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User:Moremajorthanmajor/3L 1s (perfect fifth-equivalent): Difference between revisions

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==Notation==
==Notation==
   
   
There are 6 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple, quadruple, quintuple or sextuple sesquitave (major ninth, thirteenth, seventeenth i. e. ~pentave or twenty-first or augmented twenty-fifth), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s], an ~pentave which is the Mixolydian mode of Hextone[12L 4s], a major twenty-first which is the Ionian mode of Guidotonic[15L 5s] or an augmented twenty-fifth which is the Lydian mode of Subdozenal[18L 6s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation, 16 in quadruple sesquitave notation, 20 in quintuple sesquitave notation and 24 in sextuple sesquitave notation, letters A-H (FGABHCDEF), dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle), the Guidonian names with F as the lowest ut or letters except I and O may be used.
There are 6 main ways to notate the angel scale. One method uses a simple sesquitave (fifth) repeating notation consisting of 4 naturals (eg. Do Re Mi Fa, Fa Sol La Si, Sol La Si Do). Given that 1-5/4-5/3 is fifth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate angel scales as repeating at the double, triple, quadruple, quintuple or sextuple sesquitave (major ninth, thirteenth, seventeenth i. e. ~pentave or twenty-first or augmented twenty-fifth), however it does make navigating the [[Generator|genchain]] harder. This way, 5/3 is its own pitch class, distinct from 10/9. Notating this way produces a major ninth which is the Aeolian mode of Napoli[6L 2s], a major thirteenth which is the Dorian mode of Bijou[9L 3s], an ~pentave which is the Mixolydian mode of Hextone[12L 4s], a major twenty-first which is the Ionian mode of Guidotonic[15L 5s] or an augmented twenty-fifth which is the Lydian mode of Subdozenal[18L 6s]. Since there are exactly 8 naturals in double sesquitave notation, 12 in triple sesquitave notation, 16 in quadruple sesquitave notation, 20 in quintuple sesquitave notation and 24 in sextuple sesquitave notation, letters A-H (FGABHCDEF), dozenal or hex digits (0123456789XE0 or D1234567FGACD with flats written C molle or 0123456789ABCDEF0 or G123456789ABCDEFG with flats written F molle), the Guidonian names with F as the lowest ut or letters except I and O may be used.
 
 
{| class="wikitable"
{| class="wikitable"
Line 54: Line 54:
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
 
 
|F#
|F#
Line 69: Line 69:
| 2\10, 141.176
| 2\10, 141.176
 
 
|3\13, 163.{{Overline|63}}
|3\13, 163.636
 
 
|-
|-
 
 
|Reb, Lab
|Reb, Solb, Lab
 
 
|Gb, Ge
|Gb, Ge
Line 86: Line 86:
|1\10, 70.588
|1\10, 70.588
 
 
|1\13, 54.{{Overline|54}}
|1\13, 54.545
 
 
|-
|-
 
 
|'''Re, La'''
|'''Re, Sol, La'''
 
 
|'''G'''
|'''G'''
Line 105: Line 105:
|'''3\10,''' '''211.765'''
|'''3\10,''' '''211.765'''
 
 
|'''4\13,''' '''218.{{Overline|18}}'''
|'''4\13,''' '''218.182'''
 
 
|-
|-
 
 
|Re#, La#
|Re#, Sol#, La#
 
 
|G#
|G#
Line 124: Line 124:
|5\10, 352.941
|5\10, 352.941
 
 
|7\13, 381.{{Overline|81}}
|7\13, 381.818
 
 
|-
|-
 
 
|Mib, Sib
|Mib, Lab, Sib
 
 
|Ab, Æ
|Ab, Æ
Line 141: Line 141:
| 4\10, 282.353
| 4\10, 282.353
 
 
|5\13, 272.{{Overline|72}}
|5\13, 272.727
 
 
|-
|-
 
 
| Mi, Si
| Mi, La, Si
 
 
|A
|A
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| 6\10, 423.529
| 6\10, 423.529
 
