159edo/Interval names and harmonies: Difference between revisions
All intervals now have names and descriptions... Now for the next task... |
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[[159edo]] contains all the intervals of [[53edo]], however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed. It should be noted that since 159edo does a better job of representing the 2.3.11 subgroup than [[24edo]], some of the chords listed on the page for [[24edo interval names and harmonies]] carry over to this page, even though the exact sets of enharmonics differ between the two systems. | [[159edo]] contains all the intervals of [[53edo]], however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed. It should be noted that since 159edo does a better job of representing the 2.3.11 subgroup than [[24edo]], some of the chords listed on the page for [[24edo interval names and harmonies]] carry over to this page, even though the exact sets of enharmonics differ between the two systems. | ||
== Interval chart == | |||
{| class="mw-collapsible mw-collapsed wikitable center-1" | {| class="mw-collapsible mw-collapsed wikitable center-1" | ||
Line 6: | Line 8: | ||
! Step | ! Step | ||
! Cents | ! Cents | ||
! colspan="3"| Interval Names | ! colspan="3"| Interval Names | ||
! Notes | ! Notes | ||
Line 16: | Line 13: | ||
| 0 | | 0 | ||
| 0 | | 0 | ||
| P1 | | P1 | ||
| Perfect Unison | | Perfect Unison | ||
Line 29: | Line 25: | ||
| 1 | | 1 | ||
| 7.5471698 | | 7.5471698 | ||
| R1 | | R1 | ||
| Wide Prime | | Wide Prime | ||
Line 48: | Line 39: | ||
| 2 | | 2 | ||
| 15.0943396 | | 15.0943396 | ||
| rK1 | | rK1 | ||
| Narrow Superprime | | Narrow Superprime | ||
Line 63: | Line 49: | ||
| 3 | | 3 | ||
| 22.6415094 | | 22.6415094 | ||
| K1 | | K1 | ||
| Lesser Superprime | | Lesser Superprime | ||
Line 84: | Line 65: | ||
| 4 | | 4 | ||
| 30.1886792 | | 30.1886792 | ||
| S1, kU1 | | S1, kU1 | ||
| Greater Superprime, Narrow Inframinor Second | | Greater Superprime, Narrow Inframinor Second | ||
Line 109: | Line 85: | ||
| 5 | | 5 | ||
| 37.7358491 | | 37.7358491 | ||
| um2, RkU1 | | um2, RkU1 | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
Line 133: | Line 104: | ||
| 6 | | 6 | ||
| 45.2830189 | | 45.2830189 | ||
| kkm2, Rum2, rU1 | | kkm2, Rum2, rU1 | ||
| Wide Inframinor Second, Narrow Ultraprime | | Wide Inframinor Second, Narrow Ultraprime | ||
Line 155: | Line 121: | ||
| 7 | | 7 | ||
| 52.8301887 | | 52.8301887 | ||
| U1, rKum2 | | U1, rKum2 | ||
| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
Line 179: | Line 140: | ||
| 8 | | 8 | ||
| 60.3773585 | | 60.3773585 | ||
| sm2, Kum2, uA1 | | sm2, Kum2, uA1 | ||
| Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | | Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | ||
Line 199: | Line 155: | ||
| 9 | | 9 | ||
| 67.9245283 | | 67.9245283 | ||
| km2, RuA1, kkA1 | | km2, RuA1, kkA1 | ||
| Greater Subminor Second, Diptolemaic Augmented Prime | | Greater Subminor Second, Diptolemaic Augmented Prime | ||
Line 217: | Line 168: | ||
| 10 | | 10 | ||
| 75.4716981 | | 75.4716981 | ||
| Rkm2, rKuA1 | | Rkm2, rKuA1 | ||
| Wide Subminor Second, Lesser Sub-Augmented Prime | | Wide Subminor Second, Lesser Sub-Augmented Prime | ||
Line 236: | Line 182: | ||
| 11 | | 11 | ||
| 83.0188679 | | 83.0188679 | ||
| rm2, KuA1 | | rm2, KuA1 | ||
| Narrow Minor Second, Greater Sub-Augmented Prime | | Narrow Minor Second, Greater Sub-Augmented Prime | ||
Line 253: | Line 194: | ||
| 12 | | 12 | ||
| 90.5660377 | | 90.5660377 | ||
| m2, kA1 | | m2, kA1 | ||
| Pythagorean Minor Second, Ptolemaic Augmented Prime | | Pythagorean Minor Second, Ptolemaic Augmented Prime | ||
Line 277: | Line 213: | ||
| 13 | | 13 | ||
| 98.1132075 | | 98.1132075 | ||
| Rm2, RkA1 | | Rm2, RkA1 | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
Line 296: | Line 227: | ||
| 14 | | 14 | ||
| 105.6603774 | | 105.6603774 | ||
| rKm2, rA1 | | rKm2, rA1 | ||
| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
Line 315: | Line 241: | ||
| 15 | | 15 | ||
| 113.2075472 | | 113.2075472 | ||
| Km2, A1 | | Km2, A1 | ||
