User:Moremajorthanmajor/19edX: Difference between revisions
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==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan="5" |Degrees | |||
! colspan="2" rowspan="5" |Enneatonic | |||
! colspan="8" |Minor mode Middletown temperament | |||
! colspan="2" |Neutral mode Middletown temperament | |||
! colspan="10" |Major mode Middletown temperament | |||
|- | |- | ||
! | | ! colspan="2" rowspan="3" |Aeolian-Dorian | ||
! colspan="6" |Dorian | |||
! | | ! colspan="2" rowspan="3" |Dorian-Mixolydian | ||
! | ! colspan="8" |Mixolydian | ||
! colspan="2" rowspan="3" |Mixolydian-Ionian | |||
! | | |||
! | | |||
|- | |- | ||
| | ! colspan="2" rowspan="2" |Subpental | ||
| | ! colspan="2" rowspan="2" |Pental | ||
| | ! colspan="2" rowspan="2" |Superpental | ||
| | ! colspan="2" rowspan="2" |Subpental | ||
| | ! colspan="2" rowspan="2" |Pental | ||
| | ! colspan="4" |Superpental | ||
|- | |- | ||
! colspan="2" |Soft | |||
| | ! colspan="2" |Intense | ||
| | |||
|- | |- | ||
| | | ! |Minimum | ||
| | | ! |Maximum | ||
!Minimum | |||
!Maximum | |||
!Minimum | |||
!Maximum | |||
| | !Minimum | ||
!Maximum | |||
!Minimum | |||
! |Maximum | |||
!Minimum | |||
!Maximum | |||
! |Minimum | |||
!Maximum | |||
!Minimum | |||
!Maximum | |||
!Minimum | |||
!Maximum | |||
!Minimum | |||
! |Maximum | |||
|- | |- | ||
| | | | |1 | ||
| | | | colspan="2" |Gb | ||
| | | | |75.7895 | ||
| | | | colspan="2" |77.193 | ||
| | | | colspan="2" |78.947 | ||
| | | | colspan="2" |80.383 | ||
| | | | colspan="2" |81.203 | ||
| colspan="2" |82.105 | |||
| colspan="2" |82.895 | |||
| colspan="2" |84.2105 | |||
| colspan="2" |84.9365 | |||
| colspan="2" |87.114 | |||
| |88.421 | |||
|- | |- | ||
| | | | |2 | ||
| | | | colspan="2" |F# | ||
| | | | |151.579 | ||
| | 386. | | colspan="2" |154.386 | ||
| | | | colspan="2" |157.895 | ||
| | | | colspan="2" |160.766 | ||
| | | | colspan="2" |162.406 | ||
| colspan="2" |164.2105 | |||
| colspan="2" |165.7896 | |||
| colspan="2" |168.421 | |||
| colspan="2" |169.873 | |||
| colspan="2" |174.229 | |||
| |176.842 | |||
|- | |- | ||
| | | | |3 | ||
| | | | colspan="2" |G | ||
| | | | |227.368 | ||
| | | | colspan="2" |231.579 | ||
| | | | colspan="2" |236.842 | ||
| | | | colspan="2" |241.148 | ||
| | | | colspan="2" |243.609 | ||
| colspan="2" |246.316 | |||
| colspan="2" |248.684 | |||
| colspan="2" |252.632 | |||
| colspan="2" |254.809 | |||
| colspan="2" |261.343 | |||
| |265.263 | |||
|- | |- | ||
| | | | |4 | ||
| | | |J | ||
| | | |''A'' | ||
| | | | |303.158 | ||
| | | | colspan="2" |308.772 | ||
| | | | colspan="2" |315.7895 | ||
| | | | colspan="2" |321.531 | ||
| colspan="2" |324.812 | |||
| colspan="2" |328.421 | |||
| colspan="2" |331.579 | |||
| colspan="2" |336.842 | |||
| colspan="2" |339.746 | |||
| colspan="2" |348.457 | |||
| |353.684 | |||
|- | |- | ||
| | | | |5 | ||
| | | |Ab | ||
| | | |''Bb'' | ||
| | | | |378.947 | ||
| | | | colspan="2" |385.965 | ||
| | | | colspan="2" |394.737 | ||
| | | | colspan="2" |401.914 | ||
| colspan="2" |406.015 | |||
| colspan="2" |410.526 | |||
| colspan="2" |414.474 | |||
| colspan="2" |421.053 | |||
| colspan="2" |424.682 | |||
| colspan="2" |435.527 | |||
