Keemic family: Difference between revisions
m Cleanup |
Databoxified |
||
| Line 2: | Line 2: | ||
= Supermagic = | = Supermagic = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generators: ~3/2 = 701.8733, ~5/4 = 380.4684 | |||
EDO generators: [[15edo|(9, 5)\15]], [[19edo|(11, 6)\19]], [[22edo|(13, 7)\22]] | |||
Scales: [[supermagic15]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 875/864 | [[Comma list]]: 875/864 | ||
| Line 15: | Line 30: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and 9-odd-limit | * 7- and [[9-odd-limit]] | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/4 3/4 1/4 -1/4 }}, {{monzo| 5/4 3/4 -3/4 3/4 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 5/4 3/4 1/4 -1/4 }}, {{monzo| 5/4 3/4 -3/4 3/4 }}] | ||
: Eigenmonzos: 2, 4/3, 7/5 | : Eigenmonzos: 2, 4/3, 7/5 | ||
| Line 22: | Line 37: | ||
[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
</div></div> | |||
== 11-limit == | |||
Period: 1\1 | |||
Optimal ([[POTE]]) generators: ~3/2 = 704.1985, ~5/4 = 381.5394 | |||
EDO generators: [[15edo|(9, 5)\15]], [[19edo|(11, 6)\19]], [[22edo|(13, 7)\22]] | |||
Scales: [[supermagic15]] | Scales: [[supermagic15]] | ||
== | <div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | ||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 100/99, 385/384 | Comma list: 100/99, 385/384 | ||
| Line 33: | Line 63: | ||
Badness: 0.641 × 10<sup>-3</sup> | Badness: 0.641 × 10<sup>-3</sup> | ||
</div></div> | |||
= Supernatural = | = Supernatural = | ||
Period: 1\1 | |||
Optimal ([[POTE]]) generators: ~5/4 = 380.3520, ~11/8 = 547.5758 | |||
EDO generators: [[19edo|(6, 8)\19]], [[22edo|(7, 11)\22]], [[41edo|(13, 20)\41]] | |||
Scales: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 225/224, 245/243 | Comma list: 225/224, 245/243 | ||
Mapping: [{{val| 1 0 2 -1 0 }}, {{val| 0 5 1 12 0 }}, {{val| 0 0 0 0 1 }}] | Mapping: [{{val| 1 0 2 -1 0 }}, {{val| 0 5 1 12 0 }}, {{val| 0 0 0 0 1 }}] | ||
{{Val list|legend=1| 19, 22, 41, 82e, 101cd | {{Val list|legend=1| 19, 22, 41, 82e, 101cd, 224ccde, 265ccde * }} | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | |||
Badness: 0.888 × 10<sup>-3</sup> | Badness: 0.888 × 10<sup>-3</sup> | ||
</div></div> | |||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 13:46, 24 March 2021
The keemic family of rank-3 temperaments are planar temperaments tempering out the keema, 875/864.
Supermagic
Period: 1\1
Optimal (POTE) generators: ~3/2 = 701.8733, ~5/4 = 380.4684
EDO generators: (9, 5)\15, (11, 6)\19, (13, 7)\22
Scales: supermagic15
Subgroup: 2.3.5.7
Comma list: 875/864
Mapping: [⟨1 0 0 5], ⟨0 1 0 3], ⟨0 0 1 -3]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 0 -1 3], ⟨0 1 1 0]]
Lattice basis:
- 6/5 length = 0.8879, 3/2 length = 1.3391
- Angle (6/5, 3/2) = 77.834
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [5/4 3/4 1/4 -1/4⟩, [5/4 3/4 -3/4 3/4⟩]
- Eigenmonzos: 2, 4/3, 7/5
Projection pair: 7 864/125
11-limit
Period: 1\1
Optimal (POTE) generators: ~3/2 = 704.1985, ~5/4 = 381.5394
EDO generators: (9, 5)\15, (11, 6)\19, (13, 7)\22
Scales: supermagic15
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384
Mapping: [⟨1 0 0 5 2], ⟨0 1 0 3 -2], ⟨0 0 1 -3 2]]
Badness: 0.641 × 10-3
Supernatural
Period: 1\1
Optimal (POTE) generators: ~5/4 = 380.3520, ~11/8 = 547.5758
EDO generators: (6, 8)\19, (7, 11)\22, (13, 20)\41
Scales:
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/243
Mapping: [⟨1 0 2 -1 0], ⟨0 5 1 12 0], ⟨0 0 0 0 1]]
Badness: 0.888 × 10-3