User:Eliora/Proposed concept names: Difference between revisions

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== 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


== Nitrogen ==
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.
Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7. And if that wasn't good enough, it also reaches 7th harmonic 7 generators down.


Subgroup: 2.3.5.7
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 ==


Comma list: 3955078125/3954653486, 140737488355328/140710042265625
1125 & 2460, 23-limit.


Mapping: 7 10 17 20, 0 22 -15 -7
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 ==


Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531
Described as the 1178 & 7334 temperament in the 19-limit.


Vals: 140, 1407, 1547, ...
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


== Dzelic ==
In the 23-limit, the gen is mapped to [[70/69]].
Named after the Slavic letter for 7, because it takes 7 generators to reach 3/2, and the period is 1/37th of the octave. Described as the 296 & 1665 temperament.


== Berkelium ==
== Thulium ==
A remarkable high-limit subgroup temperament with equally remarkable full 31-limit branchings.
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: 2.3.5.13.17.23.29.31
 
Comma list: 10881/10880, 13312/13311, 86411/86400, 96876/96875, 4784000/4782969, 223171875/223135744
 
Sval mapping: 97 97 55 -95 283 609 301 821, 0 1 3 8 2 -3 3 -6
 
Sval mapping generators: ~6075/6032, ~3/2
 
Optimal tuning (CTE): ~3/2 = 701.9...


Vals: 388, 2619, 3395...
Subgroup: 2.3.5.7.11


=== Variety 1: 388 & 2619 ===
Comma list: 781258401/781250000,  110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245
Subgroup: 2.3.5.7.11.13


Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Mapping generators: ~144/143, ~3/2
Mapping generators: ~100/99, ~3


Optimal tuning (CTE): ~3/2 = 701.945
{{Optimal ET sequence|legend=1| 759, 7797 }}


EDOs: 388, 2619, ...
== Rutherfordium ==
Rutherfordium is described as the 624 & 4472 temperament in the 23-limit.


=== Variety 2: 388 & 3395 ===
== Seaborgium ==
Subgroup: 2.3.5.7.11.13
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


Comma list: 1990656/1990625, 1146880/1146717, 492128/492075, 2662250409/2662000000
== Kells ==
436 & 981 temperament.


Mapping generators: ~16038/15925, ~3/2
== Meitnerium ==
981 & 3706 temperament.


Optimal tuning (CTE): ~3/2 = 701.9...
== Copernicium ==
Named after the 112th element.


EDOs: 388, 3395, ...
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
 
== 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

Revision as of 00:01, 17 March 2024

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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