Map of rank-2 temperaments: Difference between revisions
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m →Nine periods per octave: Added novemkleismic |
mNo edit summary |
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| Line 931: | Line 931: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! colspan=" | ! colspan="10" | Generator | ||
! | Cents | ! | Cents | ||
! | Comments | ! | Comments | ||
| Line 942: | Line 942: | ||
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| Line 956: | Line 955: | ||
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| | 1\30 | | | 1\30 | ||
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| Line 970: | Line 968: | ||
| | 1\27 | | | 1\27 | ||
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| Line 984: | Line 981: | ||
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| | 2\51 | | | 2\51 | ||
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| Line 998: | Line 994: | ||
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| Line 1,011: | Line 1,006: | ||
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|2\45 | |2\45 | ||
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| Line 1,026: | Line 1,020: | ||
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| Line 1,040: | Line 1,033: | ||
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| Line 1,054: | Line 1,046: | ||
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| Line 1,068: | Line 1,059: | ||
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| | 6\87 | | | 6\87 | ||
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| Line 1,083: | Line 1,073: | ||
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|11\159 | |11\159 | ||
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| Line 1,098: | Line 1,087: | ||
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|16\231 | |16\231 | ||
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|83.117 | |83.117 | ||
| Line 1,110: | Line 1,098: | ||
| | 5\72 | | | 5\72 | ||
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| Line 1,124: | Line 1,111: | ||
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| Line 1,138: | Line 1,124: | ||
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| Line 1,152: | Line 1,137: | ||
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| Line 1,163: | Line 1,147: | ||
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|3\39 | |3\39 | ||
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| Line 1,178: | Line 1,161: | ||
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|4\51 | |4\51 | ||
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| Line 1,193: | Line 1,175: | ||
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|5\63 | |5\63 | ||
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| Line 1,209: | Line 1,190: | ||
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|11\138 | |11\138 | ||
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| Line 1,222: | Line 1,202: | ||
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|6\75 | |6\75 | ||
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| Line 1,237: | Line 1,216: | ||
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|7\87 | |7\87 | ||
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| Line 1,253: | Line 1,231: | ||
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|15\186 | |15\186 | ||
|96.774 | |96.774 | ||
|Augmented/Augene/Misty | |Augmented/Augene/Misty | ||
|- | |- | ||
| Line 1,280: | Line 1,243: | ||
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|8\99 | |8\99 | ||
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|96.97 | |96.97 | ||
| Line 1,292: | Line 1,254: | ||
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| Line 1,306: | Line 1,267: | ||
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| Line 1,320: | Line 1,280: | ||
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| Line 1,334: | Line 1,293: | ||
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| Line 1,348: | Line 1,306: | ||
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| Line 1,362: | Line 1,319: | ||
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| Line 1,376: | Line 1,332: | ||
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| Line 1,386: | Line 1,341: | ||
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|5\39 | |5\39 | ||
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| Line 1,404: | Line 1,358: | ||
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| Line 1,418: | Line 1,371: | ||
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| Line 1,429: | Line 1,381: | ||
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|7\48 | |7\48 | ||
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| Line 1,444: | Line 1,395: | ||
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|11\75 | |11\75 | ||
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| Line 1,459: | Line 1,409: | ||
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|15\102 | |15\102 | ||
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| Line 1,474: | Line 1,423: | ||
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|19\129 | |19\129 | ||
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| Line 1,484: | Line 1,432: | ||
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|4\27 | |4\27 | ||
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| Line 1,502: | Line 1,449: | ||
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| Line 2,559: | Line 2,505: | ||
==Six periods per octave == | ==Six periods per octave == | ||
{| class="wikitable" | {| class="wikitable" | ||
! colspan=" | ! colspan="7" |Generator!!Cents !!Comments | ||
|- | |- | ||
|0\6|| || || | |0\6|| || || | ||
| | | | ||
| | | | ||
| Line 2,571: | Line 2,516: | ||
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|1\288 | |1\288 | ||
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| Line 2,582: | Line 2,526: | ||