 
|8\13, 436.{{Overline|36}}
|8\13, 436.364
 
 
|-
|-
 
 
|Mi#, Si#
|Mi#, La#, Si#
 
 
|A#
|A#
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|-
|-
 
 
|Fab, Dob
|Fab, Sibb, Dob
 
 
| Bbb, Bee
| Bbb, Bee
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|5\10, 352.941
|5\10, 352.941
 
 
| 6\13, 327.{{Overline|27}}
| 6\13, 327.273
 
 
|-
|-
 
 
|'''Fa, Do'''
|'''Fa, Sib, Do'''
 
 
|'''Bb, Be'''
|'''Bb, Be'''
Line 215: Line 215:
|'''7\10,''' '''494.118'''
|'''7\10,''' '''494.118'''
 
 
|'''9\13,''' '''490.{{Overline|90}}'''
|'''9\13,''' '''490.909'''
 
 
|-
|-
 
 
|Fa#, Do#
|Fa#, Si, Do#
 
 
|B
|B
Line 234: Line 234:
|9\10, 635.294
|9\10, 635.294
 
 
|12\13, 654.{{Overline|54}}
|12\13, 654.545
 
 
|-
|-
|Fax, Dox
|Fax, Si#, Dox
 
 
|B#
|B#
Line 253: Line 253:
|11\10, 776.471
|11\10, 776.471
 
 
|15\13, 818.{{Overline|18}}
|15\13, 818.182
 
 
|-
|-
 
 
|Dob, Solb
|Dob, Fab, Solb
|Hb, He
|Hb, He
|14\15, 646.154
|14\15, 646.154
Line 264: Line 264:
|14\17, 579.310
|14\17, 579.310
|8\10, 564.706
|8\10, 564.706
|10\13, 545.{{Overline|45}}
|10\13, 545.455
 
 
|-
|-
 
 
!Do, Sol
!Do, Fa, Sol
 
 
!H
!H
Line 283: Line 283:
!'''10\10,''' '''705.882'''
!'''10\10,''' '''705.882'''
 
 
!'''13\13,''' '''709.'''{{Overline|09}}
!'''13\13,''' '''709.091'''
 
 
|-
|-
 
 
|Do#, Sol#
|Do#, Fa#, Sol#
 
 
|Η#
|Η#
Line 302: Line 302:
|12\10, 847.059
|12\10, 847.059
 
 
|16\13, 872.{{Overline|72}}
|16\13, 872.727
 
 
|-
|-
 
 
|Reb, Lab
|Reb, Solb, Lab
 
 
|Cb, Ce
|Cb, Ce
Line 319: Line 319:
|11\10, 776.471
|11\10, 776.471
 
 
|14\13, 763.{{Overline|63}}
|14\13, 763.63
 
 
|-
|-
 
 
|'''Re, La'''
|'''Re, Sol, La'''
 
 
|'''C'''
|'''C'''
Line 338: Line 338:
|'''13\10,''' '''917.647'''
|'''13\10,''' '''917.647'''
 
 
|'''17\13,''' '''927.{{Overline|27}}'''
|'''17\13,''' '''927.273'''
 