| |442.105 | |||
|- | |- | ||
| | | | |6 | ||
| | | |J# | ||
| | | |''A#'' | ||
| | | | |454.737 | ||
| | | | colspan="2" |463.158 | ||
| | | | colspan="2" |473.684 | ||
| | | | colspan="2" |482.297 | ||
| colspan="2" |487.218 | |||
| colspan="2" |492.632 | |||
| colspan="2" |497.368 | |||
| colspan="2" |505.263 | |||
| colspan="2" |509.619 | |||
| colspan="2" |522.686 | |||
| |530.526 | |||
|- | |- | ||
| | | | |7 | ||
| | | |A | ||
| | | |''B'' | ||
| | | | |530.526 | ||
| | | | colspan="2" |540.351 | ||
| | | | colspan="2" |552.632 | ||
| | | | colspan="2" |592.679 | ||
| colspan="2" |568.421 | |||
| colspan="2" |574.737 | |||
| colspan="2" |580.263 | |||
| colspan="2" |589.474 | |||
| colspan="2" |594.555 | |||
| colspan="2" |609.8 | |||
| |618.947 | |||
|- | |- | ||
| | | |8 | ||
| | | |B | ||
| | | |''H'' | ||
| | | |606.316 | ||
| | | | colspan="2" |617.544 | ||
| | | | colspan="2" |631.579 | ||
| | | | colspan="2" |643.062 | ||
| colspan="2" |647.624 | |||
| colspan="2" |656.842 | |||
| colspan="2" |663.158 | |||
| colspan="2" |673.684 | |||
| colspan="2" |679.491 | |||
| colspan="2" |696.915 | |||
|707.368 | |||
|- | |- | ||
| | | |9 | ||
| | | |Hb | ||
| | | |''Cb'' | ||
| | | |682.105 | ||
| | | | colspan="2" |694.737 | ||
| | | | colspan="2" |710.526 | ||
| | | | colspan="2" |723.445 | ||
| colspan="2" |730.827 | |||
| colspan="2" |738.947 | |||
| colspan="2" |746.053 | |||
| colspan="2" |757.895 | |||
| colspan="2" |764.418 | |||
| colspan="2" |784.029 | |||
|795.7895 | |||
|- | |- | ||
| | | |10 | ||
| | | |B# | ||
| | | |''H#'' | ||
| | | |757.895 | ||
| | | | colspan="2" |771.93 | ||
| | | | colspan="2" |789.474 | ||
| | | | colspan="2" |803.828 | ||
| colspan="2" |812.03 | |||
| colspan="2" |821.053 | |||
| colspan="2" |828.947 | |||
| colspan="2" |842.105 | |||
| colspan="2" |849.365 | |||
| colspan="2" |871.143 | |||
|884.2105 | |||
|- | |- | ||
| | | |11 | ||
| | | |H | ||
| | | |''C'' | ||
| | | |833.654 | ||
| | | | colspan="2" |849.123 | ||
| | | | colspan="2" |868.421 | ||
| | | | colspan="2" |884.2105 | ||
| colspan="2" |893.233 | |||
| colspan="2" |903.158 | |||
| colspan="2" |911.843 | |||
| colspan="2" |926.316 | |||
| colspan="2" |934.302 | |||
| colspan="2" |958.258 | |||
|972.632 | |||
|- | |- | ||
| | | |12 | ||
| | | |C | ||
| | | |''D'' | ||
| | | |909.474 | ||
| | | | colspan="2" |926.326 | ||
| | | | colspan="2" |947.378 | ||
| | | | colspan="2" |964.593 | ||
| colspan="2" |974.436 | |||
| colspan="2" |985.263 | |||
| colspan="2" |994.737 | |||
| colspan="2" |1010.526 | |||
| colspan="2" |1019.238 | |||
| colspan="2" |1045.372 | |||
|1061.053 | |||
|- | |- | ||
| | | |13 | ||
| | | |Db | ||
| | | |''Sb'' | ||
| | | |985.263 | ||
| | | | colspan="2" |1003.509 | ||
| | | | colspan="2" |1026.316 | ||
| | | | colspan="2" |1044.976 | ||
| colspan="2" |1055.639 | |||
| colspan="2" |1067.368 | |||
| colspan="2" |1077.612 | |||
| colspan="2" |1094.737 | |||
| colspan="2" |1104.172 | |||
| colspan="2" |1132.486 | |||
|1149.474 | |||
|- | |- | ||
| | | |14 | ||
| | |C# | ||
| | | |''D#'' | ||
| | | |1061.053 | ||
| | | | colspan="2" |1080.702 | ||
| | | | colspan="2" |1105.263 | ||
| | | | colspan="2" |1125.359 | ||