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|1\282 | |1\282 | ||
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| Line 2,594: | Line 2,537: | ||
|1\276 | |1\276 | ||
|2\552 | |2\552 | ||
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| Line 2,606: | Line 2,548: | ||
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|3\822 | |3\822 | ||
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|4.380 | |4.380 | ||
| Line 2,618: | Line 2,559: | ||
| | | | ||
|4\1092 | |4\1092 | ||
|4.396 | |4.396 | ||
|Sextile | |Sextile | ||
|- | |- | ||
| Line 2,637: | Line 2,566: | ||
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|1\270 | |1\270 | ||
| | | | ||
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| Line 2,648: | Line 2,576: | ||
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|1\264 | |1\264 | ||
| | | | ||
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| Line 2,659: | Line 2,586: | ||
| | | | ||
|... | |... | ||
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| Line 2,670: | Line 2,596: | ||
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|1\90 | |1\90 | ||
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| Line 2,681: | Line 2,606: | ||
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|1\84 | |1\84 | ||
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| Line 2,692: | Line 2,616: | ||
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|1\78 | |1\78 | ||
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| Line 2,703: | Line 2,626: | ||
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|1\72 | |1\72 | ||
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| Line 2,709: | Line 2,631: | ||
|16.667 | |16.667 | ||
|[[Stearnscape]] | |[[Stearnscape]] | ||
|- | |- | ||
| | | | ||
| Line 2,728: | Line 2,639: | ||
| | | | ||
|4\282 | |4\282 | ||
|17.021 | |17.021 | ||
|Stearnscape | |Stearnscape | ||
| Line 2,738: | Line 2,648: | ||
| | | | ||
|3\210 | |3\210 | ||
| | | | ||
|17.143 | |17.143 | ||
| Line 2,748: | Line 2,657: | ||
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|2\138 | |2\138 | ||
| | | | ||
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| Line 2,758: | Line 2,666: | ||
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|1\66 | |1\66 | ||
| | | | ||
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| Line 2,769: | Line 2,676: | ||
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|1\60 | |1\60 | ||
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| Line 2,780: | Line 2,686: | ||
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|1\54 | |1\54 | ||
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| Line 2,791: | Line 2,696: | ||
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|1\48 | |1\48 | ||
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| Line 2,802: | Line 2,706: | ||
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|1\42 | |1\42 | ||
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| Line 2,813: | Line 2,716: | ||
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|1\36 | |1\36 | ||
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| Line 2,823: | Line 2,725: | ||
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|1\30 | |1\30 | ||
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| Line 2,835: | Line 2,736: | ||
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|2\54 | |2\54 | ||
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| Line 2,844: | Line 2,744: | ||
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|1\24 | |1\24 | ||
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| Line 2,857: | Line 2,756: | ||
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|3\66 | |3\66 | ||
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| Line 2,867: | Line 2,765: | ||
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|2\42 | |2\42 | ||
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| Line 2,879: | Line 2,776: | ||
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|3\60 | |3\60 | ||
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| Line 2,887: | Line 2,783: | ||
|- | |- | ||
|1\18 | |1\18 | ||
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| Line 2,901: | Line 2,796: | ||
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|4\66 | |4\66 | ||
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| Line 2,911: | Line 2,805: | ||
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|3\48 | |3\48 | ||
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| Line 2,923: | Line 2,816: | ||
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|5\78 | |5\78 | ||
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| Line 2,932: | Line 2,824: | ||
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|2\30 | |2\30 | ||
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| Line 2,945: | Line 2,836: | ||
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|5\72 | |5\72 | ||
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| Line 2,955: | Line 2,845: | ||
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|3\42 | |3\42 | ||
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| Line 2,967: | Line 2,856: | ||
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|4\54 | |4\54 | ||
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| Line 2,975: | Line 2,863: | ||
|- | |- | ||
|1\12 | |1\12 | ||
| | | | ||
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| Line 4,080: | Line 3,967: | ||
{| class="wikitable" | {| class="wikitable" | ||
! colspan=" | ! colspan="8" |Generator!!Cents!!Comments | ||
|- | |- | ||
|0\12|| || || | |0\12|| || || | ||
| | | | ||
| | | | ||
| | |||
| | |||0|| | ||
| ||0|| | |||
|- | |- | ||
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| Line 4,093: | Line 3,979: | ||
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|1\636 | |1\636 | ||
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| Line 4,105: | Line 3,990: | ||
