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742edo: Difference between revisions

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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|742}}
{{Harmonics in equal|742|columns=11}}
{{Harmonics in equal|742|columns=11|start=12|collapsed=1|title=Approximation of prime harmonics in 742edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
Line 17: Line 18:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
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|-
|-
| 2.3.5
| 2.3.5
| {{monzo| 23 6 -14 }}, {{monzo| -84 53 }}
| {{Monzo| 23 6 -14 }}, {{monzo| -84 53 }}
| {{mapping| 742 1176 1723 }}
| {{Mapping| 742 1176 1723 }}
| −0.0157
| −0.0157
| 0.0555
| 0.0555
Line 32: Line 33:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }}
| 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }}
| {{mapping| 742 1176 1723 2083 }}
| {{Mapping| 742 1176 1723 2083 }}
| −0.0035
| −0.0035
| 0.0525
| 0.0525
Line 39: Line 40:
| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 9801/9800, 172032/171875, 1240029/1239040
| 2401/2400, 9801/9800, 172032/171875, 1240029/1239040
| {{mapping| 742 1176 1723 2083 2567 }}
| {{Mapping| 742 1176 1723 2083 2567 }}
| −0.0123
| −0.0123
| 0.0501
| 0.0501
Line 46: Line 47:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325
| 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325
| {{mapping| 742 1176 1723 2083 2567 2746 }}
| {{Mapping| 742 1176 1723 2083 2567 2746 }}
| −0.0302
| −0.0302
| 0.0608
| 0.0608
Line 53: Line 54:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655
| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655
| {{mapping| 742 1176 1723 2083 2567 2746 3033 }}
| {{Mapping| 742 1176 1723 2083 2567 2746 3033 }}
| −0.0317
| −0.0317
| 0.0564
| 0.0564
Line 60: Line 61:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2432/2431, 2601/2600, 3213/3211
| 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2432/2431, 2601/2600, 3213/3211
| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 }}
| {{Mapping| 742 1176 1723 2083 2567 2746 3033 3152 }}
| −0.0295
| −0.0295
| 0.0531
| 0.0531
Line 67: Line 68:
| 2.3.5.7.11.13.17.19.23
| 2.3.5.7.11.13.17.19.23
| 1197/1196, 1496/1495, 1701/1700, 2025/2024, 2058/2057, 2401/2400, 2601/2600, 3213/3211
| 1197/1196, 1496/1495, 1701/1700, 2025/2024, 2058/2057, 2401/2400, 2601/2600, 3213/3211
| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 3357 }} (742i)
| {{Mapping| 742 1176 1723 2083 2567 2746 3033 3152 3357 }} (742i)
| −0.0468
| −0.0468
| 0.0699
| 0.0699
Line 79: Line 80:
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| 8388608/7381125
| 8388608/7381125
| [[Fortune]]
| [[Fortune]]
|-
| 1
| 243\742
| 392.992
| 2744/2187
| [[Emmthird]] (7-limit)
|-
|-
| 1
| 1
Line 104: Line 111:
|-
|-
| 14
| 14
| 434\742<br />(10\742)
| 434\742<br>(10\742)
| 701.886<br />(16.173)
| 701.886<br>(16.173)
| 3/2<br />(105/104)
| 3/2<br>(105/104)
| [[Silicon]]
| [[Silicon]]
|-
|-
| 53
| 53
| 239\742<br />(1\742)
| 239\742<br>(1\742)
| 386.523<br />(1.617)
| 386.523<br>(1.617)
| 5/4<br />(32805/32768)
| 5/4<br>(32805/32768)
| [[Mercator]]
| [[Mercator]]
|-
|-
| 53
| 53
| 565\742<br />(5\742)
| 565\742<br>(5\742)
| 913.746<br />(8.086)
| 913.746<br>(8.086)
| 441/260<br />(196/195)
| 441/260<br>(196/195)
| [[Iodine]]
| [[Iodine]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
* Silicon[28]: 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43
* Silicon[28]: 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43
Retrieved from "https://en.xen.wiki/w/742edo"