User:Eliora/Proposed concept names: Difference between revisions

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== Tritonopod ==
== Luminance (tuning) ==
1 generator is equal to 50/49, 17 generators are equal to 7/5, 18 generators are equal to 10/7. Named because these steps oppose the tonic and look like legs on a circular diagram, thus meaning that the spoke shape created by periods has "tritone legs". Defined as the 140 & 525 temperament.
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
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.


Comma list: 703125/702464, 68719476736/68641485507
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 ==


Mapping generators: ~50/49, ~262144/151263
1125 & 2460, 23-limit.


Vals: 140, 525, 665
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 ==


=== 11-limit ===
Described as the 1178 & 7334 temperament in the 19-limit.
Subgroup: 2.3.5.7.11


Comma list: 160083/160000, 180224/180075, 703125/702464
== Cadmium ==
Described as the 624 & 4320 temperament upwards to the 23-limit.


Mapping generators: ~50/49, ~400/231
In the 23-limit, the gen is mapped to [[70/69]].


Vals: ...
== 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


=== 13-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 4096/4095, 81675/81536, 40656/40625
 
Mapping generators: ~50/49, ~400/231
 
Vals: ...
 
== Chromium ==
Defined as the 72 & 624 temperament, and named after 24th element for being period 24.
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325
 
Mapping generators: ~250/243, ~10/7
 
Vals: 72, 552, 624, ...
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 936/935, 1716/1715, 2080/2079, 2500/2499, 11016/11011
 
Mapping generators: ~35/34, ~10/7
 
Vals: 72, 552, 624, ...


== Playing cards ==
Comma list: 781258401/781250000,  110341894140625/110336743047168, 3590222893590025814933504/3589489938459262943851245
It is the 31-limit temperament defined as 2860 & 3224 by tempering out the 2.29.31 [-5 -52 52] comma, which sets a stack of 52 31/29s equal to 5 octaves.


Since it is conceived in the 31-limit, it makes no sense to define it for smaller subgroups.
Mapping: [{{val|69 0 4316 -2431 8769}}, {{val|0 1 -38 24 -78}}]


Subgroup: 2.3.5.7.11.13.17.19.23.29.31
Mapping generators: ~100/99, ~3


Comma list: ...
{{Optimal ET sequence|legend=1| 759, 7797 }}


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


Optimal tuning (CTE): ~?
== Seaborgium ==
Named after the 106th element, most likely 2756 & 3498 in the 23-limit, but other options are likely.


== Binilnilium ==
== Kells ==
Named after the provisional name for the 200th element, tempers out the 200-comma ([-317 200>) and the ragisma (4375/4374).
436 & 981 temperament.


== Nuclear matter ==
== Meitnerium ==
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.
981 & 3706 temperament.


Subgroup: 2.3.5
== Copernicium ==
Named after the 112th element.


Comma list: [-41, 1, 17⟩
1904 & 3920 temperament.
== Tenessine ==


Optimal tuning (CTE): ~5/4
Described as the 234 & 1053 temperament, defined by tempering together the septimal ennealimma and the aluminium comma.


Vals: 22, 69
== Unpentennium ==
Described as the 795 & 3498 temperament and splits the octave into 159.

Latest 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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