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|1\624 | |1\624 | ||
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| Line 4,118: | Line 4,002: | ||
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|2\1236 | |2\1236 | ||
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| Line 4,131: | Line 4,014: | ||
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|3\1848 | |3\1848 | ||
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| Line 4,144: | Line 4,026: | ||
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|4\2460 | |4\2460 | ||
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|1.951 | |1.951 | ||
| Line 4,153: | Line 4,034: | ||
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|1\612 | |1\612 | ||
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| Line 4,165: | Line 4,045: | ||
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|1\600 | |1\600 | ||
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| Line 4,177: | Line 4,056: | ||
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|1\588 | |1\588 | ||
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| Line 4,189: | Line 4,067: | ||
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|1\576 | |1\576 | ||
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| Line 4,201: | Line 4,078: | ||
| | | | ||
|... | |... | ||
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| Line 4,213: | Line 4,089: | ||
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|1\108 | |1\108 | ||
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| Line 4,225: | Line 4,100: | ||
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|1\96 | |1\96 | ||
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| Line 4,237: | Line 4,111: | ||
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|1\84 | |1\84 | ||
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| Line 4,251: | Line 4,124: | ||
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|3\240 | |3\240 | ||
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| Line 4,262: | Line 4,134: | ||
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|2\156 | |2\156 | ||
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| Line 4,275: | Line 4,146: | ||
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|3\228 | |3\228 | ||
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| Line 4,285: | Line 4,155: | ||
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|1\72 | |1\72 | ||
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| Line 4,296: | Line 4,165: | ||
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|1\60 | |1\60 | ||
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| Line 4,309: | Line 4,177: | ||
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|2\108 | |2\108 | ||
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| Line 4,319: | Line 4,186: | ||
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|1\48 | |1\48 | ||
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| Line 4,333: | Line 4,199: | ||
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|3\132 | |3\132 | ||
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| Line 4,344: | Line 4,209: | ||
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| 2\84 | | 2\84 | ||
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| Line 4,357: | Line 4,221: | ||
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|3\120 | |3\120 | ||
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| Line 4,366: | Line 4,229: | ||
|- | |- | ||
|1\36 | |1\36 | ||
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| Line 4,381: | Line 4,243: | ||
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|4\132 | |4\132 | ||
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| Line 4,392: | Line 4,253: | ||
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|3\96 | |3\96 | ||
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| Line 4,405: | Line 4,265: | ||
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|5\156 | |5\156 | ||
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| Line 4,415: | Line 4,274: | ||
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|2\60 | |2\60 | ||
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| Line 4,429: | Line 4,287: | ||
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|5\144 | |5\144 | ||
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| Line 4,440: | Line 4,297: | ||
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|3\84 | |3\84 | ||
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| Line 4,457: | Line 4,313: | ||
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|43.182 | |43.182 | ||
|Magnesium | |Magnesium | ||
| Line 4,469: | Line 4,324: | ||
| | | | ||
|16\444 | |16\444 | ||
|43.243 | |43.243 | ||
|Magnesium | |Magnesium | ||
| Line 4,480: | Line 4,334: | ||
| | | | ||
|13\360 | |13\360 | ||
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|43.333 | |43.333 | ||
| Line 4,491: | Line 4,344: | ||
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|10\276 | |10\276 | ||
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| Line 4,502: | Line 4,354: | ||
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|7\192 | |7\192 | ||
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| Line 4,513: | Line 4,364: | ||
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|4\108 | |4\108 | ||
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| Line 4,522: | Line 4,372: | ||
|- | |- | ||
|1\24 | |1\24 | ||
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| | | | ||
Revision as of 11:09, 3 March 2024
This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only rank-2 temperaments not appearing here should be ones like Bohlen-Pierce that completely lack octaves.
Please make sure each fraction of an octave is always the mediant of the ones directly above and below.
One period per octave
Since this is the largest subset, it has its own page: Map of linear temperaments.
