User:FloraC/Temperament name proposal: Difference between revisions

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Ideas welcome!  
Ideas welcome!  
[[User:Xenllium #Rank two temperaments which this user proposed names]] needs to be treated seriously someday.


=  22 & 46 & 72 =
=  22 & 46 & 72 =
An 11-limit rank-3 temperament. Announced in FB group. To be called "quasiquarter".  
An 11-limit rank-3 temperament. Announced in FB group. <s>To be called "quasiquarter"</s> I don't like this name.  


It tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, [[385/384]], the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit.  
It tempers out 1500625/1492992 = {{monzo| -11 -6 4 4 }} in the 7-limit, and the keenanisma, [[385/384]], the kalisma, [[9801/9800]], as well as the [[Alpharabian comma]], 131769/131072 = {{monzo| -17 2 0 0 4 }}, in the 11-limit.  
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== 7-limit ==
== 7-limit ==


Comma: 1500625/1492992
[[Comma list]]: 1500625/1492992


Map: [<2 1 0 7|, <0 2 0 3|, <0 0 1 -1|]
[[Mapping]]: [<2 1 0 7|, <0 2 0 3|, <0 0 1 -1|]


Mapping generators: ~1225/864, ~35/24, ~5
Mapping generators: ~1225/864, ~35/24, ~5


Wedgie: <<< 4 -4 -6 11 |||
{{Multival|legend=1|rank=3| 4 -4 -6 11 }}


POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326
[[POTE generator]]s: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326


EDOs: {{EDOs| 22, 46, 68, 72, 118, 140, 212, 330, 470 }}
{{Val list|legend=1| 22, 46, 68, 72, 118, 140, 212, 330, 470 }}


Badness: 0.7042 × 10<sup>-3</sup>
[[Badness]]: 0.7042 × 10<sup>-3</sup>


== 11-limit ==
== 11-limit ==


Commas: 385/384, 9801/9800
Comma list: 385/384, 9801/9800


Map: [<2 1 0 7 8|, <0 2 0 3 -1|, <0 0 1 -1 0|]
Mapping: [<2 1 0 7 8|, <0 2 0 3 -1|, <0 0 1 -1 0|]


Mapping generators: ~99/70, ~16/11, ~5
Mapping generators: ~99/70, ~16/11, ~5
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POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315
POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315


EDOs: {{EDOs| 22, 46, 68, 72, 118, 190, 212, 284, 330e }}
Vals: {{val list| 22, 46, 68, 72, 118, 190, 212, 284, 330e }}


Badness: 0.5292 × 10<sup>-3</sup>
Badness: 0.5292 × 10<sup>-3</sup>
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An unnamed 13-limit rank-3 temperament.  
An unnamed 13-limit rank-3 temperament.  


Commas: 352/351, 847/845, 14641/14580
[[Comma list]]: 352/351, 847/845, 14641/14580


Map: [<1 0 2 12 1 6|, <0 1 2 -4 2 -1|, <0 0 4 4 1 1|]
[[Mapping]]: [<1 0 2 12 1 6|, <0 1 2 -4 2 -1|, <0 0 4 4 1 1|]


EDOs: 7, 17c, 24d, 87, 111, 181, 198
{{Val list|legend=1| 7, 17c, 24d, 87, 111, 181, 198 }}


Badness: 0.0540 × 10<sup>-3</sup>
[[Badness]]: 0.0540 × 10<sup>-3</sup>


= 41 & 46 & 53 & 58 =
= 41 & 46 & 53 & 58 =
An unnamed 13-limit rank-4 temperament.  
An unnamed 13-limit rank-4 temperament.  


Commas: 352/351, 847/845
[[Comma list]]: 352/351, 847/845


Map: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]
[[Mapping]]: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]


Wedgie: <<<<0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0||||
{{Multival|legend=1|rank=4| 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 }}


POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538
POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538


EDOs: 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198
{{Val list|legend=1| 12f, 17c, 29, 41, 46, 53, 58, 87, 111, 140, 198 }}


Badness: 2.550 × 10<sup>-6</sup>
[[Badness]]: 2.550 × 10<sup>-6</sup>

Revision as of 08:02, 28 April 2021

Ideas welcome!

22 & 46 & 72

An 11-limit rank-3 temperament. Announced in FB group. To be called "quasiquarter" I don't like this name.

It tempers out 1500625/1492992 = [-11 -6 4 4⟩ in the 7-limit, and the keenanisma, 385/384, the kalisma, 9801/9800, as well as the Alpharabian comma, 131769/131072 = [-17 2 0 0 4⟩, in the 11-limit.

It features splitting the whole tone into four equal parts, each representing 36/35~33/32. Therefore, it is most valuable for those who would like to make extensive use of quartertones.

It can be viewed as one which is joined by the three quartertone-sized edos: 22edo, 24edo, and 26edo. It shares the optimal patent val, 284edo with keenanismic.

7-limit

Comma list: 1500625/1492992

Mapping: [<2 1 0 7|, <0 2 0 3|, <0 0 1 -1|]

Mapping generators: ~1225/864, ~35/24, ~5

Wedgie: ⟨⟨⟨ 4 -4 -6 11 ]]]

POTE generators: ~36/35 = 50.9529 or ~48/35 = 549.0471, ~5/4 = 385.3326

Template:Val list

Badness: 0.7042 × 10-3

11-limit

Comma list: 385/384, 9801/9800

Mapping: [<2 1 0 7 8|, <0 2 0 3 -1|, <0 0 1 -1 0|]

Mapping generators: ~99/70, ~16/11, ~5

POTE generators: ~33/32 = 50.7404 or ~11/8 = 549.2596, ~5/4 = 385.0315

Vals: Template:Val list

Badness: 0.5292 × 10-3

87 & 94 & 111

An unnamed 13-limit rank-3 temperament.

Comma list: 352/351, 847/845, 14641/14580

Mapping: [<1 0 2 12 1 6|, <0 1 2 -4 2 -1|, <0 0 4 4 1 1|]

Template:Val list

Badness: 0.0540 × 10-3

41 & 46 & 53 & 58

An unnamed 13-limit rank-4 temperament.

Comma list: 352/351, 847/845

Mapping: [<1 0 0 10 0 5|, <0 1 0 -6 0 -3|, <0 0 1 1 0 0|, <0 0 0 0 1 1|]

Wedgie: ⟨⟨⟨⟨ 0 1 1 1 1 0 6 6 -3 -3 10 10 -5 -5 0 ]]]]

POTE generators: ~3/2 = 702.9075, ~5/4 = 387.0723, ~11/8 = 551.4538

Template:Val list

Badness: 2.550 × 10-6

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