| Ptolemaic Minor Second, Pythagorean Augmented Prime | | Ptolemaic Minor Second, Pythagorean Augmented Prime | ||
Line 339: | Line 260: | ||
| 16 | | 16 | ||
| 120.7547170 | | 120.7547170 | ||
| RKm2, kn2, RA1 | | RKm2, kn2, RA1 | ||
| Wide Minor Second, Artoretromean Augmented Prime | | Wide Minor Second, Artoretromean Augmented Prime | ||
Line 356: | Line 272: | ||
| 17 | | 17 | ||
| 128.3018868 | | 128.3018868 | ||
| kN2, rKA1 | | kN2, rKA1 | ||
| Lesser Supraminor Second, Tendoretromean Augmented Prime | | Lesser Supraminor Second, Tendoretromean Augmented Prime | ||
Line 375: | Line 286: | ||
| 18 | | 18 | ||
| 135.8490566 | | 135.8490566 | ||
| KKm2, rn2, KA1 | | KKm2, rn2, KA1 | ||
| Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | | Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | ||
Line 393: | Line 299: | ||
| 19 | | 19 | ||
| 143.3962264 | | 143.3962264 | ||
| n2, SA1 | | n2, SA1 | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
Line 415: | Line 316: | ||
| 20 | | 20 | ||
| 150.9433962 | | 150.9433962 | ||
| N2, RkUA1 | | N2, RkUA1 | ||
| Tendoneutral Second, Greater Super-Augmented Prime | | Tendoneutral Second, Greater Super-Augmented Prime | ||
Line 436: | Line 332: | ||
|- | |- | ||
| 21 | | 21 | ||
| 561/512, 1024/935 | | 561/512, 1024/935 | ||
| kkM2, RN2, rUA1 | | kkM2, RN2, rUA1 | ||
Line 453: | Line 344: | ||
| 22 | | 22 | ||
| 166.0377358 | | 166.0377358 | ||
| Kn2, UA1 | |||
| Greater Submajor Second, Ultra-Augmented Prime | |||
| Kn2, UA1 | |||
| Greater Submajor Second, Ultra-Augmented Prime | |||
| Ed<↑, Dt#<, Fb↓/ | | Ed<↑, Dt#<, Fb↓/ | ||
| This interval… | | This interval… | ||
Line 472: | Line 358: | ||
| 23 | | 23 | ||
| 173.5849057 | | 173.5849057 | ||
| rkM2, KN2 | | rkM2, KN2 | ||
| Narrow Major Second | | Narrow Major Second | ||
Line 488: | Line 369: | ||
| 24 | | 24 | ||
| 181.1320755 | | 181.1320755 | ||
| kM2 | | kM2 | ||
| Ptolemaic Major Second | | Ptolemaic Major Second | ||
Line 510: | Line 386: | ||
| 25 | | 25 | ||
| 188.6792458 | | 188.6792458 | ||
| RkM2 | | RkM2 | ||
| Artomean Major Second | | Artomean Major Second | ||
Line 527: | Line 398: | ||
| 26 | | 26 | ||
| 196.2264151 | | 196.2264151 | ||
| rM2 | | rM2 | ||
| Tendomean Major Second | | Tendomean Major Second | ||
Line 544: | Line 410: | ||
| 27 | | 27 | ||
| 203.7735849 | | 203.7735849 | ||
| M2 | | M2 | ||
| Pythagorean Major Second | | Pythagorean Major Second | ||
Line 567: | Line 428: | ||
| 28 | | 28 | ||
| 211.3207547 | | 211.3207547 | ||
| RM2 | | RM2 | ||
| Wide Major Second | | Wide Major Second | ||
Line 584: | Line 440: | ||
| 29 | | 29 | ||
| 218.8679245 | | 218.8679245 | ||
| rKM2 | | rKM2 | ||
| Narrow Supermajor Second | | Narrow Supermajor Second | ||
Line 604: | Line 455: | ||
| 30 | | 30 | ||
| 226.4150943 | | 226.4150943 | ||
| KM2 | | KM2 | ||
| Lesser Supermajor Second | | Lesser Supermajor Second | ||
Line 623: | Line 469: | ||
| 31 | | 31 | ||
| 233.9622642 | | 233.9622642 | ||
| SM2, kUM2 | | SM2, kUM2 | ||
| Greater Supermajor Second, Narrow Inframinor Third | | Greater Supermajor Second, Narrow Inframinor Third | ||
Line 644: | Line 485: | ||
| 32 | | 32 | ||
| 241.5094340 | | 241.5094340 | ||
| um3, RkUM2 | |||
| um3, RkUM2 | |||
| Inframinor Third, Wide Supermajor Second | | Inframinor Third, Wide Supermajor Second | ||
| Fd>, Et>↓ | | Fd>, Et>↓ | ||
Line 662: | Line 498: | ||
| 33 | | 33 | ||
| 249.0566038 | | 249.0566038 | ||
| kkm3, KKM2, Rum3, rUM2 | | kkm3, KKM2, Rum3, rUM2 | ||
| Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | | Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | ||
Line 681: | Line 512: | ||
| 34 | | 34 | ||
| 256.6037736 | | 256.6037736 | ||
| UM2, rKum3 | | UM2, rKum3 | ||
| Ultramajor Second, Narrow Subminor Third | | Ultramajor Second, Narrow Subminor Third | ||
Line 698: | Line 524: | ||
| 35 | | 35 | ||
| 264.1509434 | | 264.1509434 | ||
| sm3, Kum3 | | sm3, Kum3 | ||
| Lesser Subminor Third, Wide Ultramajor Second | | Lesser Subminor Third, Wide Ultramajor Second | ||
Line 718: | Line 539: | ||
| 36 | | 36 | ||
| 271.6981132 | | 271.6981132 | ||
| km3 | | km3 | ||
| Greater Subminor Third | | Greater Subminor Third | ||
Line 738: | Line 554: | ||
| 37 | | 37 | ||
| 279.2452830 | | 279.2452830 | ||
| Rkm3 | | Rkm3 | ||
| Wide Subminor Third | | Wide Subminor Third | ||
Line 755: | Line 566: | ||
| 38 | | 38 | ||
| 286.7924528 | | 286.7924528 | ||
| rm3 | | rm3 | ||
| Narrow Minor Third | | Narrow Minor Third | ||
Line 773: | Line 579: | ||
| 39 | | 39 | ||
| 294.3396226 | | 294.3396226 | ||
| m3 | | m3 | ||
| Pythagorean Minor Third | | Pythagorean Minor Third | ||
Line 793: | Line 594: | ||
| 40 | | 40 | ||
| 301.8867925 | | 301.8867925 | ||
| Rm3 | | Rm3 | ||
| Artomean Minor Third | | Artomean Minor Third | ||
Line 810: | Line 606: | ||
| 41 | | 41 | ||
| 309.4339622 | | 309.4339622 | ||
| rKm3 | |||
| rKm3 | |||
| Tendomean Minor Third | | Tendomean Minor Third | ||
| F↑\ | | F↑\ | ||
Line 829: | Line 620: | ||
| 42 | | 42 | ||
| 316.9811321 | | 316.9811321 | ||
| Km3 | | Km3 | ||
| Ptolemaic Minor Third | | Ptolemaic Minor Third | ||
Line 850: | Line 636: | ||
| 43 | | 43 | ||
| 324.5283019 | | 324.5283019 | ||
| RKm3, kn3 | | RKm3, kn3 | ||
| Wide Minor Third | | Wide Minor Third | ||
Line 868: | Line 649: | ||
| 44 | | 44 | ||
| 332.0754717 | | 332.0754717 | ||
| kN3, ud4 | | kN3, ud4 | ||
| Lesser Supraminor Third, Infra-Diminished Fourth | | Lesser Supraminor Third, Infra-Diminished Fourth | ||
Line 884: | Line 660: | ||
| 45 | | 45 | ||
| 339.6226415 | | 339.6226415 | ||
| KKm3, rn3, Rud4 | | KKm3, rn3, Rud4 | ||
| Greater Supraminor Third, Diretroptolemaic Diminished Fourth | | Greater Supraminor Third, Diretroptolemaic Diminished Fourth | ||
Line 904: | Line 675: | ||
| 46 | | 46 | ||
| 347.1698113 | | 347.1698113 | ||
| n3, rKud4 | | n3, rKud4 | ||
| Artoneutral Third, Lesser Sub-Diminished Fourth | | Artoneutral Third, Lesser Sub-Diminished Fourth | ||
Line 927: | Line 693: | ||
| 47 | | 47 | ||
| 354.7169811 | | 354.7169811 | ||
| N3, sd4, Kud4 | | N3, sd4, Kud4 | ||
| Tendoneutral Third, Greater Sub-Diminished Fourth | | Tendoneutral Third, Greater Sub-Diminished Fourth | ||
Line 947: | Line 708: | ||
| 48 | | 48 | ||
| 362.2641509 | | 362.2641509 | ||
| kkM3, RN3, kd4 | | kkM3, RN3, kd4 | ||
| Lesser Submajor Third, Retroptolemaic Diminished Fourth | | Lesser Submajor Third, Retroptolemaic Diminished Fourth | ||
Line 965: | Line 721: | ||
| 49 | | 49 | ||
| 369.8113208 | | 369.8113208 | ||
| Kn3, Rkd4 | | Kn3, Rkd4 | ||
| Greater Submajor Third, Artoretromean Diminished Fourth | | Greater Submajor Third, Artoretromean Diminished Fourth | ||
Line 982: | Line 733: | ||
| 50 | | 50 | ||
| 377.3584906 | | 377.3584906 | ||
| rkM3, KN3, rd4 | | rkM3, KN3, rd4 | ||
| Narrow Major Third, Tendoretromean Diminished Fourth | | Narrow Major Third, Tendoretromean Diminished Fourth | ||
Line 1,001: | Line 747: | ||
| 51 | | 51 | ||
| 384.9056604 | | 384.9056604 | ||
| kM3, d4 | | kM3, d4 | ||
| Ptolemaic Major Third, Pythagorean Diminished Fourth | | Ptolemaic Major Third, Pythagorean Diminished Fourth | ||
Line 1,025: | Line 766: | ||
| 52 | | 52 | ||
| 392.4528302 | | 392.4528302 | ||
| RkM3, Rd4 | | RkM3, Rd4 | ||
| Artomean Major Third, Artomean Diminished Fourth | | Artomean Major Third, Artomean Diminished Fourth | ||
Line 1,040: | Line 776: | ||
| 53 | | 53 | ||
| 400 | | 400 | ||
| rM3, rKd4 | | rM3, rKd4 | ||
| Tendomean Major Third, Tendomean Diminished Fourth | | Tendomean Major Third, Tendomean Diminished Fourth | ||
Line 1,059: | Line 790: | ||
| 54 | | 54 | ||
| 407.5471698 | | 407.5471698 | ||
| M3, Kd4 | | M3, Kd4 | ||
| Pythagorean Major Third, Ptolemaic Diminished Fourth | | Pythagorean Major Third, Ptolemaic Diminished Fourth | ||
Line 1,081: | Line 807: | ||
| 55 | | 55 | ||
| 415.0943396 | | 415.0943396 | ||
| RM3, kUd4 | | RM3, kUd4 | ||
| Wide Major Third, Lesser Super-Diminished Fourth | | Wide Major Third, Lesser Super-Diminished Fourth | ||
Line 1,100: | Line 821: | ||
| 56 | | 56 | ||
| 422.6415094 | | 422.6415094 | ||
| rKM3, RkUd4 | | rKM3, RkUd4 | ||
| Narrow Supermajor Third, Greater Super-Diminished Fourth | | Narrow Supermajor Third, Greater Super-Diminished Fourth | ||
