User:Eliora/Proposed concept names: Difference between revisions

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== Prequartismic ==
== Anemoian (name later to be changed) ==
Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259 & 3125 temperament.
384p & 324p, 11-limit.


== Mercury ==
[[Subgroup]]: 2.3.5.7.11
Defined as 720 & 1600, and named after the 80th element.


Subgroup: 2.3.5
[[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325


Comma list: {{monzo|-1377 400 320}}
[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}
: Mapping generators: ~1375/1296, ~243/200


Mapping: [{{val|80 1 343}}, {{val|0 4 -5}}]
[[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 }}


Mapping generators: {{monzo|-568 165 132}}, {{monzo|142 -41 -33}}
{{Optimal ET sequence|legend=1| 60, 444, 384 }}


Optimal tuning (CTE): ~{{monzo|142 -41 -33}} = 471.738
[[Badness]] (Sintel): 21.211


=== 7-limit ===
== Luminance (tuning) ==
Subgroup: 2.3.5.7
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


Comma list: 31528360107421875/31525197391593472, 3671492030322070514237964288/3666984506893654025644140625
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:[{{val| 80 1 343 -27}}, {{val|0 4 -5 8}}]
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: ~31637227888/31381059609, ~7381125/5619712
1125 & 2460, 23-limit.


Optimal tuning (CTE): ~7381125/5619712 = 471.734
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


=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 9801/9800, 928760463360/928426965851, 68116944363978752/68116827392578125
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 }}


Mapping:[{{val|80 1 343 -27 434}}, {{val|0 4 -5 8 5}}]
== Rutherfordium ==
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.


Mapping generators: ~262144/259875, ~2278125/1734656
== Seaborgium ==
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


Optimal tuning (CTE): ~2278125/1734656 = 471.734
== Kells ==
436 & 981 temperament.


=== 13-limit ===
== Meitnerium ==
Subgroup: 2.3.5.7.11.13
981 & 3706 temperament.


Comma list: 9801/9800, 4100625/4100096, 14236560/14235529, 143327232/143286143
== Copernicium ==
Named after the 112th element.


Mapping: [{{val|80 1 343 -27 434 13}}, {{val|0 4 -5 8 5 9}}]
1904 & 3920 temperament.
== Tenessine ==


Mapping generators: ~77760/77077, ~130/99
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.


Optimal tuning (CTE): ~130/99 = 471.734
== 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

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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