 
|-
|-
 
 
|Re#, La#
|Re#, Sol#, La#
 
 
| C#
| C#
Line 357: Line 357:
|15\10, 1058.824
|15\10, 1058.824
 
 
|20\13, 1090.{{Overline|90}}
|20\13, 1090.909
 
 
|-
|-
 
 
|Mib, Sib
|Mib, Lab, Sib
 
 
|Db, De
|Db, De
Line 374: Line 374:
|14\10, 988.235
|14\10, 988.235
 
 
|18\13, 981.{{Overline|81}}
|18\13, 981.818
 
 
|-
|-
 
 
|Mi, Si
|Mi, La, Si
 
 
| D
| D
Line 393: Line 393:
| 16\10, 1129.412
| 16\10, 1129.412
 
 
|21\9, 1145.{{Overline|45}}
|21\9, 1145.455
 
 
|-
|-
 
 
|Mi#, Si#
|Mi#, La#, Si#
 
 
|D#
|D#
Line 412: Line 412:
|18\10, 1270.588
|18\10, 1270.588
 
 
| 24\13, 1309.{{Overline|09}}
| 24\13, 1309.091
 
 
|-
|-
 
 
| Fab, Dob
| Fab, Sibb, Dob
 
 
|Ebb, Eee
|Ebb, Eee
Line 429: Line 429:
|15\10, 1058.824
|15\10, 1058.824
 
 
|19\13, 1036.{{Overline|36}}
|19\13, 1036.364
 
 
|-
|-
 
 
|'''Fa, Do'''
|'''Fa, Sib, Do'''
 
