742edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table |
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== Theory == | == Theory == | ||
742edo is a very strong 19-limit system and a [[ | 742edo is a very strong 19-limit system and a [[zeta peak edo]], and is uniquely [[consistent]] in the [[21-odd-limit]]. It tempers out the vishnuzma and the fortune comma in the 5-limit, supporting [[vishnu]] and [[fortune]]; [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]], [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 24: | Line 24: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 23 6 -14 }}, {{monzo| -84 53 }} | | {{monzo| 23 6 -14 }}, {{monzo| -84 53 }} | ||
| | | {{mapping| 742 1176 1723 }} | ||
| -0.0157 | | -0.0157 | ||
| 0.0555 | | 0.0555 | ||
| Line 31: | Line 31: | ||
| 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 }} | ||
| -0.0035 | | -0.0035 | ||
| 0.0525 | | 0.0525 | ||
| Line 38: | Line 38: | ||
| 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 }} | ||
| -0.0123 | | -0.0123 | ||
| 0.0501 | | 0.0501 | ||
| Line 45: | Line 45: | ||
| 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 }} | ||
| -0.0302 | | -0.0302 | ||
| 0.0608 | | 0.0608 | ||
| Line 52: | Line 52: | ||
| 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 }} | ||
| -0.0317 | | -0.0317 | ||
| 0.0564 | | 0.0564 | ||
| Line 59: | Line 59: | ||
| 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 }} | ||
| -0.0295 | | -0.0295 | ||
| 0.0531 | | 0.0531 | ||
| Line 66: | Line 66: | ||
| 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) | ||
| -0.0468 | | -0.0468 | ||
| 0.0699 | | 0.0699 | ||
| Line 77: | Line 77: | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
| Line 118: | Line 118: | ||
| [[Iodine]] | | [[Iodine]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||