Two periods per octave
| Generator | Cents | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0\2 | 0.000 | |||||||||
| 1\26 | 46.154 | |||||||||
| 1\24 | 50.000 | Shrutar | ||||||||
| 2\46 | 52.174 | Shrutar | ||||||||
| 1\22 | 54.545 | Shrutar | ||||||||
| 1\20 | 60.000 | |||||||||
| 1\18 | 66.667 | |||||||||
| 2\34 | 70.588 | Vishnu | ||||||||
| 7\118 | 71.186 | Vishnu | ||||||||
| 5\84 | 71.429 | Vishnu | ||||||||
| 3\50 | 72.000 | |||||||||
| 1\16 | 75.000 | |||||||||
| 2\30 | 80.000 | |||||||||
| 3\44 | 81.818 | |||||||||
| 4\58 | 82.759 | Harry | ||||||||
| 9\130 | 83.077 | Harry | ||||||||
| 5\72 | 83.333 | Harry | ||||||||
| 1\14 | 85.714 | |||||||||
| 2\26 | 92.308 | Injera | ||||||||
| 3\38 | 94.737 | Injera | ||||||||
| 1\12 | 100.000 | Injera/Diaschismic | ||||||||
| 5\58 | 103.448 | Diaschismic | ||||||||
| 4\46 | 104.348 | Diaschismic/Srutal | ||||||||
| 7\80 | 105.000 | Srutal | ||||||||
| 3\34 | 105.882 | Srutal/Pajara | ||||||||
| 5\56 | 107.143 | Pajara | ||||||||
| 2\22 | 109.091 | Pajara | ||||||||
| 3\32 | 112.500 | |||||||||
| 1\10 | 120.000 | Octokaidecal | ||||||||
| 3\28 | 128.571 | Octokaidecal | ||||||||
| 2\18 | 133.333 | Octokaidecal | ||||||||
| 3\26 | 138.462 | |||||||||
| 6\60 | 140.000 | |||||||||
| 11\94 | 140.126 | Fifive | ||||||||
| 15\128 | 140.625 | Fifive | ||||||||
| 4\34 | 141.176 | Fifive | ||||||||
| 5\42 | 142.857 | |||||||||
| 1\8 | 150.000 | |||||||||
| 4\30 | 160.000 | |||||||||
| 3\22 | 163.636 | Hedgehog/Echidna | ||||||||
| 11\80 | 165.000 | Hedgehog/Echidna | ||||||||
| 8\58 | 165.517 | Hedgehog/Echidna | ||||||||
| 5\36 | 166.667 | |||||||||
| 2\14 | 171.429 | |||||||||
| 3\20 | 180.000 | |||||||||
| 7\46 | 182.609 | Unidec/Hendec | ||||||||
| 11\72 | 183.333 | Unidec/Hendec | ||||||||
| 4\26 | 184.615 | Unidec/Hendec | ||||||||
| 5\32 | 187.500 | |||||||||
| 1\6 | 200.000 | |||||||||
| 6\34 | 211.765 | |||||||||
| 5\28 | 214.286 | Antikythera | ||||||||
| 9\50 | 216.000 | Antikythera/Wizard | ||||||||
| 13\72 | 216.667 | Antikythera/Wizard | ||||||||
| 4\22 | 218.182 | Antikythera/Wizard/Astrology | ||||||||
| 15\82 | 219.512 | Astrology | ||||||||
| 11\60 | 220.000 | Astrology | ||||||||
| 7\38 | 221.053 | |||||||||
| 225.000 | Lemba | |||||||||
| 5\26 | 230.769 | Lemba | ||||||||
| 12\62 | 232.258 | Lemba | ||||||||
| 7\36 | 233.333 | |||||||||
| 9\46 | 234.783 | Echidnic | ||||||||
| 29\148 | 235.135 | Echidnic | ||||||||
| 20\102 | 235.294 | Echidnic | ||||||||
| 11\56 | 235.714 | |||||||||
| 2\10 | 240.000 | Decimal | ||||||||
| 5\24 | 250.000 | Decimal | ||||||||
| 8\38 | 252.632 | Decimal | ||||||||
| 257.143 | Decimal | |||||||||
| 4\18 | 266.667 | |||||||||
| 5\22 | 272.727 | Doublewide | ||||||||
| 16\70 | 274.286 | Doublewide | ||||||||
| 11\48 | 275.000 | Doublewide | ||||||||
| 6\26 | 276.923 | |||||||||
| 1\4 | 300.000 | |||||||||
Three periods per octave
| Generator | Cents | Comments | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0\3 | 0.000 | ||||||||||
| 1\30 | 40.000 | ||||||||||
| 1\27 | 44.444 | Semiaug | |||||||||