| colspan="2" |1136.842 | |||
| colspan="2" |1149.474 | |||
| colspan="2" |1160.526 | |||
| colspan="2" |1178.947 | |||
| colspan="2" |1189.111 | |||
| colspan="2" |1220.601 | |||
|1237.895 | |||
|- | |- | ||
| | | |15 | ||
| | | |D | ||
| | | |''S'' | ||
| | | |1136.842 | ||
| | | | colspan="2" |1107.895 | ||
| | | | colspan="2" |1184.2105 | ||
| | | | colspan="2" |1205.742 | ||
| colspan="2" |1218.045 | |||
| colspan="2" |1231.579 | |||
| colspan="2" |1243.421 | |||
| colspan="2" |1263.158 | |||
| colspan="2" |1274.047 | |||
| colspan="2" |1306.715 | |||
|1326.316 | |||
|- | |- | ||
| | 19 | |16 | ||
| | F | | colspan="2" |Eb | ||
|1212.632 | |||
| | 1466. | | colspan="2" |1235.088 | ||
| | 1560 | | colspan="2" |1363.156 | ||
| | | | colspan="2" |1286.124 | ||
| | 1680 | | colspan="2" |1299.248 | ||
| colspan="2" |1313.684 | |||
| colspan="2" |1326.316 | |||
| colspan="2" |1347.378 | |||
| colspan="2" |1359.984 | |||
| colspan="2" |1393.829 | |||
|1414.737 | |||
|- | |||
|17 | |||
|D# | |||
|''S#'' | |||
|1288.421 | |||
| colspan="2" |1312.181 | |||
| colspan="2" |1042.105 | |||
| colspan="2" |1366.507 | |||
| colspan="2" |1380.451 | |||
| colspan="2" |1395.7895 | |||
| colspan="2" |1408.2105 | |||
| colspan="2" |1431.579 | |||
| colspan="2" |1443.98 | |||
| colspan="2" |1480.944 | |||
|1503.158 | |||
|- | |||
|18 | |||
| colspan="2" |E | |||
|1364.2105 | |||
| colspan="2" |1389.474 | |||
| colspan="2" |1421.053 | |||
| colspan="2" |1446.89 | |||
| colspan="2" |1461.654 | |||
| colspan="2" |1477.895 | |||
| colspan="2" |1491.105 | |||
| colspan="2" |1515.7895 | |||
| colspan="2" |1526.8275 | |||
| colspan="2" |1568.058 | |||
|1591.579 | |||
|- | |||
|19 | |||
| colspan="2" |F | |||
|1440 | |||
| colspan="2" |1466.667 | |||
| colspan="2" |1500 | |||
| colspan="2" |1527.273 | |||
| colspan="2" |1542.857 | |||
| colspan="2" |1560 | |||
| colspan="2" |1575 | |||
| colspan="2" |1600 | |||
| colspan="2" |1613.793 | |||
| colspan="2" |1655.172 | |||
|1680 | |||
|}Golden tunings | |||
{| class="wikitable" | |||
|+ | |||
! rowspan="4" |Degrees | |||
! colspan="2" rowspan="4" |Enneatonic | |||
! colspan="4" |Minor mode Middletown temperament | |||
!Neutral mode Middletown temperament | |||
! colspan="5" |Major mode Middletown temperament | |||
|- | |||
! rowspan="3" |Aeolian-Dorian | |||
! colspan="3" |Dorian | |||
! rowspan="3" |Dorian-Mixolydian | |||
! colspan="4" |Mixolydian | |||
! rowspan="3" |Mixolydian-Ionian | |||
|- | |||
! rowspan="2" |Subpental | |||
! rowspan="2" |Pental | |||
! rowspan="2" |Superpental | |||
! rowspan="2" |Subpental | |||
! rowspan="2" |Pental | |||
! colspan="2" |Superpental | |||
|- | |||
!Soft | |||
!Intense | |||
|- | |||
|1 | |||
| colspan="2" |Gb | |||
|76.834 | |||
|77.571 | |||
|80.119 | |||
|80.614 | |||
|81.833 | |||
|82.675 | |||
|83.031 | |||
|84.893 | |||
|86.2825 | |||
|87.24 | |||
|- | |||
|2 | |||
| colspan="2" |F# | |||
|153.6685 | |||
|155.142 | |||
|160.239 | |||
|161.229 | |||
|163.666 | |||
|165.3495 | |||
|166.063 | |||
|169.786 | |||
|172.565 | |||
|174.48 | |||
|- | |||
|3 | |||
| colspan="2" |G | |||
|230.503 | |||
|232.713 | |||
|240.358 | |||
|241.843 | |||
|245.498 | |||
|248.024 | |||