 
|'''Eb, Ee'''
|'''Eb, Ee'''
Line 452: Line 452:
|-
|-
 
 
|Fa#, Do#
|Fa#, Si, Do#
 
 
| E
| E
Line 467: Line 467:
|19\10, 1341.176
|19\10, 1341.176
 
 
|25\13, 1363.{{Overline|63}}
|25\13, 1363.636
 
 
|-
|-
 
 
|Fax, Dox
|Fax, Si#, Dox
 
 
|E#
|E#
Line 486: Line 486:
|21\10, 1482.353
|21\10, 1482.353
 
 
|28\13, 1527.{{Overline|27}}
|28\13, 1527.273
 
 
|-
|-
 
 
|Dob, Solb
|Dob, Fab, Solb
 
 
| Fb, Fe
| Fb, Fe
Line 503: Line 503:
|18\10, 1270.588
|18\10, 1270.588
 
 
|23\13, 1254.{{Overline|54}}
|23\13, 1254.545
 
 
|-
|-
 
 
!Do, Sol
!Do, Fa, Sol
 
 
!F
!F
Line 522: Line 522:
!20\10, 1411.765
!20\10, 1411.765
 
 
!26\13, 1418.{{Overline|18}}
!26\13, 1418.182
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 553: Line 553:
|3\17, 124.138
|3\17, 124.138
|2\10, 141.176
|2\10, 141.176
|3\13, 163.{{Overline|63}}
|3\13, 163.636
|-
|-
|1b, 1c
|1b, 1c
Line 562: Line 562:
|2\17, 82.759
|2\17, 82.759
|1\10, 70.588
|1\10, 70.588
| 1\13, 54.{{Overline|54}}
| 1\13, 54.545
|-
|-
|'''1'''
|'''1'''
Line 572: Line 572:
|'''5\17,''' '''206.897'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.{{Overline|18}}'''
|'''4\13,''' '''218.182'''
|-
|-
| 1#
| 1#
Line 582: Line 582:
|8\17, 331.034
|8\17, 331.034
|5\10, 352.941
|5\10, 352.941
| 7\13, 381.{{Overline|81}}
| 7\13, 381.818
|-
|-
|2b, 2c
|2b, 2c
Line 591: Line 591:
|7\17, 289.655
|7\17, 289.655
| 4\10, 282.353
| 4\10, 282.353
|5\13, 272.{{Overline|72}}
|5\13, 272.727
|-
|-
|2
|2
Line 601: Line 601:
|10\17, 413.793
|10\17, 413.793
| 6\10, 423.529
| 6\10, 423.529
|8\13, 436.{{Overline|36}}
|8\13, 436.364
|-
|-
|2#
|2#
Line 620: Line 620:
|9\17, 372.414
|9\17, 372.414
|5\10, 352.941
|5\10, 352.941
|6\13, 327.{{Overline|27}}
|6\13, 327.273
|-
|-
|'''3'''
|'''3'''
Line 630: Line 630:
|'''12\17,''' '''496.552'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.{{Overline|90}}'''
|'''9\13,''' '''490.909'''
|-
|-
| 3#
| 3#
Line 640: Line 640:
|15\17, 620.690
|15\17, 620.690
|9\10, 635.294
|9\10, 635.294
|12\13, 654.{{Overline|54}}
|12\13, 654.545
|-
|-
|3x
|3x
Line 650: Line 650:
|18\17, 744.828
|18\17, 744.828
|11\10, 776.471
|11\10, 776.471
|15\13, 818.{{Overline|18}}
|15\13, 818.182
|-
|-
|4b, 4c
|4b, 4c
Line 659: Line 659:
|14\17, 579.310
|14\17, 579.310
|8\10, 564.706
|8\10, 564.706
|10\13, 545.{{Overline|45}}
|10\13, 545.455
|-
|-
!4
!4
Line 669: Line 669:
!'''17\17,''' '''703.448'''
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.'''{{Overline|09}}
!'''13\13,''' '''709.091'''
|-
|-
|4#
|4#
Line 679: Line 679:
|20\17, 827.586
|20\17, 827.586
| 12\10, 847.059
| 12\10, 847.059
|16\13, 872.{{Overline|72}}
|16\13, 872.727
|-
|-
|5b, 5c
|5b, 5c
Line 688: Line 688:
|19\17, 786.207
|19\17, 786.207
| 11\10, 776.471
| 11\10, 776.471
|14\13, 763.{{Overline|63}}
|14\13, 763.63
|-
|-
|'''5'''
|'''5'''
Line 698: Line 698:
|'''22\17,''' '''910.345'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.{{Overline|27}}'''
|'''17\13,''' '''927.273'''
|-
|-
|5#
|5#
