User:Eliora/Proposed concept names: Difference between revisions

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== Aluminium ==
== Luminance (tuning) ==
Aluminium is a rank-2 temperament associated with the comma, which sets a stack of 13 [[135/128]]<nowiki/>s equal to the octave. Therfore the name for the 5-limit comma is logically ''alumina''.
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


Aluminium can be extended consistently as high as the 13-limit, which is a nice coincidence.
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.


Subgroup: 2.3.5
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: [92 -39 -13]
1125 & 2460, 23-limit.


Mapping: [13 13 53], [0 1 -3]
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 generators: ~135/128, ~3/2
Described as the 1178 & 7334 temperament in the 19-limit.


Optimal tuning (CTE): ~3/2 = ...
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


Vals: 494, 1547, ...
In the 23-limit, the gen is mapped to [[70/69]].
 
== Sekaceauikuk-tritrizo equivalence continuum ==
All temperaments are 2.3.7 and satisfy 4760622968832/4747561509943^n ~ 40353607/40310784
 
The just value of n = 2.587611611349098
 
If n = 1: 36 & 400
 
if n = 2: 36 & 571
 
If n = 3: 36 & 706
 
If n = 4: 36 & 877
 
...
 
Fractional values of n closer to just:
 
If n = 2.5: 36 & 1277
 
== Pseudovishnuzma ==
Comma: 6106906624/6103515625
 
Name reasoning: The denominator is the same as for vishnuzma, numerator is close, yet it's different.
 
Temperaments:
 
Rank 2: 1261 & 1789 (2.5.7.11.13), 1236 & 764, 1236 & 1084, 1236 & 441, 764 & 1084, 1236 & 87
 
== Major Arcana JI scale (detempering of 22edo) ==
A Factor 9-Grid style detempering, where in the first octave which goes from A = 432 Hz to A = 864 Hz all frequency values are integers.
{| class="wikitable"
|+
!Step
!Card
!Frequency
!JI ratio
|-
|0
|The Fool
|432
|1/1
|-
|1
|
|448
|
|-
|2
|
|464
|
|-
|3
|
|486
|
|-
|4
|
|495
|
|-
|5
|
|504
|7/6
|-
|6
|
|513
|19/16
|-
|7
|
|540
|
|-
|8
|
|558
|
|-
|9
|
|576
|
|-
|10
|
|594
|
|-
|11
|
|612
|
|-
|12
|
|630
|
|-
|13
|
|648
|
|-
|14
|
|672
|
|-
|15
|
|696
|
|-
|16
|
|720
|
|-
|17
|
|744
|
|-
|18
|
|768
|
|-
|19
|
|792
|
|-
|20
|
|816
|
|-
|21
|
|840
|
|-
|22
|
|864
|2/1
|}


== Thulium ==
== 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.
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
 
== Nuclear matter ==
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
 
Comma list: [-41, 1, 17⟩
 
Optimal tuning (CTE): ~5/4
 
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 in the 17-limit. Originally intended to be no-11, Eliora later included the 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
 
=== 13-limit ===
10 generators map to 13/11.
 
Subgroup: 2.3.5.7.13
 
Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096
 
Sval mapping: 17 10 31 9 106 98, 0 14 7 32 -39 -29
 
Sval maping generators: ~25/24, ~1024/975
 
Optimal tuning (CTE): ~1024/975 = ...
 
=== 17-limit ===
2 generators correspond to 17/13.


Subgroup:
Subgroup: 2.3.5.7.11


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


Sval mapping: 17 10 31 9 106 98 107, 0 14 7 32 -39 -29 -31
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Sval mapping generators: ~25/24, ~765/728
Mapping generators: ~100/99, ~3


Optimal tuning (CTE): ~765/728 = 85.424
{{Optimal ET sequence|legend=1| 759, 7797 }}


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


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


=== Grand lamina ===
== Kells ==
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.
436 & 981 temperament.


== Triskaififths ==
== Meitnerium ==
89 & 289, 11-limit.
981 & 3706 temperament.


Gen = 33/32,
== 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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