Line 1,117: | Line 833: | ||
| 57 | | 57 | ||
| 430.1886792 | | 430.1886792 | ||
| KM3, rUd4, KKd4 | | KM3, rUd4, KKd4 | ||
| Lesser Supermajor Third, Diptolemaic Diminished Fourth | | Lesser Supermajor Third, Diptolemaic Diminished Fourth | ||
Line 1,134: | Line 845: | ||
| 58 | | 58 | ||
| 437.7358491 | | 437.7358491 | ||
| SM3, kUM3, rm4, Ud4 | | SM3, kUM3, rm4, Ud4 | ||
| Greater Supermajor Third, Ultra-Diminished Fourth | | Greater Supermajor Third, Ultra-Diminished Fourth | ||
Line 1,152: | Line 858: | ||
| 59 | | 59 | ||
| 445.2830189 | | 445.2830189 | ||
| m4, RkUM3 | | m4, RkUM3 | ||
| Paraminor Fourth, Wide Supermajor Third | | Paraminor Fourth, Wide Supermajor Third | ||
Line 1,173: | Line 874: | ||
| 60 | | 60 | ||
| 452.8301887 | | 452.8301887 | ||
| Rm4, KKM3, rUM3 | | Rm4, KKM3, rUM3 | ||
| Wide Paraminor Fourth, Narrow Ultramajor Third | | Wide Paraminor Fourth, Narrow Ultramajor Third | ||
Line 1,189: | Line 885: | ||
| 61 | | 61 | ||
| 460.3773585 | | 460.3773585 | ||
| UM3, rKm4 | | UM3, rKm4 | ||
| Ultramajor Third, Narrow Grave Fourth | | Ultramajor Third, Narrow Grave Fourth | ||
Line 1,207: | Line 898: | ||
| 62 | | 62 | ||
| 467.9245283 | | 467.9245283 | ||
| s4, Km4 | | s4, Km4 | ||
| Lesser Grave Fourth, Wide Ultramajor Third | | Lesser Grave Fourth, Wide Ultramajor Third | ||
Line 1,224: | Line 910: | ||
| 63 | | 63 | ||
| 475.4716981 | | 475.4716981 | ||
| k4 | | k4 | ||
| Greater Grave Fourth | | Greater Grave Fourth | ||
Line 1,239: | Line 920: | ||
| 64 | | 64 | ||
| 483.0188679 | | 483.0188679 | ||
| Rk4 | | Rk4 | ||
| Wide Grave Fourth | | Wide Grave Fourth | ||
Line 1,255: | Line 931: | ||
| 65 | | 65 | ||
| 490.5660377 | | 490.5660377 | ||
| r4 | | r4 | ||
| Narrow Fourth | | Narrow Fourth | ||
Line 1,273: | Line 944: | ||
| 66 | | 66 | ||
| 498.1132075 | | 498.1132075 | ||
| P4 | | P4 | ||
| Perfect Fourth | | Perfect Fourth | ||
Line 1,301: | Line 967: | ||
| 67 | | 67 | ||
| 505.6603774 | | 505.6603774 | ||
| R4 | | R4 | ||
| Wide Fourth | | Wide Fourth | ||
Line 1,319: | Line 980: | ||
| 68 | | 68 | ||
| 513.2075472 | | 513.2075472 | ||
| rK4 | | rK4 | ||
| Narrow Acute Fourth | | Narrow Acute Fourth | ||
Line 1,336: | Line 992: | ||
| 69 | | 69 | ||
| 520.7547170 | | 520.7547170 | ||
| K4 | | K4 | ||
| Lesser Acute Fourth | | Lesser Acute Fourth | ||
Line 1,355: | Line 1,006: | ||
| 70 | | 70 | ||
| 528.3018868 | | 528.3018868 | ||
| S4, kM4 | | S4, kM4 | ||
| Greater Acute Fourth | | Greater Acute Fourth | ||
Line 1,371: | Line 1,017: | ||
| 71 | | 71 | ||
| 535.8490566 | | 535.8490566 | ||
| RkM4, ud5 | |||
| Wide Acute Fourth, Infra-Diminished Fifth | |||
| RkM4, ud5 | |||
| Wide Acute Fourth, Infra-Diminished Fifth | |||
| Gt>↓, Adb> | | Gt>↓, Adb> | ||
| This interval… | | This interval… | ||
Line 1,389: | Line 1,030: | ||
| 72 | | 72 | ||
| 543.3962264 | | 543.3962264 | ||
| rM4, Rud5 | | rM4, Rud5 | ||
| Narrow Paramajor Fourth, Diretroptolemaic Diminished Fifth | | Narrow Paramajor Fourth, Diretroptolemaic Diminished Fifth | ||
Line 1,406: | Line 1,042: | ||
| 73 | | 73 | ||
| 550.9433962 | | 550.9433962 | ||
| M4, rKud5 | | M4, rKud5 | ||
| Paramajor Fourth, Lesser Sub-Diminished Fifth | | Paramajor Fourth, Lesser Sub-Diminished Fifth | ||
Line 1,430: | Line 1,061: | ||
| 74 | | 74 | ||
| 558.4905660 | | 558.4905660 | ||
| RM4, uA4, Kud5 | | RM4, uA4, Kud5 | ||
| Infra-Augmented Fourth, Greater Sub-Diminished Fifth | | Infra-Augmented Fourth, Greater Sub-Diminished Fifth | ||
Line 1,468: | Line 1,094: | ||
| 76 | | 76 | ||
| 573.5849057 | | 573.5849057 | ||
| rKuA4, Rkd5 | | rKuA4, Rkd5 | ||
| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | | Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | ||
Line 1,484: | Line 1,105: | ||
| 77 | | 77 | ||
| 581.1320755 | | 581.1320755 | ||
| KuA4, rd5 | | KuA4, rd5 | ||
| Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | | Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | ||
Line 1,501: | Line 1,117: | ||
| 78 | | 78 | ||
| 588.6792458 | | 588.6792458 | ||
| kA4, d5 | | kA4, d5 | ||
| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | | Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | ||
Line 1,519: | Line 1,130: | ||
| 79 | | 79 | ||
| 596.2264151 | | 596.2264151 | ||
| RkA4, Rd5 | | RkA4, Rd5 | ||
| Artomean Augmented Fourth, Artomean Diminished Fifth | | Artomean Augmented Fourth, Artomean Diminished Fifth | ||
Line 1,537: | Line 1,143: | ||
| 80 | | 80 | ||
| 603.7735849 | | 603.7735849 | ||
| rKd5, rA4 | | rKd5, rA4 | ||
| Tendomean Diminished Fifth, Tendomean Augmented Fourth | | Tendomean Diminished Fifth, Tendomean Augmented Fourth | ||
Line 1,555: | Line 1,156: | ||
| 81 | | 81 | ||
| 611.3207547 | | 611.3207547 | ||
| Kd5, A4 | | Kd5, A4 | ||
| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | | Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | ||
Line 1,573: | Line 1,169: | ||
| 82 | | 82 | ||
| 618.8679245 | | 618.8679245 | ||
| kUd5, RA4 | | kUd5, RA4 | ||
| Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | | Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | ||
Line 1,590: | Line 1,181: | ||
| 83 | | 83 | ||
| 626.4150943 | | 626.4150943 | ||
| RkUd5, rKA4 | | RkUd5, rKA4 | ||
| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | | Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | ||
Line 1,606: | Line 1,192: | ||
| 84 | | 84 | ||
| 633.9622642 | | 633.9622642 | ||
| KKd5, rUDd5, KA4 | | KKd5, rUDd5, KA4 | ||
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | | Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | ||
Line 1,626: | Line 1,207: | ||
| 85 | | 85 | ||
| 641.5094340 | | 641.5094340 | ||
| rm5, Ud5, kUA4 | | rm5, Ud5, kUA4 | ||
| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | | Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | ||
Line 1,643: | Line 1,219: | ||
| 86 | | 86 | ||
| 649.0566038 | | 649.0566038 | ||
| m5, RkUA4 | | m5, RkUA4 | ||
| Paraminor Fifth, Greater Super-Augmented Fourth | | Paraminor Fifth, Greater Super-Augmented Fourth | ||
Line 1,667: | Line 1,238: | ||
| 87 | | 87 | ||
| 656.6037736 | | 656.6037736 | ||
| Rm5, rUA4 | | Rm5, rUA4 | ||
| Wide Paraminor Fifth, Diretroptolemaic Augmented Fourth | | Wide Paraminor Fifth, Diretroptolemaic Augmented Fourth | ||
Line 1,684: | Line 1,250: | ||
| 88 | | 88 | ||
| 664.1509434 | | 664.1509434 | ||
| rKm5, UA4 | | rKm5, UA4 | ||
| Narrow Grave Fifth, Ultra-Augmented Fourth | | Narrow Grave Fifth, Ultra-Augmented Fourth | ||
Line 1,702: | Line 1,263: | ||
| 89 | | 89 | ||
| 671.6981132 | | 671.6981132 | ||
| s5, Km5 | | s5, Km5 | ||
| Lesser Grave Fifth | | Lesser Grave Fifth | ||
Line 1,717: | Line 1,273: | ||
| 90 | | 90 | ||
| 679.2452830 | | 679.2452830 | ||
| k5 | | k5 | ||
| Greater Grave Fifth | | Greater Grave Fifth | ||
Line 1,736: | Line 1,287: | ||
| 91 | | 91 | ||
| 686.7924528 | | 686.7924528 | ||
| Rk5 | | Rk5 | ||
| Wide Grave Fifth | | Wide Grave Fifth | ||
Line 1,753: | Line 1,299: | ||
| 92 | | 92 | ||
| 694.3396226 | | 694.3396226 | ||
| r5 | | r5 | ||
| Narrow Fifth | | Narrow Fifth | ||
Line 1,772: | Line 1,313: | ||
| 93 | | 93 | ||
| 701.8867925 | | 701.8867925 | ||
| P5 | | P5 | ||
| Perfect Fifth | | Perfect Fifth | ||
Line 1,800: | Line 1,336: | ||
| 94 | | 94 | ||
| 709.4339622 | | 709.4339622 | ||
| R5 | | R5 | ||
| Wide Fifth | | Wide Fifth | ||
Line 1,819: | Line 1,350: | ||
| 95 | | 95 | ||
| 716.9811321 | | 716.9811321 | ||
| rK5 | | rK5 | ||
| Narrow Acute Fifth | | Narrow Acute Fifth | ||
Line 1,835: | Line 1,361: | ||
| 96 | | 96 | ||
| 724.5283019 | | 724.5283019 | ||
| K5 | | K5 | ||
| Lesser Acute Fifth | | Lesser Acute Fifth | ||
Line 1,866: | Line 1,387: | ||
| 98 | | 98 | ||
| 739.6226415 | | 739.6226415 | ||
| um6, RkM5 | | um6, RkM5 | ||
| Inframinor Sixth, Wide Acute Fifth | | Inframinor Sixth, Wide Acute Fifth | ||
Line 1,883: | Line 1,399: | ||
| 99 | | 99 | ||
| 747.1698113 | | 747.1698113 | ||
| Rm4, KKM3, rUM3 | | Rm4, KKM3, rUM3 | ||
| Narrow Paramajor Fifth, Wide Inframinor Sixth | | Narrow Paramajor Fifth, Wide Inframinor Sixth | ||
Line 1,899: | Line 1,411: | ||
| 100 | | 100 | ||
| 754.7169811 | | 754.7169811 | ||
| M5, rKum6 | | M5, rKum6 | ||
| Paramajor Fifth, Narrow Subminor Sixth | | Paramajor Fifth, Narrow Subminor Sixth | ||