| 2\51 | 47.059 | Semiaug | |||||||||
| 1\24 | 50.000 | Semiaug/Hemiug | |||||||||
| 2\45 | 53.333 | Hemiug | |||||||||
| 1\21 | 57.143 | Hemiug | |||||||||
| 1\18 | 66.667 | ||||||||||
| 1\15 | 80.000 | ||||||||||
| 6\87 | 82.759 | ||||||||||
| 11\159 | 83.019 | Tritikleismic | |||||||||
| 16\231 | 83.117 | Tritikleismic | |||||||||
| 5\72 | 83.333 | Tritikleismic | |||||||||
| 4\57 | 84.211 | Tritikleismic | |||||||||
| 3\42 | 85.714 | ||||||||||
| 2\27 | 88.889 | Augmented/Augene | |||||||||
| 3\39 | 92.308 | Augmented/Augene/Fog | |||||||||
| 4\51 | 94.118 | Augmented/Augene/Fog | |||||||||
| 5\63 | 95.238 | Augmented/Augene/Fog | |||||||||
| 11\138 | 95.652 | Augmented Augene/Fog | |||||||||
| 6\75 | 96 | Augmented/Augene/Fog | |||||||||
| 7\87 | 96.552 | Augmented/Augene/Misty | |||||||||
| 15\186 | 96.774 | Augmented/Augene/Misty | |||||||||
| 8\99 | 96.97 | Augmented/Augene/Misty | |||||||||
| 1\12 | 100.000 | Augmented/Augene/August | |||||||||
| 3\33 | 109.091 | August | |||||||||
| 2\21 | 114.286 | August | |||||||||
| 3\30 | 120.000 | ||||||||||
| 1\9 | 133.333 | ||||||||||
| 4\33 | 145.455 | ||||||||||
| 3\24 | 150.000 | Triforce | |||||||||
| 5\39 | 153.846 | Triforce | |||||||||
| 2\15 | 160.000 | Triforce | |||||||||
| 3\21 | 171.429 | Oodako | |||||||||
| 7\48 | 175 | Oodako | |||||||||
| 11\75 | 176 | Oodako | |||||||||
| 15\102 | 176.471 | Oodako | |||||||||
| 19\129 | 176.744 | Oodako | |||||||||
| 4\27 | 177.778 | Oodako | |||||||||
| 1\6 | 200.000 | ||||||||||
Four periods per octave
| Generator | Cents | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| 0\4 | 0 | |||||||
| 1\76 | 15.789 | |||||||
| 1\72 | 16.667 | Quadritikleismic | ||||||
| 2\140 | 17.143 | Quadritikleismic | ||||||
| 1\68 | 17.647 | Quadritikleismic | ||||||
| 1\64 | 18.75 | |||||||
| 1\60 | 20 | |||||||
| 1\56 | 21.429 | |||||||
| 1\52 | 23.068 | |||||||
| 1\48 | 25 | |||||||
| 1\44 | 27.273 | |||||||
| 1\40 | 30 | |||||||
| 1\36 | 33.333 | |||||||
| 1\32 | 37.5 | |||||||
| 1\28 | 42.857 | |||||||
| 2\52 | 46.154 | Hemidim | ||||||
| 3\76 | 47.368 | Hemidim | ||||||
| 1\24 | 50 | Hemidim/Darian calendar | ||||||
| 1\20 | 60 | |||||||
| 1\16 | 75 | |||||||
| 2\28 | 85.714 | Demolished | ||||||
| 3\40 | 90 | Demolished | ||||||
| 1\12 | 100 | Demolished/Diminished | ||||||
| 14\164 | 102.439 | Diminished | ||||||
| 27\316 | 102.532 | Diminished/Unlit | ||||||
| 40\468 | 102.564 | Diminished/Unlit | ||||||
| 53\620 | 102.581 | Diminished/Unlit | ||||||
| 13\152 | 102.632 | Diminished/Unlit/Undim | ||||||
| 51\596 | 102.685 | Diminished/Undim | ||||||
| 38\444 | 102.703 | Diminished/Undim | ||||||
| 25\292 | 102.740 | Diminished/Undim | ||||||
| 12\140 | 102.857 | Diminished/Undim | ||||||
| 11\128 | 103.125 | Diminished | ||||||
| 10\116 | 103.448 | Diminished | ||||||
| 9\104 | 103.846 | Diminished | ||||||
| 8\92 | 104.348 | Diminished | ||||||
| 7\80 | 105 | Diminished/Bidia | ||||||
| 20\228 | 105.263 | Diminished/Bidia | ||||||
| 33\376 | 105.319 | Diminished/Bidia | ||||||
| 13\148 | 105.405 | Diminished/Bidia | ||||||
| 6\68 | 105.882 | Diminished/Bidia | ||||||
| 5\56 | 107.143 | Diminished/Bidia | ||||||
| 4\44 | 109.091 | Diminished | ||||||
| 3\32 | 112.5 | Diminished | ||||||
| 2\20 | 120 | Diminished | ||||||
| 1\8 | 150 | |||||||
Five periods per octave
| Generator | Cents | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0\5 | 0 | |||||||||
| 1\140 | 8.571 | |||||||||
| 1\135 | 8.889 | Slendrismic | ||||||||
| 3\400 | 9 | Slendrismic | ||||||||
| 2\265 | 9.057 | Slendrismic | ||||||||
| 1\130 | 9.231 | Slendrismic/Hemipental | ||||||||
| 3\385 | 9.351 | Hemipental | ||||||||
| 2\255 | 9.412 | Hemipental | ||||||||
| 1\125 | 9.6 | Hemipental | ||||||||
| 1\120 | 10 | |||||||||
| 1\115 | 10.435 | |||||||||
| ... | ... | |||||||||
| 1\70 | 17.143 | |||||||||
| 1\65 | 18.462 | Pental | ||||||||
| 3\190 | 18.947 | Pental | ||||||||
| 2\125 | 19.2 | Pental | ||||||||
| 3\185 | 19.459 | Pental | ||||||||
| 1\60 | 20 | Pental | ||||||||
| 1\55 | 21.818 | |||||||||
| 1\50 | 24 | |||||||||
| 1\45 | 26.67 | |||||||||
| 1\40 | 30 | |||||||||
| 1\35 | 34.286 | |||||||||
| 1\30 | 40 | |||||||||
| 2\55 | 43.636 | |||||||||
| 1\25 | 48 | |||||||||
| 3\70 | 51.429 | |||||||||
| 2\45 | 53.3 | |||||||||
| 3\65 | 55.385 | |||||||||
| 1\20 | 60 | |||||||||
| 4\75 | 64 | |||||||||
| 3\55 | 65.455 | |||||||||
| 5\90 | 66.667 | |||||||||
| 2\35 | 68.571 | Coblack | ||||||||
| 5\85 | 70.588 | Coblack | ||||||||
| 3\50 | 72 | Coblack | ||||||||
| 7\115 | 73.043 | Coblack | ||||||||
| 4\65 | 73.846 | Coblack | ||||||||
| 1\15 | 80 | Blackwood/Blacksmith | ||||||||
| 5\70 | 85.714 | Blackwood/Blacksmith | ||||||||
| 4\55 | 87.273 | Blackwood/Blacksmith | ||||||||
| 7\95 | 88.421 | Blackwood/Blacksmith | ||||||||
| 3\40 | 90 | Blackwood/Blacksmith | ||||||||
| 8\105 | 91.429 | Blackwood/Blacksmith | ||||||||
| 5\65 | 92.308 | Blackwood/Blacksmith | ||||||||
| 7\90 | 93.333 | Blackwood/Blacksmith | ||||||||
| 2\25 | 96 | Blackwood/Blacksmith | ||||||||
| 5\60 | 100 | Blackwood | ||||||||
| 8\95 | 101.053 | Blackwood | ||||||||
| 3\35 | 102.857 | Blackwood | ||||||||
| 7\80 | 105 | Blackwood | ||||||||
| 4\45 | 106.667 | Blackwood | ||||||||
| 5\55 | 109.091 | Blackwood | ||||||||
| 6\65 | 110.769 | Blackwood/Quintosec/Sengasec | ||||||||
| 25\270 | Blackwood/Quintosec/Sengasec/Qintosec | |||||||||
| 19\205 | Blackwood/Quintosec/SengasecQintosec | |||||||||
| 13\140 | Blackwood/Quintosec/Sengasec/Qintosec | |||||||||
| 20\215 | Blackwood/Qintosec | |||||||||
| 7\75 | 112 | Blackwood/Qinto | ||||||||
| 15\160 | Blackwood/Qinto | |||||||||
| 8\85 | 112.941 | Blackwood/Elderthing | ||||||||
| 9\95 | 113.684 | Blackwood | ||||||||
| 10\105 | 114.286 | Blackwood | ||||||||
| 1\10 | 120 | Blackwood | ||||||||
Six periods per octave
| Generator | Cents | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| 0\6 | 0 | |||||||
| 1\288 | 4.167 | |||||||
| 1\282 | 4.255 | |||||||
| 1\276 | 2\552 | 4.348 | Sextile | |||||
| 3\822 | 4.380 | Sextile | ||||||
