1289edo: Difference between revisions

m Theory: nullity-1 temps are best given by commas
ArrowHead294 (talk | contribs)
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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
Line 32: Line 24:
| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
| {{mapping|1289 2043 2993}}
| {{mapping|1289 2043 2993}}
| -0.0014
| &minus;0.0014
| 0.0097
| 0.0097
| 1.04
| 1.04
Line 39: Line 31:
| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
| {{mapping|1289 2043 2993 3619}}
| {{mapping|1289 2043 2993 3619}}
| -0.0275
| &minus;0.0275
| 0.0461
| 0.0461
| 4.95
| 4.95
Line 46: Line 38:
| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
| {{mapping|1289 2043 2993 3619 4459}}
| {{mapping|1289 2043 2993 3619 4459}}
| -0.0109
| &minus;0.0109
| 0.0530
| 0.0530
| 5.69
| 5.69
Line 53: Line 45:
| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
| {{mapping|1289 2043 2993 3619 4459 4770}}
| {{mapping|1289 2043 2993 3619 4459 4770}}
| -0.0146
| &minus;0.0146
| 0.0491
| 0.0491
| 5.27
| 5.27
Line 60: Line 52:
| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
| {{mapping|1289 2043 2993 3619 4459 4770 5269}}
| {{mapping|1289 2043 2993 3619 4459 4770 5269}}
| -0.0210
| &minus;0.0210
| 0.0481
| 0.0481
| 5.17
| 5.17
Line 67: Line 59:
| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
| -0.0299
| &minus;0.0299
| 0.0508
| 0.0508
| 5.46
| 5.46
Line 73: Line 65:


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 98: Line 84:
| 8388608/7381125
| 8388608/7381125
| [[Fortune]]
| [[Fortune]]
|}
{{rank-2 end}}
 
{{orf}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct