User:Eliora/Proposed concept names: Difference between revisions

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== Anemoian (name later to be changed) ==

384p & 324p, 11-limit.

[[Subgroup]]: 2.3.5.7.11

~~== Phosphorus ==~~

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

~~1125 & 2460~~, ~~23-limit.~~

[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}

: Mapping generators: ~1375/1296, ~243/200

~~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~~.

[[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 }}

=~~= Gold ==~~

~~Described as a 1106 & 1817 temperament, and with an extension for the 2.3.5.7.11.13.17.37 subgroup which sets~~ [[~~39/37~~]] ~~to 6 steps of 79edo~~.

[[Badness]] (Sintel): 21.211

== ~~Polonium~~ ==

== Luminance (tuning) ==

~~Polonium is described as the 1848 & 14196 tmeperament~~. ~~It tempers out the 11~~-~~limit comma which sets 43\84~~ to ~~[[77/54]].~~

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

~~http://x31eq~~.~~com/cgi-bin/rt~~.~~cgi?ets=1848_14196&limit=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.

== ~~Point Zero Seven~~ ==

Increasingly larger luminance values: {{EDOs|2, 3, 5, 7, 10, 12, 22, 24, 31, 41, 53, 87, ...}}

~~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~~.

== 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 ==

~~Subgroup: 2~~.~~3.5.7~~

1125 & 2460, 23-limit.

~~Comma list: 81/80~~, ~~121500/117649~~

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 ==

~~Mapping: [1 2 4 4], [0~~ -~~6 -24 -17]~~

Described as the 1178 & 7334 temperament in the 19-limit.

~~Optimal tuning (CTE): ~21/20~~ = 83.~~888~~

== Cadmium ==

Described as the 624 & 4320 temperament upwards to the 23-limit.

~~{{Optimal ET sequence|legend=1| 14~~, ~~43, 100 }}~~

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

~~== Playing cards ==~~

~~''Work in progress''~~

== 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

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== 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.

@@ Line 1: / Line 1: @@
+== Anemoian (name later to be changed) ==
+p & 324p, 11-limit.
+[[Subgroup]]: 2.3.5.7.11
-== Phosphorus ==
+[[Comma list]]: 26411/26244, 250047/250000, 2097152/2096325
-& 2460, 23-limit.
+[[Mapping]]: {{mapping| 13 0 92 -355 | 0 5 12 14 -16 }}
+: Mapping generators: ~1375/1296, ~243/200
-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.
+[[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 }}
-== Gold ==
+{{Optimal ET sequence|legend=1| 60, 444, 384 }}
-Described as a 1106 & 1817 temperament, and with an extension for the 2.3.5.7.11.13.17.37 subgroup which sets [[39/37]] to 6 steps of 79edo.
+[[Badness]] (Sintel): 21.211
-== Polonium ==
+== Luminance (tuning) ==
-Polonium is described as the 1848 & 14196 tmeperament. It tempers out the 11-limit comma which sets 43\84 to [[77/54]].
+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
-http://x31eq.com/cgi-bin/rt.cgi?ets=1848_14196&limit=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.
-== Point Zero Seven ==
+Increasingly larger luminance values: {{EDOs|2, 3, 5, 7, 10, 12, 22, 24, 31, 41, 53, 87, ...}}
-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.
+== 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 ==
-Subgroup: 2.3.5.7
+& 2460, 23-limit.
-Comma list: 81/80, 121500/117649
+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 ==
-Mapping: [1 2 4 4], [0 -6 -24 -17]
+Described as the 1178 & 7334 temperament in the 19-limit.
-Optimal tuning (CTE): ~21/20 = 83.888
+== Cadmium ==
+Described as the 624 & 4320 temperament upwards to the 23-limit.
-{{Optimal ET sequence|legend=1| 14, 43, 100 }}
+In the 23-limit, the gen is mapped to [[70/69]].
-== Playing cards ==
-''Work in progress''
 == 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
@@ Line 43: / Line 53: @@
 {{Optimal ET sequence|legend=1| 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 ==
+& 981 temperament.
+== Meitnerium ==
+& 3706 temperament.
+== Copernicium ==
+Named after the 112th element.
+& 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.