| 4\1092 | 4.396 | Sextile | ||||||
| 1\270 | 4.444 | Sextile | ||||||
| 1\264 | 4.545 | |||||||
| ... | ... | |||||||
| 1\90 | 13.333 | |||||||
| 1\84 | 14.286 | |||||||
| 1\78 | 15.385 | |||||||
| 1\72 | 16.667 | Stearnscape | ||||||
| 4\282 | 17.021 | Stearnscape | ||||||
| 3\210 | 17.143 | Stearnscape | ||||||
| 2\138 | 17.391 | |||||||
| 1\66 | 18.182 | |||||||
| 1\60 | 20 | |||||||
| 1\54 | 22.222 | |||||||
| 1\48 | 25 | |||||||
| 1\42 | 28.571 | |||||||
| 1\36 | 33.333 | |||||||
| 1\30 | 40 | |||||||
| 2\54 | 44.444 | |||||||
| 1\24 | 50 | |||||||
| 3\66 | 54.545 | |||||||
| 2\42 | 57.143 | |||||||
| 3\60 | 60 | |||||||
| 1\18 | 66.667 | |||||||
| 4\66 | 72.727 | |||||||
| 3\48 | 75 | |||||||
| 5\78 | 76.923 | |||||||
| 2\30 | 80 | Hexe | ||||||
| 5\72 | 83.333 | Hexe | ||||||
| 3\42 | 85.714 | Hexe | ||||||
| 4\54 | 88.889 | Hexe | ||||||
| 1\12 | 100 | Hexe | ||||||
Seven periods per octave
| Generator | Cents | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 0\7 | 0 | ||||||||
| 1\91 | 13.187 | ||||||||
| 1\84 | 14.286 | Absurdity | |||||||
| 4\329 | 14.59 | Absurdity | |||||||
| 3\245 | 14.69 | ||||||||
| 2\161 | 14.907 | ||||||||
| 1\77 | 15.584 | Septant | |||||||
| 4\301 | 15.947 | Septant | |||||||
| 3\224 | 16.071 | Septant | |||||||
| 2\147 | 16.327 | Septant | |||||||
| 1\70 | 17.143 | ||||||||
| 1\63 | 19.048 | Sevond | |||||||
| 2\119 | 20.168 | Sevond | |||||||
| 1\56 | 21.429 | Sevond | |||||||
| 1\48 | 25 | ||||||||
| 1\42 | 28.571 | Neutron | |||||||
| 3\119 | 30.252 | Neutron | |||||||
| 5\196 | 30.612 | Neutron | |||||||
| 7\273 | 30.769 | Neutron | |||||||
| 2\77 | 31.169 | Neutron | |||||||
| 1\35 | 34.286 | Redwood | |||||||
| 2\63 | 38.095 | Redwood | |||||||
| 1\28 | 42.857 | Redwood/Whitewood | |||||||
| 3\77 | 46.753 | Whitewood | |||||||
| 2\49 | 48.980 | Whitewood | |||||||
| 3\70 | 51.429 | Whitewood | |||||||
| 1\21 | 57.143 | Whitewood/Jamesbond/Septimal | |||||||
| 4\77 | 62.338 | Jamesbond/Septimal | |||||||
| 3\56 | 64.286 | Jamesbond/Septimal | |||||||
| 5\91 | 65.934 | Jamesbond/Septimal | |||||||
| 2\35 | 68.571 | Jamesbond/Septimal/Greenwood | |||||||
| 5\84 | 71.429 | Jamesbond/Septimal/Greenwood | |||||||
| 3\49 | 73.469 | Jamesbond/Septimal/Greenwood | |||||||
| 4\63 | 76.190 | Jamesbond/Septimal/Greenwood | |||||||
| 1\14 | 85.714 | Jamesbond/Septimal/Greenwood | |||||||
Eight periods per octave
| Generator | Cents | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0\8 | 0 | |||||||||
| 1\80 | 15 | |||||||||
| 2\152 | 15.789 | Octoid | ||||||||
| 3\224 | 16.071 | Octoid | ||||||||
| 1\72 | 16.667 | Octoid | ||||||||
| 1\64 | 18.75 | |||||||||
| 1\56 | 21.429 | |||||||||
| 1\48 | 25 | |||||||||
| 1\40 | 30 | |||||||||
| 2\72 | 33.333 | |||||||||
| 1\32 | 37.5 | Semidim | ||||||||
| 3\88 | 40.909 | Semidim | ||||||||
| 2\56 | 42.857 | Semidim | ||||||||
| 3\80 | 45 | Semidim | ||||||||
| 4\104 | 46.154 | Semidim | ||||||||
| 5\128 | 46.875 | Semidim | ||||||||
| 6\152 | 47.368 | Semidim | ||||||||
| 7\176 | 47.727 | Semidim | ||||||||
