User:Eliora/Proposed concept names: Difference between revisions

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== Pseudovishnuzma ==
== Luminance (tuning) ==
Comma: 6106906624/6103515625
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


Name reasoning: The denominator is the same as for vishnuzma, numerator is close, yet it's different.  
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.


Temperaments:
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 ==


Rank 2: 1261 & 1789 (2.5.7.11.13), 1236 & 764, 1236 & 1084, 1236 & 441, 764 & 1084, 1236 & 87
1125 & 2460, 23-limit.


== Thulium ==
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.
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.
== Strontium ==


== Nuclear matter ==
Described as the 1178 & 7334 temperament in the 19-limit.
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
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


Comma list: [-41, 1, 17⟩
In the 23-limit, the gen is mapped to [[70/69]].


Optimal tuning (CTE): ~5/4
== 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
Vals: 22, 69
 
== Berkelium (two varieties) ==
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.
 
=== Variety 1: 388 & 2619 ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
 
Mapping generators: ~144/143, ~3/2
 
Optimal tuning (CTE): ~3/2 = 701.945
 
EDOs: 388, 2619, ...
 
=== Variety 2: 388 & 3395 ===
...
 
== Point Zero Seven ==
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
 
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
 
== 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
Subgroup: 2.3.5.7.11


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


Sval maping generators: ~25/24, ~1024/975
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Optimal tuning (CTE): ~1024/975 = ...
Mapping generators: ~100/99, ~3


=== 2.3.5.7.13.17 subgroup ===
{{Optimal ET sequence|legend=1| 759, 7797 }}
9 periods and 2 generators correspond to 17/13.


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


Comma list: 57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000
== Seaborgium ==
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


Sval mapping: 17 10 31 9 98 107, 0 14 7 32 -29 -31
== Kells ==
436 & 981 temperament.


Sval mapping generators: ~25/24, ~765/728
== Meitnerium ==
981 & 3706 temperament.


Optimal tuning (CTE): ~765/728 = 85.424
== Copernicium ==
Named after the 112th element.


== Tritonopod ==
1904 & 3920 temperament.
''Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.''
== Tenessine ==


''Possibly rank-3?''
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.


== Playing cards ==
== Unpentennium ==
''Work in progress''
Described as the 795 & 3498 temperament and splits the octave into 159.

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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