Meantone family: Difference between revisions
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{{main|Semaphore and Godzilla}} | {{main|Semaphore and Godzilla}} | ||
Godzilla tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes. | |||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: ~8/7 = 252.635 | |||
EDO generators: [[19edo|4\19]], [[24edo|5\24]], [[43edo|9\43]], [[62edo|13\62]] | |||
Scales (Scala files): | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div> | |||
<div class="mw-collapsible-content"> | |||
{| class="wikitable right-1 right-2 sortable" | |||
|+ | |||
|- | |||
! #Gens up | |||
! Cents <ref>octave-reduced</ref> | |||
! class="unsortable"| Approximate ratios<ref>2.3.5.7, odd limit ≤ 27. JI readings in parentheses are outside the subgroup but are supported by the defining EDOs.</ref> | |||
|- | |||
| 0 | |||
| 0.00 | |||
| 1/1 | |||
|- | |||
| 1 | |||
| 252.635 | |||
| 7/6, 8/7, (15/13) | |||
|- | |||
| 2 | |||
| 505.27 | |||
| 4/3 | |||
|- | |||
| 3 | |||
| 757.905 | |||
| 14/9, (20/13) | |||
|- | |||
| 4 | |||
| 1010.54 | |||
| 9/5, 16/9 | |||
|- | |||
| 5 | |||
| 63.175 | |||
| | |||
|- | |||
| 6 | |||
| 315.81 | |||
| 6/5 | |||
|- | |||
| 7 | |||
| 568.4 | |||
| 7/5, (18/13) | |||
|- | |||
| 8 | |||
| 821.08 | |||
| 8/5 | |||
|} | |||
<references/></div></div> | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:400px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
[[Mappings|Period-generator mapping]]: [{{val|1 0 -4 2}}, {{val|0 2 8 1}}] | |||
[[Comma]]s: 49/48, 81/80 | [[Comma]]s: 49/48, 81/80 | ||
valid range: [240.000, 257.143] (5 to 14c) | valid range: [240.000, 257.143] (5 to 14c) | ||
| Line 713: | Line 773: | ||
strict range: [240.000, 257.143] | strict range: [240.000, 257.143] | ||
Mapping generator: ~7/4 | Mapping generator: ~7/4 | ||
[[Wedgie]]: <<2 8 1 8 -4 -20|| | [[Wedgie]]: <<2 8 1 8 -4 -20|| | ||
| Line 725: | Line 781: | ||
[[Badness]]: 0.0267 | [[Badness]]: 0.0267 | ||
</div></div> | |||
== 11-limit == | == 11-limit == | ||
Commas: 45/44, 49/48, 81/80 | Commas: 45/44, 49/48, 81/80 | ||