|249.094 | |||
|254.679 | |||
|258.847 | |||
|261.7205 | |||
|- | |||
|4 | |||
|J | |||
|''A'' | |||
|307.337 | |||
|310.284 | |||
|320.4775 | |||
|322.457 | |||
|327.331 | |||
|330.7 | |||
|332.1255 | |||
|339.571 | |||
|345.13 | |||
|348.961 | |||
|- | |||
|5 | |||
|Ab | |||
|''Bb'' | |||
|384.171 | |||
|387.855 | |||
|400.597 | |||
|403.3715 | |||
|409.164 | |||
|413.374 | |||
|415.157 | |||
|424.464 | |||
|431.412 | |||
|436.201 | |||
|- | |||
|6 | |||
|J# | |||
|''A#'' | |||
|491.055 | |||
|465.426 | |||
|480.716 | |||
|483.686 | |||
|490.997 | |||
|496.0485 | |||
|498.188 | |||
|509.357 | |||
|517.695 | |||
|523.441 | |||
|- | |||
|7 | |||
|A | |||
|''B'' | |||
|537.84 | |||
|542.997 | |||
|560.836 | |||
|564.3 | |||
|572.83 | |||
|578.723 | |||
|581.22 | |||
|594.25 | |||
|603.977 | |||
|610.681 | |||
|- | |||
|8 | |||
|B | |||
|''H'' | |||
|614.074 | |||
|620.568 | |||
|640.955 | |||
|644.9145 | |||
|654.662 | |||
|661.398 | |||
|664.251 | |||
|679.143 | |||
|690.26 | |||
|697.921 | |||
|- | |||
|9 | |||
|Hb | |||
|''Cb'' | |||
|691.508 | |||
|698.139 | |||
|721.074 | |||
|725.529 | |||
|736.495 | |||
|744.073 | |||
|747.282 | |||
|764.036 | |||
|776.542 | |||
|785.1615 | |||
|- | |||
|10 | |||
|B# | |||
|''H#'' | |||
|768.3425 | |||
|775.71 | |||
|801.194 | |||
|806.143 | |||
|818.327 | |||
|826.748 | |||
|830.314 | |||
|848.9285 | |||
|862.825 | |||
|872.402 | |||
|- | |||
|11 | |||
|H | |||
|''C'' | |||
|845.177 | |||
|853.281 | |||
|881.313 | |||
|886.757 | |||
|900.161 | |||
|909.422 | |||
|913.345 | |||
|933.821 | |||
|949.107 | |||
|959.642 | |||
|- | |||
|12 | |||
|C | |||
|''D'' | |||
|922.011 | |||
|930.852 | |||
|964.4325 | |||
|967.372 | |||
|981.994 | |||
|992.097 | |||
|996.3765 | |||
|1018.714 | |||
|1035.39 | |||
|1046.882 | |||
|- | |||
|13 | |||
|Db | |||
|''Sb'' | |||
|998.845 | |||
|1008.4235 | |||
|1041.552 | |||
|1047.986 | |||
|1063.826 | |||
|1074.772 | |||
|1079.408 | |||
|1103.607 | |||
|1121.672 | |||
|1134.122 | |||
|- | |||
|14 | |||
|C# | |||
|''D#'' | |||
|1075.68 | |||
|1085.9945 | |||
|1121.671 | |||
|1128.6 | |||
|1145.659 | |||
|1157.44 | |||
|1162.439 | |||
|1188.5 | |||
|1207.955 | |||
|1221.362 | |||
|- | |||
|15 | |||
|D | |||
|''S'' | |||
|1152.514 | |||
|1163.566 | |||
|1201.791 | |||
|1209.215 | |||
|1227.492 | |||
|1240.121 | |||
|1245.471 | |||
|1273.392 | |||
|1294.237 | |||
|1308.6025 | |||
|- | |||
|16 | |||
| colspan="2" |Eb | |||
|1229.348 | |||
|1241.137 | |||
|1281.91 | |||
|1289.829 | |||
|1309.325 | |||
|1322.796 | |||
|1328.502 | |||
|1358.286 | |||
|1380.5195 | |||
|1395.843 | |||
|- | |||
|17 | |||
|D# | |||
|''S#'' | |||
|1306.182 | |||
|1318.708 | |||
|1362.029 | |||
|1370.443 | |||
|1391.158 | |||
|1405.471 | |||
|1411.533 | |||
|1443.1785 | |||
|1466.802 | |||
|1483.083 | |||
|- | |||
|18 | |||
| colspan="2" |E | |||
|1383.017 | |||
|1396.279 | |||
|1442.149 | |||
|1451.0575 | |||
|1472.99 | |||
|1488.149 | |||
|1494.565 | |||
|1528.071 | |||
|1553.0845 | |||
|1570.323 | |||
|- | |||
|19 | |||
| colspan="2" |F | |||
|1459.851 | |||
|1473.85 | |||
|1522.268 | |||
|1531.672 | |||
|1554.823 | |||
|1570.82 | |||
|1577.596 | |||
|1612.964 | |||
|1639.367 | |||
|1657.563 | |||
|} | |} |