User:Eliora/Proposed concept names: Difference between revisions

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== Minutes ==
== Anemoian (name later to be changed) ==
Defined as the 2460 & 4320 temperament, and named "minutes" for period-60, since there's 60 minutes in an hour. In the limits below 13, it's a contorted atomic temperament.
384p & 324p, 11-limit.


Subgroup: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11


Comma list: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125
[[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325


Mapping: 60 60 385 730 1085 573, 0 1 7 -16 -25 -10
[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}
: Mapping generators: ~1375/1296, ~243/200


Mapping generators: ~2704/2673, ~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 = 701.948
{{Optimal ET sequence|legend=1| 60, 444, 384 }}


=== 17-limit ===
[[Badness]] (Sintel): 21.211
Subgroup: 2.3.5.7.11.13.17


Comma list: 9801/9800, 12376/12375, 28561/28560, 250047/250000, 253755392/253746675
== 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


Mapping: 60 60 385 730 1085 573 877, 0 1 7 -16 -25 -10 -18
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.


Mapping generators: ~3520/3213, ~3/2
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 ==


Optimal tuning (CTE): ~3/2 = 701.948
1125 & 2460, 23-limit.


=== 19-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.
Subgroup: 2.3.5.7.11.13.17.19
== Strontium ==


Comma list: ''to be filled in''
Described as the 1178 & 7334 temperament in the 19-limit.


Mapping: ''to be filled in''
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


Mapping generators: ~3520/3213, ~3/2
In the 23-limit, the gen is mapped to [[70/69]].


Optimal tuning (CTE): ~3/2 = 701.948
== 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


== Nuclear matter ==
Subgroup: 2.3.5.7.11
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.


Subgroup: 2.3.5
Comma list: 781258401/781250000,  110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245


Comma list: [-41, 1, 17⟩
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Optimal tuning (CTE): ~5/4
Mapping generators: ~100/99, ~3


Vals: 22, 69
{{Optimal ET sequence|legend=1| 759, 7797 }}


== Berkelium ==
== Rutherfordium ==
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.
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.


Subgroup: 2.3.5.7.11.13
== Seaborgium ==
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
== Kells ==
436 & 981 temperament.


Mapping generators: ~144/143, ~3/2
== Meitnerium ==
981 & 3706 temperament.


Optimal tuning (CTE): ~3/2 = 701.945
== Copernicium ==
Named after the 112th element.


EDOs: 388, 2619, ...
1904 & 3920 temperament.
== Tenessine ==


== Point Zero Seven ==
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.
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
== Unpentennium ==
 
Described as the 795 & 3498 temperament and splits the octave into 159.
Comma list: 81/80, 121500/117649
 
Mapping: [1 2 4 4], [0 -6 -24 -17]
 
Optimal tuning (CTE): ~21/20 = 83.888
 
Vals: 14, 43, 100
 
== Mabon ==
Named after the celebration of the autumn equinox, and defined as the 11 & 62 temperament in the 2.9.7, since the 11/62 solar calendar leap rule representes the autumn equinox. Three below 600c generators amount to 16/9.
 
Subgroup: 2.9.7
 
Comma list: 44957696/43046721
 
Sval mapping: [1 1 -3], [0 3 8]
 
Optimal tuning (CTE): ~729/448 = 870.792
 
Vals: 11, 29, 40, 51, 62, ...
 
=== 11-limit ===
In the 11-limit, the 11th harmonic plus an octave is reached by stacking two 16/11.
 
Subgroup: 2.9.7.11
 
Comma list: 896/891, 1331/1296
 
Sval mapping: [1 1 -3 2], [0 3 8 2]
 
Optimal tuning (CTE): ~18/11
 
== Leaves ==
Defined as the 323 & 2023 temperament, and also as the no-11s temperament, because both 323edo and 2023edo have a bad 11th harmonic.
 
Subgroup: 2.3.5.7
 
Comma list: -21 11  10 -7, 31 28 -24 -7
 
Mapping: 17 10 31 9, 0 14 7 32
 
Mapping generators: ~25/24, ~6125/5832
 
Optimal tuning (CTE): ~6125/5832 = 85.427
 
Vals: 323, 1700, 2023
 
=== 2.3.5.7.13 subgroup ===
Subgroup: 2.3.5.7.13
 
Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096
 
Sval mapping:
 
Sval maping generators: ~25/24, ~1024/975
 
Optimal tuning (CTE): ~1024/975 = ...
 
=== 2.3.5.7.13.17 subgroup ===
9 periods and 2 generators correspond to 17/13.
 
Subgroup:
 
Comma list: 57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000
 
Sval mapping: 17 10 31 9 98 107, 0 14 7 32 -29 -31
 
Sval mapping generators: ~25/24, ~765/728
 
Optimal tuning (CTE): ~765/728 = 85.424
 
== 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''

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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