, 1146880/1146717, 492128/492075, 2662250409/2662000000
== 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
Mapping generators: ~16038/15925, ~3/2
 
Optimal tuning (CTE): ~3/2 = 701.9...
 
EDOs: 388, 3395, ...


== Point Zero Seven ==
Subgroup: 2.3.5.7.11
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.


Subgroup: 2.3.5.7
Comma list: 781258401/781250000,  110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245


Comma list: 81/80, 121500/117649
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Mapping: [1 2 4 4], [0 -6 -24 -17]
Mapping generators: ~100/99, ~3


Optimal tuning (CTE): ~21/20 = 83.888
{{Optimal ET sequence|legend=1| 759, 7797 }}


Vals: 14, 43, 100
== Rutherfordium ==
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.


== Lamina ==
== Seaborgium ==
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]].  
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


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.
== Kells ==
436 & 981 temperament.


=== Grand lamina ===
== Meitnerium ==
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.
981 & 3706 temperament.


== Tritonopod ==
== Copernicium ==
''Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.''
Named after the 112th element.


''Possibly rank-3?''
1904 & 3920 temperament.
== Tenessine ==


== Playing cards ==
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.
''Work in progress''
== Titanium II ==
https://sintel.pythonanywhere.com/result?subgroup=13&reduce=on&tenney=on&target=&edos=198+%26+1012&submit_edo=submit&commas=


198 & 1012 temperament.
== Unpentennium ==
 
Described as the 795 & 3498 temperament and splits the octave into 159.
== 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

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

Optimal tunings:

  • 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)

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: 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

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: [⟨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.

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