Line 1,920: | Line 1,427: | ||
| 101 | | 101 | ||
| 762.2641509 | | 762.2641509 | ||
| sm6, Kum6, RM5, uA5 | | sm6, Kum6, RM5, uA5 | ||
| Lesser Subminor Sixth, Infra-Augmented Fifth | | Lesser Subminor Sixth, Infra-Augmented Fifth | ||
Line 1,937: | Line 1,439: | ||
| 102 | | 102 | ||
| 769.8113208 | | 769.8113208 | ||
| km6, RuA5, kkA5 | | km6, RuA5, kkA5 | ||
| Greater Subminor Sixth, Diptolemaic Augmented Fifth | | Greater Subminor Sixth, Diptolemaic Augmented Fifth | ||
Line 1,956: | Line 1,453: | ||
| 103 | | 103 | ||
| 777.3584906 | | 777.3584906 | ||
| Rkm6, rKuA5 | | Rkm6, rKuA5 | ||
| Wide Subminor Sixth, Lesser Sub-Augmented Fifth | | Wide Subminor Sixth, Lesser Sub-Augmented Fifth | ||
Line 1,973: | Line 1,465: | ||
| 104 | | 104 | ||
| 784.9056604 | | 784.9056604 | ||
| rm6, KuA5 | | rm6, KuA5 | ||
| Narrow Minor Sixth, Greater Sub-Augmented Fifth | | Narrow Minor Sixth, Greater Sub-Augmented Fifth | ||
Line 1,991: | Line 1,478: | ||
| 105 | | 105 | ||
| 792.4528302 | | 792.4528302 | ||
| m6, kA5 | | m6, kA5 | ||
| Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | | Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | ||
Line 2,011: | Line 1,493: | ||
| 106 | | 106 | ||
| 800 | | 800 | ||
| Rm6, RkA5 | | Rm6, RkA5 | ||
| Artomean Minor Sixth, Artomean Augmented Fifth | | Artomean Minor Sixth, Artomean Augmented Fifth | ||
Line 2,028: | Line 1,505: | ||
| 107 | | 107 | ||
| 807.5471698 | | 807.5471698 | ||
| rKm6, rA5 | | rKm6, rA5 | ||
| Tendomean Minor Sixth, Tendomean Augmented Fifth | | Tendomean Minor Sixth, Tendomean Augmented Fifth | ||
Line 2,042: | Line 1,514: | ||
| 108 | | 108 | ||
| 815.0943396 | | 815.0943396 | ||
| Km6, A5 | | Km6, A5 | ||
| Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | | Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | ||
Line 2,066: | Line 1,533: | ||
| 109 | | 109 | ||
| 822.6415094 | | 822.6415094 | ||
| RKm6, kn6, RA5 | | RKm6, kn6, RA5 | ||
|Wide Minor Sixth, Artoretromean Augmented Fifth | |Wide Minor Sixth, Artoretromean Augmented Fifth | ||
Line 2,084: | Line 1,546: | ||
| 110 | | 110 | ||
| 830.1886792 | | 830.1886792 | ||
| kN6, rKA5 | | kN6, rKA5 | ||
| Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | | Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | ||
Line 2,100: | Line 1,557: | ||
| 111 | | 111 | ||
| 837.7358491 | | 837.7358491 | ||
| KKm6, rn6, KA5 | | KKm6, rn6, KA5 | ||
| Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | | Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | ||
Line 2,118: | Line 1,570: | ||
| 112 | | 112 | ||
| 845.2830189 | | 845.2830189 | ||
| n6, SA5, kUA5 | | n6, SA5, kUA5 | ||
| Artoneutral Sixth, Lesser Super-Augmented Fifth | | Artoneutral Sixth, Lesser Super-Augmented Fifth | ||
Line 2,137: | Line 1,584: | ||
| 113 | | 113 | ||
| 852.8301887 | | 852.8301887 | ||
| N6, RkUA5 | | N6, RkUA5 | ||
| Tendoneutral Sixth, Greater Super-Augmented Fifth | | Tendoneutral Sixth, Greater Super-Augmented Fifth | ||
Line 2,160: | Line 1,602: | ||
| 114 | | 114 | ||
| 860.3773585 | | 860.3773585 | ||
| kkM6, RN6, rUA5 | | kkM6, RN6, rUA5 | ||
| Lesser Submajor Sixth, Diretroptolemaic Augmented Fifth | | Lesser Submajor Sixth, Diretroptolemaic Augmented Fifth | ||
Line 2,179: | Line 1,616: | ||
| 115 | | 115 | ||
| 867.9245283 | | 867.9245283 | ||
| Kn6, UA5 | | Kn6, UA5 | ||
| Greater Submajor Sixth, Ultra-Augmented Fifth | | Greater Submajor Sixth, Ultra-Augmented Fifth | ||
Line 2,193: | Line 1,625: | ||
| 116 | | 116 | ||
| 875.4716981 | | 875.4716981 | ||
| rkM6, KN6 | | rkM6, KN6 | ||
| Narrow Major Sixth | | Narrow Major Sixth | ||
Line 2,209: | Line 1,636: | ||
| 117 | | 117 | ||
| 883.0188679 | | 883.0188679 | ||
| kM6 | | kM6 | ||
| Ptolemaic Major Sixth | | Ptolemaic Major Sixth | ||
Line 2,231: | Line 1,653: | ||
| 118 | | 118 | ||
| 890.5660377 | | 890.5660377 | ||
| RkM6 | | RkM6 | ||
| Artomean Major Sixth | | Artomean Major Sixth | ||
Line 2,247: | Line 1,664: | ||
| 119 | | 119 | ||
| 898.1132075 | | 898.1132075 | ||
| rM6 | | rM6 | ||
| Tendomean Major Sixth | | Tendomean Major Sixth | ||