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|25\17, 1034.483
|25\17, 1034.483
|15\10, 1058.824
|15\10, 1058.824
|20\13, 1090.{{Overline|90}}
|20\13, 1090.909
|-
|-
|6b, 6c
|6b, 6c
Line 717: Line 717:
|24\17, 993.103
|24\17, 993.103
|14\10, 988.235
|14\10, 988.235
|18\13, 981.{{Overline|81}}
|18\13, 981.818
|-
|-
|6
|6
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|27\17, 1117.241
|27\17, 1117.241
| 16\10, 1129.412
| 16\10, 1129.412
|21\9, 1145.{{Overline|45}}
|21\9, 1145.455
|-
|-
|6#
|6#
Line 737: Line 737:
|30\17, 1241.379
|30\17, 1241.379
|18\10, 1270.588
|18\10, 1270.588
|24\13, 1309.{{Overline|09}}
|24\13, 1309.091
|-
|-
|7b, 7c
|7b, 7c
Line 746: Line 746:
|26\17, 1075.862
|26\17, 1075.862
| 15\10, 1058.824
| 15\10, 1058.824
|19\13, 1036.{{Overline|36}}
|19\13, 1036.364
|-
|-
|'''7'''
|'''7'''
Line 766: Line 766:
|32\17, 1324.138
|32\17, 1324.138
|19\10, 1341.176
|19\10, 1341.176
|25\13, 1363.{{Overline|63}}
|25\13, 1363.636
|-
|-
|7x
|7x
Line 776: Line 776:
|35\17, 1448.275
|35\17, 1448.275
|21\10, 1482.353
|21\10, 1482.353
|28\13, 1527.{{Overline|27}}
|28\13, 1527.273
|-
|-
|8b, Fc
|8b, Fc
Line 785: Line 785:
|31\17, 1282.759
|31\17, 1282.759
|18\10, 1270.588
|18\10, 1270.588
|23\13, 1254.{{Overline|54}}
|23\13, 1254.545
|-
|-
!8, F
!8, F
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!34\17, 1406.897
!34\17, 1406.897
!20\10, 1411.765
!20\10, 1411.765
!26\13, 1418.{{Overline|18}}
!26\13, 1418.182
|-
|-
|8#, F#
|8#, F#
Line 805: Line 805:
|37\17, 1531.034
|37\17, 1531.034
|22\10, 1552.941
|22\10, 1552.941
|29\13, 1581.{{Overline|81}}
|29\13, 1581.818
|-
|-
|9b, Gc
|9b, Gc
Line 814: Line 814:
|36\17, 1489.655
|36\17, 1489.655
| 21\10, 1482.759
| 21\10, 1482.759
|27\13, 1472.{{Overline|72}}
|27\13, 1472.273
|-
|-
|'''9, G'''
|'''9, G'''
Line 824: Line 824:
|'''39\17,''' '''1613.793'''
|'''39\17,''' '''1613.793'''
|'''23\10,''' '''1623.529'''
|'''23\10,''' '''1623.529'''
|'''30\13,''' '''1636.{{Overline|36}}'''
|'''30\13,''' '''1636.364'''
|-
|-
| 9#, G#
| 9#, G#
Line 843: Line 843:
| 41\17, 1696.552
| 41\17, 1696.552
| 24\10, 1694.118
| 24\10, 1694.118
|31\13, 1690.{{Overline|90}}
|31\13, 1690.909
|-
|-
| X, A
| X, A
Line 853: Line 853:
|44\17, 1820.690
|44\17, 1820.690
| 26\10, 1835.294
| 26\10, 1835.294
| 34\13, 1854.{{Overline|54}}
| 34\13, 1854.545
|-
|-
|X#, A#
|X#, A#
Line 863: Line 863:
|47\17, 1944.828
|47\17, 1944.828
|28\10, 1976.471
|28\10, 1976.471
|37\13, 2018.{{Overline|18}}
|37\13, 2018.182
|-
|-
| Ebb, Ccc
| Ebb, Ccc
Line 872: Line 872:
|43\17, 1779.310
|43\17, 1779.310
|25\10, 1764.706
|25\10, 1764.706
|32\13, 1745.{{Overline|45}}
|32\13, 1745.545
|-
|-
|'''Eb, Cc'''
|'''Eb, Cc'''
Line 882: Line 882:
|'''46\17,''' '''1903.448'''
|'''46\17,''' '''1903.448'''
|'''27\10,''' '''1905.882'''
|'''27\10,''' '''1905.882'''
|'''35\13,''' '''1909.{{Overline|09}}'''
|'''35\13,''' '''1909.091'''
|-
|-
|E, C
|E, C
Line 892: Line 892:
| 49\17, 2027.586
| 49\17, 2027.586
|29\10, 2047.059
|29\10, 2047.059
