Xenharmonic Wiki

Gamelismic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
m →Miracle: cleanup
m →Rodan: cleanup
Line 246: Line 246:
= Rodan =
= Rodan =
{{main|Rodan}}
{{main|Rodan}}
[[Comma|Commas]]: 245/243, 1029/1024
[[Comma list]]: 245/243, 1029/1024


7+9 limit minimax tuning: [|1 0 0 0>, |5/3 0 1/6 -1/6>,
[[POTE generator]]: ~8/7 = 234.417
|25/9 0 17/18 -17/18&gt;, |25/9 0 -1/18 1/18&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 7/5
Mapping: [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1 }}]


[[POTE_tuning|POTE generator]]: ~8/7 = 234.417
[[Minimax tuning]]:
* 7- and 9-odd-limit:
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [[Eigenmonzo]]s: 2, 7/5


Algebraic generator: [[Algebraic_number|larger root]] of 20x^2-36x+15, or (9+√6)/10.
Algebraic generator: [[Algebraic number|larger root]] of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.


Map: [&lt;1 1 -1 3|, &lt;0 3 17 -1|]
{{Val list|legend=1| 5, 41, 87, 128, 215d }}
 
EDOs: {{EDOs|5, 41, 87, 128, 215d}}


Badness: 0.0371
Badness: 0.0371


== 11-limit ==
== 11-limit ==
[[Comma|Commas]]: 245/243, 385/384, 441/440
[[Comma list]]: 245/243, 385/384, 441/440


[[Minimax_tuning|Minimax tuning]]: [|1 0 0 0 0&gt;, |31/19 6/19 0 0 -3/19&gt;,
[[POTE generator]]: ~8/7 = 234.459
|49/19 34/19 0 0 -17/19&gt;, |53/19 -2/19 0 0 1/19&gt;,
|62/19 -26/19 0 0 13/19&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 11/9
Mapping: [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13 }}]


[[POTE_tuning|POTE generator]]: ~8/7 = 234.459
[[Minimax tuning]]:
* 11-odd-limit:
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: [[Eigenmonzo]]s: 2, 11/9


Algebraic generator: [[Algebraic_number|positive root]] of x^2+16x-31, or √95-8.
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.


Map: [&lt;1 1 -1 3 6|, &lt;0 3 17 -1 -13|]
{{Val list|legend=1| 5, 41, 46, 87 }}
 
EDOs: {{EDOs|5, 41, 46, 87}}


Badness: 0.0231
Badness: 0.0231


{{see also|Chords of rodan}}
{{see also| Chords of rodan }}


=== 13-limit ===
=== 13-limit ===
Commas: 196/195, 245/243, 352/351, 364/363
Comma list: 196/195, 245/243, 352/351, 364/363
 
13 and 15 limit minimax
 
[|1 0 0 0 0 0&gt;, |23/14 3/14 0 0 0 -3/28&gt;,
|37/14 17/14 0 0 0 -17/28&gt;, |39/14 -1/14 0 0 0 1/28&gt;,
|45/14 -13/14 0 0 0 13/28&gt;, |23/7 -11/7 0 0 0 11/14&gt;<nowiki>]</nowiki>
 
Eigenmonzos: 2, 13/9


[[POTE_tuning|POTE generator]]: ~8/7 = 234.482
[[POTE generator]]: ~8/7 = 234.482


Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.
Mapping: [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22 }}]


Map: [&lt;1 1 -1 3 6 8|, &lt;0 3 17 -1 -13 -22|]
Minimax tuning:
* 13- and 15-odd-limit:
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: Eigenmonzos: 2, 13/9


Generators: 2, 8/7
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.


