User:Eliora/Proposed concept names: Difference between revisions

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== ~~Prequartismic~~ ==

== Luminance (tuning) ==

~~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 1259e & 3125 temperament, but in terms of patent vals it can also be described as 3125 & 4991 or 3125 & 1866~~.

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

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.

~~Comma list: [24, -6, 0, 1,~~ -5⟩, [~~-1, 4, 11, -11, 0⟩,~~ [~~-19 -25 14 13 -3⟩~~

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

~~Mapping~~: ~~to be filled in~~

== 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

~~Optimal tuning (CTE)~~: ~~~64/33 = 1146~~.~~624~~

Subgroup: 2.3.5.7.11

~~Vals~~: ~~1259e~~, ~~1866~~, ~~3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de~~

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

~~=== 13~~-~~limit ===~~

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

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list~~: ~~1990656~~/~~1990625~~, ~~14236560/14235529, 117440512/117406179, 1181640625/1181599328~~

Mapping generators: ~100/99, ~3

~~Mapping: to be filled in~~

~~Optimal tuning (CTE): ~64/33~~ = ~~1146~~.~~624~~

== Rutherfordium ==

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

== ~~Moulin~~ ==

== Seaborgium ==

~~It's bright generator is 22/13~~, ~~and it is named after a Law~~ & ~~Order: Special Victims Unit episode Season 22, Episode 13. Trick~~-~~Rolled At The Moulin. Defined as the 494 & 1619 temperament~~, ~~which~~ are ~~both highly precise 13-limit EDOs~~.

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

~~[[Subgroup]]: 2~~.~~3.5.7.11.13~~

== Kells ==

436 & 981 temperament.

~~[[Comma list]]: 4225/4224, 4375/4374, 6656/6655, 91125/91091~~

== Meitnerium ==

981 & 3706 temperament.

~~[[Mapping]]: [{{val|1 57 38 248 -14 -13}}, {{val|0 -73 -47 -323 23 22}}]~~

== Copernicium ==

Named after the 112th element.

~~[[Optimal tuning]] ([[CTE]]): ~22/13~~ = ~~910.932~~

1904 & 3920 temperament.

== Tenessine ==

~~Vals: {{EDOs|137d~~, ~~357d, 494, 631, 851d, 1125, 1482d, 1619, 2113}}~~

Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.

== ~~1619edo test~~ ==

== Unpentennium ==

~~{{Primes in edo|1619|columns=22}}~~

Described as the 795 & 3498 temperament and splits the octave into 159.

@@ Line 1: / Line 1: @@
-== Prequartismic ==
+== Luminance (tuning) ==
-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 1259e & 3125 temperament, but in terms of patent vals it can also be described as 3125 & 4991 or 3125 & 1866.
+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
+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 ==
+& 2460, 23-limit.
+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.
-Comma list: [24, -6, 0, 1, -5⟩, [-1, 4, 11, -11, 0⟩, [-19 -25 14  13 -3⟩
+In the 23-limit, the gen is mapped to [[70/69]].
-Mapping: to be filled in
+== 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
-Optimal tuning (CTE): ~64/33 = 1146.624
+Subgroup: 2.3.5.7.11
-Vals: 1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de
+Comma list: 781258401/781250000,  110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245
-=== 13-limit ===
+Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]
-Subgroup: 2.3.5.7.11.13
-Comma list: 1990656/1990625, 14236560/14235529, 117440512/117406179, 1181640625/1181599328
+Mapping generators: ~100/99, ~3
-Mapping:  to be filled in
+{{Optimal ET sequence|legend=1| 759, 7797 }}
-Optimal tuning (CTE): ~64/33 = 1146.624
+== Rutherfordium ==
+Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.
-== Moulin ==
+== Seaborgium ==
-It's bright generator is 22/13, and it is named after a Law & Order: Special Victims Unit episode Season 22, Episode 13. Trick-Rolled At The Moulin. Defined as the 494 & 1619 temperament, which are both highly precise 13-limit EDOs.
+Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.
-[[Subgroup]]: 2.3.5.7.11.13
+== Kells ==
+& 981 temperament.
-[[Comma list]]: 4225/4224, 4375/4374, 6656/6655, 91125/91091
+== Meitnerium ==
+& 3706 temperament.
-[[Mapping]]: [{{val|1 57 38 248 -14 -13}}, {{val|0 -73 -47 -323 23 22}}]
+== Copernicium ==
+Named after the 112th element.
-[[Optimal tuning]] ([[CTE]]): ~22/13 = 910.932
+& 3920 temperament.
+== Tenessine ==
-Vals: {{EDOs|137d, 357d, 494, 631, 851d, 1125, 1482d, 1619, 2113}}
+Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.
-== 1619edo test ==
+== Unpentennium ==
-{{Primes in edo|1619|columns=22}}
+Described as the 795 & 3498 temperament and splits the octave into 159.