| 8\200 | 48 | Semidim | ||||||||
| 9\224 | 48.214 | Semidim/Octant | ||||||||
| 28\696 | 48.276 | Semidim/Octant | ||||||||
| 19\472 | 48.305 | Semidim/Octant | ||||||||
| 10\248 | 48.387 | Semidim | ||||||||
| 1\24 | 50 | Semidim | ||||||||
| 4\88 | 54.545 | |||||||||
| 3\64 | 56.250 | |||||||||
| 5\104 | 57.692 | |||||||||
| 2\40 | 60 | |||||||||
| 5\96 | 62.5 | |||||||||
| 3\56 | 64.286 | |||||||||
| 4\72 | 66.667 | |||||||||
| 1\16 | 75 | |||||||||
Nine periods per octave
| Generator | Cents | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 0\9 | 0 | ||||||||
| 1\72 | 16.667 | Enneaportent | |||||||
| 4\279 | 17.204 | Enneaportent | |||||||
| 3\207 | 17.391 | Enneaportent | |||||||
| 2\135 | 17.778 | Enneaportent | |||||||
| 1\63 | 19.048 | Enneaportent | |||||||
| 1\54 | 22.222 | ||||||||
| 1\45 | 26.667 | ||||||||
| 2\81 | 29.63 | ||||||||
| 1\36 | 33.333 | No-five tritrizo | |||||||
| 4\135 | 35.556 | No-five tritrizo | |||||||
| 3\99 | 36.364 | No-five tritrizo | |||||||
| 2\63 | 38.095 | Niner | |||||||
| 3\90 | 40 | Niner | |||||||
| 1\27 | 44.444 | Niner | |||||||
| 4\99 | 48.485 | Ennealimmal | |||||||
| 7\171 | 49.123 | Ennealimmal | |||||||
| 3\72 | 50 | Ennealimmal | |||||||
| 20\477 | 50.314 | Novemkleismic | |||||||
| 17\405 | 50.370 | Novemkleismic | |||||||
| 14\333 | 50.451 | Novemkleismic | |||||||
| 11\261 | 50.575 | Novemkleismic | |||||||
| 8\189 | 50.794 | Novemkleismic | |||||||
| 5\117 | 51.282 | ||||||||
| 2\45 | 53.333 | ||||||||
| 5\108 | 55.556 | ||||||||
| 3\63 | 57.143 | ||||||||
| 4\81 | 59.259 | ||||||||
| 1\18 | 66.667 | ||||||||
Twelve periods per octave
See also: Compton family
| Generator | Cents | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 0\12 | 0 | ||||||||
| 1\636 | 1.887 | ||||||||
| 1\624 | 1.923 | ||||||||
| 2\1236 | 1.942 | Atomic | |||||||
| 3\1848 | 1.948 | Atomic | |||||||
| 4\2460 | 1.951 | Atomic | |||||||
| 1\612 | 1.961 | Atomic | |||||||
| 1\600 | 2 | ||||||||
| 1\588 | 2.041 | ||||||||
| 1\576 | 2.083 | ||||||||
| ... | ... | ||||||||
| 1\108 | 11.111 | ||||||||
| 1\96 | 12.5 | Compton | |||||||
| 1\84 | 14.286 | Compton | |||||||
| 3\240 | 15 | Compton | |||||||
| 2\156 | 15.385 | Compton | |||||||
| 3\228 | 15.789 | Compton | |||||||
| 1\72 | 16.667 | Compton | |||||||
| 1\60 | 20 | Compton | |||||||
| 2\108 | 22.222 | ||||||||
| 1\48 | 25 | Catler | |||||||
| 3\132 | 27.273 | Catler | |||||||
| 2\84 | 28.571 | Catler | |||||||
| 3\120 | 30 | Catler | |||||||
| 1\36 | 33.333 | Catler/Catnip | |||||||
| 4\132 | 36.364 | Catnip | |||||||
| 3\96 | 37.5 | Catnip | |||||||
| 5\156 | 38.462 | Catnip | |||||||
| 2\60 | 40 | Catnip | |||||||
| 5\144 | 41.667 | ||||||||
| 3\84 | 42.857 | Magnesium | |||||||
| 43.182 | Magnesium | ||||||||
| 16\444 | 43.243 | Magnesium | |||||||
| 13\360 | 43.333 | Magnesium | |||||||
| 10\276 | 43.378 | ||||||||
| 7\192 | 43.75 | ||||||||
| 4\108 | 44.444 | ||||||||
| 1\24 | 50 | ||||||||
See also
- Fractional-octave temperaments: Lists dozens more temperaments that have not yet been listed here.