User:Eliora/Proposed concept names: Difference between revisions

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== Berkelium ==
== Anemoian (name later to be changed) ==
A remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings. Since it was conceived in this specific subgroup, it makes no sense to name it for smaller subgroups.
384p & 324p, 11-limit.


Subgroup: 2.3.5.13.17.23.29.31
[[Subgroup]]: 2.3.5.7.11


Comma list: 10881/10880, 13312/13311, 86411/86400, 96876/96875, 4784000/4782969, 223171875/223135744
[[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325


Sval mapping: [{{val|97 97 55 -95 283 609 301 821}}, {{val|0 1 3 8 2 -3 3 -6}}]
[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}
: Mapping generators: ~1375/1296, ~243/200


Sval mapping generators: ~6075/6032, ~3/2
[[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 tuning (CTE): ~3/2 = 701.9...
{{Optimal ET sequence|legend=1| 60, 444, 384 }}


Vals: 388, 2619, 3395...
[[Badness]] (Sintel): 21.211


=== Berkelium-248 ===
== Luminance (tuning) ==
The temperament with higher TE error of the two branchings, therefore named after the second most stable berkelium isotope.
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


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.


Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
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 ==


Mapping generators: ~144/143, ~3/2
1125 & 2460, 23-limit.


Optimal tuning (CTE): ~3/2 = 701.945
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 ==


EDOs: 388, 2619, ...
Described as the 1178 & 7334 temperament in the 19-limit.


=== Berkelium-247 ===
== Cadmium ==
The temperament with lower TE error of the two branchings, therefore named after the most stable berkelium isotope.
Described as the 624 & 4320 temperament upwards to the 23-limit.


Subgroup: 2.3.5.7
In the 23-limit, the gen is mapped to [[70/69]].


Comma list: 12824703626379264/12822723388671875, {{monzo|56 -57 16 -1}}
== 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: [{{val|97 97 55 783}}, {{val|0 1 3 -9}}]
 
Mapping generators: ~13839047287569/13743895347200 = 1\97, ~3/2 = 701.973


Optimal tuning (CTE):~ 3/2 = 701.973
==== 11-limit ====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 21437500/21434787, 44660948992/44659644435, 1573159698432/1572763671875
Comma list: 781258401/781250000, 110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245
 
Mapping: [{{val|97 97 55 783 903}}, {{val|0 1 3 -9 -10}}]
 
Mapping generators: ~4125/4096 = 1\97, ~3/2 = 701.976
 
Optimal tuning (CTE):~ 3/2 = 701.976
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 1990656/1990625, 1146880/1146717, 492128/492075, 2662250409/2662000000
 
Mapping: [{{val|97 97 55 783 903 -95}}, {{val|0 1 3 -9 -10 8}}]
 
Mapping generators: ~16038/15925, ~3/2
 
Optimal tuning (CTE): ~3/2 = 701.976
 
==== 17-limit ====
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 12376/12375, 37180/37179, 1990656/1990625, 1146880/1146717, 263299491/263296000
 
Mapping: [{{val|97 97 55 783 903 -95 283}}, {{val|0 1 3 -9 -10 8 2}}]
 
Mapping generators: ~1547/1536, ~3/2
 
Optimal tuning (CTE): ~3/2 = 701.976


==== 19-limit ====
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Subgroup: 2.3.5.7.11.13
Mapping generators: ~100/99, ~3


Comma list: 12376/12375, 13377/13376, 14080/14079, 27456/27455, 37180/37179, 165376/165375, 722007/722000
{{Optimal ET sequence|legend=1| 759, 7797 }}


Mapping: [{{val|97 97 55 783 903 -95 283}}, {{val|0 1 3 -9 -10 8 2}}]
== Rutherfordium ==
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.


Mapping generators: ~16038/15925, ~3/2
== Seaborgium ==
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


Optimal tuning (CTE): ~3/2 = 701.976
== Kells ==
436 & 981 temperament.


== Point Zero Seven ==
== Meitnerium ==
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.
981 & 3706 temperament.


Subgroup: 2.3.5.7
== Copernicium ==
Named after the 112th element.


Comma list: 81/80, 121500/117649
1904 & 3920 temperament.
== Tenessine ==


Mapping: [1 2 4 4], [0 -6 -24 -17]
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.


Optimal tuning (CTE): ~21/20 = 83.888
== Unpentennium ==
 
Described as the 795 & 3498 temperament and splits the octave into 159.
Vals: 14, 43, 100
 
== 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]].
 
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.
 
=== Grand lamina ===
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.
 
== Tritonopod ==
''Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.''
 
''Possibly rank-3?''
 
== Playing cards ==
''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.
 
== 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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