| 38\13, 2072.{{Overline|72}}
| 38\13, 2072.727
|-
|-
|Ex, Cx
|Ex, Cx
Line 902: Line 902:
|52\17, 2151.725
|52\17, 2151.725
|31\10, 2188.235
|31\10, 2188.235
| 41\13, 2236.{{Overline|36}}
| 41\13, 2236.364
|-
|-
|0b, Dc
|0b, Dc
Line 911: Line 911:
| 48\17, 1986.207
| 48\17, 1986.207
|28\10, 1976.471
|28\10, 1976.471
|36\13, 1963.{{Overline|63}}
|36\13, 1963.636
|-
|-
!0, D
!0, D
Line 921: Line 921:
!51\17, 2110.345
!51\17, 2110.345
!30\10, 2117.647
!30\10, 2117.647
!39\13, 2127.{{Overline|27}}
!39\13, 2127.273
|-
|-
|0#, D#
|0#, D#
Line 931: Line 931:
|54\17, 2234.483
|54\17, 2234.483
|32\10, 2258.824
|32\10, 2258.824
|42\13, 2090.{{Overline|90}}
|42\13, 2090.909
|-
|-
|1b, 1c
|1b, 1c
Line 940: Line 940:
|53\17, 2193.103
|53\17, 2193.103
|31\10, 2188.235
|31\10, 2188.235
|40\13, 2181.{{Overline|81}}
|40\13, 2181.818
|-
|-
|'''1'''
|'''1'''
Line 950: Line 950:
|'''56\17, 2317.241'''
|'''56\17, 2317.241'''
|'''33\10, 2329.412'''
|'''33\10, 2329.412'''
|'''43\13,''' '''2345.{{Overline|45}}'''
|'''43\13,''' '''2345.455'''
|-
|-
|1#
|1#
Line 960: Line 960:
|59\17, 2441.379
|59\17, 2441.379
|35\10, 2470.588
|35\10, 2470.588
|46\13, 2509.{{Overline|09}}
|46\13, 2509.091
|-
|-
|2b, 2c
|2b, 2c
Line 979: Line 979:
|61\17, 2524.138
|61\17, 2524.138
|36\10, 2541.176
|36\10, 2541.176
|47\13, 2563.{{Overline|63}}
|47\13, 2563.636
|-
|-
|2#
|2#
Line 989: Line 989:
|64\17, 2648.275
|64\17, 2648.275
|38\10, 2682.353
|38\10, 2682.353
|50\13, 2727.{{Overline|27}}
|50\13, 2727.273
|-
|-
|3b, 3c
|3b, 3c
Line 998: Line 998:
|60\17, 2482.759
|60\17, 2482.759
|35\10, 2470.588
|35\10, 2470.588
|45\13, 2454.{{Overline|54}}
|45\13, 2454.545
|-
|-
|'''3'''
|'''3'''
Line 1,008: Line 1,008:
|'''63\17, 2606.897'''
|'''63\17, 2606.897'''
|'''37\10, 2611.765'''
|'''37\10, 2611.765'''
|'''48\13,''' '''2618.{{Overline|18}}'''
|'''48\13,''' '''2618.182'''
|-
|-
|3#
|3#
Line 1,018: Line 1,018:
|66\17, 2731.034
|66\17, 2731.034
|39\10, 2752.941
|39\10, 2752.941
|51\13, 2781.{{Overline|81}}
|51\13, 2781.818
|-
|-
|3x
|3x
Line 1,028: Line 1,028:
|69\17, 2855.172
|69\17, 2855.172
|41\10, 2894.118
|41\10, 2894.118
|54\13, 2945.{{Overline|45}}
|54\13, 2945.455
|-
|-
|4bb, 4cc
|4bb, 4cc
Line 1,037: Line 1,037:
|62\17, 2565.517
|62\17, 2565.517
|36\10, 2541.176
|36\10, 2541.176
|46\13, 2509.{{Overline|09}}
|46\13, 2509.091
|-
|-
|4b, 4c
|4b, 4c
Line 1,047: Line 1,047:
|65\17, 2689.552
|65\17, 2689.552
|38\10, 2682.353
|38\10, 2682.353
|49\13, 2672.{{Overline|72}}
|49\13, 2672.273
|-
|-
!4
!4
Line 1,057: Line 1,057:
!68\17, 2813.793
!68\17, 2813.793
!40\10, 2823.529
!40\10, 2823.529
!52\13, 2836.{{Overline|36}}
!52\13, 2836.364
|}
|}
{| class="wikitable"
{| class="wikitable"
Line 1,088: Line 1,088:
|3\17, 124.138
|3\17, 124.138
|2\10, 141.176
|2\10, 141.176
|3\13, 163.{{Overline|63}}
|3\13, 163.636
|-
|-
|G reb
|G reb
Line 1,097: Line 1,097:
|2\17, 82.759
|2\17, 82.759
|1\10, 70.588
|1\10, 70.588
| 1\13, 54.{{Overline|54}}
| 1\13, 54.545
|-
|-
|'''G re'''
|'''G re'''
