157edo: Difference between revisions

Cleanup
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 249 -157 }}
| {{monzo| 249 -157 }}
| {{mapping| 157 249 }}
| {{mapping| 157 249 }}
| -0.388
| &minus;0.388
| 0.388
| 0.388
| 5.08
| 5.08
Line 32: Line 24:
| 78732/78125, {{val| 37 -16 -5 }}
| 78732/78125, {{val| 37 -16 -5 }}
| {{mapping| 157 249 365 }}
| {{mapping| 157 249 365 }}
| -0.760
| &minus;0.760
| 0.614
| 0.614
| 8.04
| 8.04
Line 39: Line 31:
| 2401/2400, 5120/5103, 78732/78125
| 2401/2400, 5120/5103, 78732/78125
| {{mapping| 157 249 365 441 }}
| {{mapping| 157 249 365 441 }}
| -0.737
| &minus;0.737
| 0.533
| 0.533
| 6.98
| 6.98
Line 46: Line 38:
| 176/175, 1331/1323, 2401/2400, 5120/5103
| 176/175, 1331/1323, 2401/2400, 5120/5103
| {{mapping| 157 249 365 441 543 }}
| {{mapping| 157 249 365 441 543 }}
| -0.532
| &minus;0.532
| 0.629
| 0.629
| 8.24
| 8.24
Line 53: Line 45:
| 176/175, 351/350, 847/845, 1331/1323, 2197/2187
| 176/175, 351/350, 847/845, 1331/1323, 2197/2187
| {{mapping| 157 249 365 441 543 581 }}
| {{mapping| 157 249 365 441 543 581 }}
| -0.454
| &minus;0.454
| 0.600
| 0.600
| 7.86
| 7.86
Line 60: Line 52:
| 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187
| 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187
| {{mapping| 157 249 365 441 543 581 642 }}
| {{mapping| 157 249 365 441 543 581 642 }}
| -0.461
| &minus;0.461
| 0.556
| 0.556
| 7.28
| 7.28
Line 67: Line 59:
| 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475
| 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475
| {{mapping| 157 249 365 441 543 581 642 667 }}
| {{mapping| 157 249 365 441 543 581 642 667 }}
| -0.420
| &minus;0.420
| 0.531
| 0.531
| 6.95
| 6.95
Line 73: Line 65:


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all right-3 left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperament
|-
|-
| 1
| 1
Line 116: Line 102:
| 250/189
| 250/189
| [[Catafourth]]
| [[Catafourth]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}