Line 2,263: | Line 1,675: | ||
| 120 | | 120 | ||
| 905.6603774 | | 905.6603774 | ||
| M6 | | M6 | ||
| Pythagorean Major Sixth | | Pythagorean Major Sixth | ||
Line 2,284: | Line 1,691: | ||
| 121 | | 121 | ||
| 913.2075472 | | 913.2075472 | ||
| RM6 | | RM6 | ||
| Wide Major Sixth | | Wide Major Sixth | ||
Line 2,301: | Line 1,703: | ||
| 122 | | 122 | ||
| 920.7547170 | | 920.7547170 | ||
| rKM6 | | rKM6 | ||
| Narrow Supermajor Sixth | | Narrow Supermajor Sixth | ||
Line 2,318: | Line 1,715: | ||
| 123 | | 123 | ||
| 928.3018868 | | 928.3018868 | ||
| KM6 | | KM6 | ||
| Lesser Supermajor Sixth | | Lesser Supermajor Sixth | ||
Line 2,338: | Line 1,730: | ||
| 124 | | 124 | ||
| 935.8490566 | | 935.8490566 | ||
| SM6, kUM6 | | SM6, kUM6 | ||
| Greater Supermajor Second, Narrow Inframinor Seventh | | Greater Supermajor Second, Narrow Inframinor Seventh | ||
Line 2,357: | Line 1,744: | ||
| 125 | | 125 | ||
| 943.3962264 | | 943.3962264 | ||
| um7, RkUM6 | | um7, RkUM6 | ||
| Inframinor Seventh, Wide Supermajor Sixth | | Inframinor Seventh, Wide Supermajor Sixth | ||
Line 2,373: | Line 1,755: | ||
| 126 | | 126 | ||
| 950.9433962 | | 950.9433962 | ||
| KKM6, kkm7, rUM6, Rum7 | | KKM6, kkm7, rUM6, Rum7 | ||
| Narrow Ultramajor Sixth, Wide Inframinor Seventh, Semitwelfth | | Narrow Ultramajor Sixth, Wide Inframinor Seventh, Semitwelfth | ||
Line 2,392: | Line 1,769: | ||
| 127 | | 127 | ||
| 958.4905660 | | 958.4905660 | ||
| UM6, rKum7 | | UM6, rKum7 | ||
| Ultramajor Sixth, Narrow Subminor Seventh | | Ultramajor Sixth, Narrow Subminor Seventh | ||
Line 2,409: | Line 1,781: | ||
| 128 | | 128 | ||
| 966.0377358 | | 966.0377358 | ||
| sm7, Kum7 | | sm7, Kum7 | ||
| Lesser Subminor Seventh, Wide Ultramajor Sixth | | Lesser Subminor Seventh, Wide Ultramajor Sixth | ||
Line 2,429: | Line 1,796: | ||
| 129 | | 129 | ||
| 973.5849057 | | 973.5849057 | ||
| km7 | | km7 | ||
| Greater Subminor Seventh | | Greater Subminor Seventh | ||
Line 2,448: | Line 1,810: | ||
| 130 | | 130 | ||
| 981.1320755 | | 981.1320755 | ||
| Rkm7 | | Rkm7 | ||
| Wide Subminor Seventh | | Wide Subminor Seventh | ||
Line 2,467: | Line 1,824: | ||
| 131 | | 131 | ||
| 988.6792458 | | 988.6792458 | ||
| rm7 | | rm7 | ||
| Narrow Minor Seventh | | Narrow Minor Seventh | ||
Line 2,483: | Line 1,835: | ||
| 132 | | 132 | ||
| 996.2264151 | | 996.2264151 | ||
| m7 | | m7 | ||
| Pythagorean Minor Seventh | | Pythagorean Minor Seventh | ||
Line 2,503: | Line 1,850: | ||
| 133 | | 133 | ||
| 1003.7735849 | | 1003.7735849 | ||
| Rm7 | | Rm7 | ||
| Artomean Minor Seventh | | Artomean Minor Seventh | ||
Line 2,520: | Line 1,862: | ||
| 134 | | 134 | ||
| 1011.3207547 | | 1011.3207547 | ||
| rKm7 | | rKm7 | ||
| Tendomean Minor Seventh | | Tendomean Minor Seventh | ||
Line 2,536: | Line 1,873: | ||
| 135 | | 135 | ||
| 1018.8679245 | | 1018.8679245 | ||
| kM2 | | kM2 | ||
| Ptolemaic Minor Seventh | | Ptolemaic Minor Seventh | ||
Line 2,556: | Line 1,888: | ||
| 136 | | 136 | ||
| 1026.4150943 | | 1026.4150943 | ||
| RKm7, kn7 | | RKm7, kn7 | ||
| Wide Minor Seventh | | Wide Minor Seventh | ||
Line 2,571: | Line 1,898: | ||
| 137 | | 137 | ||
| 1033.9622642 | | 1033.9622642 | ||
| kN7, ud8 | | kN7, ud8 | ||
| Lesser Supraminor Seventh, Infra-Diminished Octave | | Lesser Supraminor Seventh, Infra-Diminished Octave | ||
Line 2,589: | Line 1,911: | ||
| 138 | | 138 | ||
| 1041.5094340 | | 1041.5094340 | ||
| KKm7, rn7, Rud8 | | KKm7, rn7, Rud8 | ||
| Greater Supraminor Seventh, Diretroptolemaic Diminished Octave | | Greater Supraminor Seventh, Diretroptolemaic Diminished Octave | ||
Line 2,604: | Line 1,921: | ||
| 139 | | 139 | ||
| 1049.0566038 | | 1049.0566038 | ||
| n7, rKud8 | | n7, rKud8 | ||
| Artoneutral Seventh, Lesser Sub-Diminished Octave | | Artoneutral Seventh, Lesser Sub-Diminished Octave | ||
Line 2,624: | Line 1,936: | ||
| 140 | | 140 | ||
| 1056.6037736 | | 1056.6037736 | ||
| N7, sd8 | | N7, sd8 | ||
| Tendoneutral Seventh, Greater Sub-Diminished Octave | | Tendoneutral Seventh, Greater Sub-Diminished Octave | ||
Line 2,643: | Line 1,950: | ||
| 141 | | 141 | ||