EDOs: {{EDOs|41, 46, 87}}
{{Val list|legend=1| 41, 46, 87 }}


Badness: 0.0184
Badness: 0.0184


==== 17-limit ====
==== 17-limit ====
Commas: 154/153, 196/195, 245/243, 256/255, 273/272
Comma list: 154/153, 196/195, 245/243, 256/255, 273/272


Eigenmonzos: 2, 18/17
[[POTE generator]]: ~8/7 = 234.524


[[POTE_tuning|POTE generator]]: ~8/7 = 234.524
Mapping: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}]


Map: [&lt;1 1 -1 3 6 8 8|, &lt;0 3 17 -1 -13 -22 -20|]
Minimax tuning:  
* 17-odd-limit eigenmonzos: 2, 18/17


Edos: {{EDOs|41, 46, 87, 220dg, 307dgg}}
{{Val list|legend=1| 41, 46, 87, 220dg, 307dgg }}


Badness: 0.0167
Badness: 0.0167


=== Aerodactyl ===
=== Aerodactyl ===
Commas: 91/90, 245/243, 385/384, 441/440
Comma list: 91/90, 245/243, 385/384, 441/440


[[POTE_tuning|POTE generator]]: ~8/7 = 234.639
[[POTE generator]]: ~8/7 = 234.639


Map: [&lt;1 1 -1 3 6 -1|, &lt;0 3 17 -1 -13 24|
Mapping: [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24 }}]


EDOs: {{EDOs|5, 41f, 46, 51c}}
{{Val list|legend=1| 5, 41f, 46, 51c }}


Badness: 0.0340
Badness: 0.0340


== Aerodino ==
== Aerodino ==
Commas: 176/175, 245/243, 1029/1024
Comma list: 176/175, 245/243, 1029/1024


POTE generator: ~8/7 = 234.728
POTE generator: ~8/7 = 234.728


Map: [&lt;1 1 -1 3 -3|, &lt;0 3 17 -1 33|
Mapping: [{{val| 1 1 -1 3 -3 }}, {{val| 0 3 17 -1 33 }}]


EDOS: {{EDOs|5e, 41e, 46}}
{{Val list|legend=1| 5e, 41e, 46 }}


Badness: 0.0543
Badness: 0.0543


=== 13-limit ===
=== 13-limit ===
Commas: 91/90, 176/175, 245/243, 847/845
Comma list: 91/90, 176/175, 245/243, 847/845


POTE generator: ~8/7 = 234.782
POTE generator: ~8/7 = 234.782


Map: [&lt;1 1 -1 3 -3 -1|, &lt;0 3 17 -1 33 24|
Mapping: [{{val| 1 1 -1 3 -3 -1 }}, {{val| 0 3 17 -1 33 24 }}]


EDOs: {{EDOs|5e, 46}}
{{Val list|legend=1| 5e, 46 }}


Badness: 0.0358
Badness: 0.0358


== Varan ==
== Varan ==
Commas: 100/99, 245/243, 1029/1024
Comma list: 100/99, 245/243, 1029/1024


POTE generator: ~8/7 = 234.145
POTE generator: ~8/7 = 234.145


Map: [&lt;1 1 -1 3 -2|, &lt;0 3 17 -1 28|
Mapping: [{{val| 1 1 -1 3 -2 }}, {{val| 0 3 17 -1 28 }}]


EDOs: {{EDOs|5e, 41, 46e}}
{{Val list|legend=1| 5e, 41, 46e }}


Badness: 0.0449
Badness: 0.0449


=== 13-limit ===
=== 13-limit ===
Commas: 100/99, 105/104, 245/243, 352/351
Comma list: 100/99, 105/104, 245/243, 352/351


POTE generator: ~8/7 = 234.089
POTE generator: ~8/7 = 234.089


Map: [&lt;1 1 -1 3 -2 0|, &lt;0 3 17 -1 28 19|
Mapping: [{{val| 1 1 -1 3 -2 0 }}, {{val| 0 3 17 -1 28 19 }}]


EDOs: {{EDOs|5e, 41}}
{{Val list|legend=1| 5e, 41 }}


Badness: 0.0323
Badness: 0.0323
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"