| 1064.1509434 | | 1064.1509434 | ||
| kkM7, RN7, kd8 | | kkM7, RN7, kd8 | ||
| Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | | Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | ||
Line 2,659: | Line 1,961: | ||
| 142 | | 142 | ||
| 1071.6981132 | | 1071.6981132 | ||
| Kn7, Rkd8 | | Kn7, Rkd8 | ||
| Greater Submajor Seventh, Artoretromean Diminished Octave | | Greater Submajor Seventh, Artoretromean Diminished Octave | ||
Line 2,677: | Line 1,974: | ||
| 143 | | 143 | ||
| 1079.2452830 | | 1079.2452830 | ||
| rkM7, KN7, rd8 | | rkM7, KN7, rd8 | ||
| Narrow Major Seventh, Tendoretromean Diminished Octave | | Narrow Major Seventh, Tendoretromean Diminished Octave | ||
Line 2,693: | Line 1,985: | ||
| 144 | | 144 | ||
| 1086.7924528 | | 1086.7924528 | ||
| kM7, d8 | | kM7, d8 | ||
| Ptolemaic Major Seventh, Pythagorean Diminished Octave | | Ptolemaic Major Seventh, Pythagorean Diminished Octave | ||
Line 2,714: | Line 2,001: | ||
| 145 | | 145 | ||
| 1094.3396226 | | 1094.3396226 | ||
| RkM7, Rd8 | | RkM7, Rd8 | ||
| Artomean Major Seventh, Artomean Diminished Octave | | Artomean Major Seventh, Artomean Diminished Octave | ||
Line 2,733: | Line 2,015: | ||
| 146 | | 146 | ||
| 1101.8867925 | | 1101.8867925 | ||
| rM7, rKd8 | | rM7, rKd8 | ||
| Tendomean Major Seventh, Tendomean Diminished Octave | | Tendomean Major Seventh, Tendomean Diminished Octave | ||
Line 2,751: | Line 2,028: | ||
| 147 | | 147 | ||
| 1109.4339622 | | 1109.4339622 | ||
| M7, Kd8 | | M7, Kd8 | ||
| Pythagorean Major Seventh, Ptolemaic Diminished Octave | | Pythagorean Major Seventh, Ptolemaic Diminished Octave | ||
Line 2,772: | Line 2,044: | ||
| 148 | | 148 | ||
| 1116.9811321 | | 1116.9811321 | ||
| RM7, kUd8 | | RM7, kUd8 | ||
| Wide Major Seventh, Lesser Super-Diminished Octave | | Wide Major Seventh, Lesser Super-Diminished Octave | ||
Line 2,788: | Line 2,055: | ||
| 149 | | 149 | ||
| 1124.5283019 | | 1124.5283019 | ||
| rKM7, RkUd8 | | rKM7, RkUd8 | ||
| Narrow Supermajor Seventh, Greater Super-Diminished Octave | | Narrow Supermajor Seventh, Greater Super-Diminished Octave | ||
Line 2,806: | Line 2,068: | ||
| 150 | | 150 | ||
| 1132.0754717 | | 1132.0754717 | ||
| km2, RuA1, kkA1 | | km2, RuA1, kkA1 | ||
| Lesser Supermajor Seventh, Diptolemaic Diminished Octave | | Lesser Supermajor Seventh, Diptolemaic Diminished Octave | ||
Line 2,823: | Line 2,080: | ||
| 151 | | 151 | ||
| 1139.6226415 | | 1139.6226415 | ||
| SM7, kUM7, Ud8 | | SM7, kUM7, Ud8 | ||
| Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | | Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | ||
Line 2,842: | Line 2,094: | ||
| 152 | | 152 | ||
| 1147.1698113 | | 1147.1698113 | ||
| | | u8, RkUM7 | ||
| Infraoctave, Wide Supermajor Seventh | | Infraoctave, Wide Supermajor Seventh | ||
| Dd>, Ct#>↓ | | Dd>, Ct#>↓ | ||
Line 2,865: | Line 2,112: | ||
| 153 | | 153 | ||
| 1154.7169811 | | 1154.7169811 | ||
| KKM7, rUM7, Ru8 | | KKM7, rUM7, Ru8 | ||
| Narrow Ultramajor Seventh, Wide Infraoctave | | Narrow Ultramajor Seventh, Wide Infraoctave | ||
Line 2,886: | Line 2,128: | ||
| 154 | | 154 | ||
| 1162.2641509 | | 1162.2641509 | ||
| UM7, rKu8 | | UM7, rKu8 | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
Line 2,909: | Line 2,146: | ||
| 155 | | 155 | ||
| 1169.8113208 | | 1169.8113208 | ||
| s8, Ku8 | | s8, Ku8 | ||
| Lesser Suboctave, Wide Ultramajor Seventh | | Lesser Suboctave, Wide Ultramajor Seventh | ||
Line 2,933: | Line 2,165: | ||
| 156 | | 156 | ||
| 1177.3584906 | | 1177.3584906 | ||
| k8 | | k8 | ||
| Greater Suboctave | | Greater Suboctave | ||
Line 2,952: | Line 2,179: | ||
| 157 | | 157 | ||
| 1184.9056604 | | 1184.9056604 | ||
| Rk8 | | Rk8 | ||
| Wide Suboctave | | Wide Suboctave | ||
Line 2,967: | Line 2,189: | ||
| 158 | | 158 | ||
| 1192.4528302 | | 1192.4528302 | ||
| r8 | | r8 | ||
| Narrow Octave | | Narrow Octave | ||
Line 2,984: | Line 2,201: | ||
| 159 | | 159 | ||
| 1200 | | 1200 | ||
| P8 | | P8 | ||
| Perfect Octave | | Perfect Octave | ||
Line 2,996: | Line 2,212: | ||
|- | |- | ||
|} | |} | ||
== Harmonies == | |||
== References == | == References == |