Line 1,107: Line 1,107:
|'''5\17,''' '''206.897'''
|'''5\17,''' '''206.897'''
|'''3\10,''' '''211.765'''
|'''3\10,''' '''211.765'''
|'''4\13,''' '''218.{{Overline|18}}'''
|'''4\13,''' '''218.182'''
|-
|-
| G re#
| G re#
Line 1,117: Line 1,117:
|8\17, 331.034
|8\17, 331.034
|5\10, 352.941
|5\10, 352.941
|7\13, 381.{{Overline|81}}
|7\13, 381.818
|-
|-
| A mib
| A mib
Line 1,126: Line 1,126:
| 7\17, 289.655
| 7\17, 289.655
|4\10, 282.353
|4\10, 282.353
|5\13, 272.{{Overline|72}}
|5\13, 272.727
|-
|-
|A mi
|A mi
Line 1,136: Line 1,136:
| 10\17, 413.793
| 10\17, 413.793
| 6\10, 423.529
| 6\10, 423.529
|8\13, 436.{{Overline|36}}
|8\13, 436.364
|-
|-
|A mi#
|A mi#
Line 1,155: Line 1,155:
|9\17, 372.414
|9\17, 372.414
|5\10, 352.941
|5\10, 352.941
| 6\13, 327.{{Overline|27}}
| 6\13, 327.273
|-
|-
|'''B fa ut'''
|'''B fa ut'''
Line 1,165: Line 1,165:
|'''12\17,''' '''496.552'''
|'''12\17,''' '''496.552'''
|'''7\10,''' '''494.118'''
|'''7\10,''' '''494.118'''
|'''9\13,''' '''490.{{Overline|90}}'''
|'''9\13,''' '''490.909'''
|-
|-
|B fa ut#
|B fa ut#
Line 1,175: Line 1,175:
|15\17, 620.690
|15\17, 620.690
|9\10, 635.294
|9\10, 635.294
| 12\13, 654.{{Overline|54}}
| 12\13, 654.545
|-
|-
|B fa utx
|B fa utx
Line 1,185: Line 1,185:
|18\17, 744.828
|18\17, 744.828
|11\10, 776.471
|11\10, 776.471
|15\13, 818.{{Overline|18}}
|15\13, 818.182
|-
|-
|C sol reb
|C sol re utb
|Kb, Ke
|Kb, Ke
|14\15, 646.154
|14\15, 646.154
Line 1,194: Line 1,194:
|14\17, 579.310
|14\17, 579.310
|8\10, 564.706
|8\10, 564.706
| 10\13, 545.{{Overline|45}}
| 10\13, 545.455
|-
|-
!C sol re
!C sol re ut
!K
!K
!'''15\15,''' '''692.308'''
!'''15\15,''' '''692.308'''
Line 1,204: Line 1,204:
!'''17\17,''' '''703.448'''
!'''17\17,''' '''703.448'''
!'''10\10,''' '''705.882'''
!'''10\10,''' '''705.882'''
!'''13\13,''' '''709.'''{{Overline|09}}
!'''13\13,''' '''709.091'''
|-
|-
|C sol re#
|C sol re ut#
|K#
|K#
|16\15, 738.462
|16\15, 738.462
Line 1,214: Line 1,214:
|20\17, 827.586
|20\17, 827.586
|12\10, 847.059
|12\10, 847.059
|16\13, 872.{{Overline|72}}
|16\13, 872.727
|-
|-
|D la mib
|D la mi reb
|Lb, Le
|Lb, Le
|18\15, 830.769
|18\15, 830.769
Line 1,223: Line 1,223:
|19\17, 786.207
|19\17, 786.207
|11\10, 776.471
|11\10, 776.471
|14\13, 763.{{Overline|63}}
|14\13, 763.63
|-
|-
|'''D la mi'''
|'''D la mi re'''
|'''L'''
|'''L'''
|'''19\15,''' '''876.923'''
|'''19\15,''' '''876.923'''
Line 1,233: Line 1,233:
|'''22\17,''' '''910.345'''
|'''22\17,''' '''910.345'''
|'''13\10,''' '''917.647'''
|'''13\10,''' '''917.647'''
|'''17\13,''' '''927.{{Overline|27}}'''
|'''17\13,''' '''927.273'''
|-
|-
|D la mi#
|D la mi re#
|L#
|L#
|20\15, 923.077
|20\15, 923.077
Line 1,243: Line 1,243:
|25\17, 1034.483
|25\17, 1034.483
|15\10, 1058.824
|15\10, 1058.824
|20\13, 1090.{{Overline|90}}
|20\13, 1090.909
|-
|-
|E fa utb
|E fa mib
|Mb, Me
|Mb, Me
|22\15, 1015.385
|22\15, 1015.385
Line 1,252: Line 1,252:
|24\17, 993.103
|24\17, 993.103
|14\10, 988.235
|14\10, 988.235
|18\13, 981.{{Overline|81}}
|18\13, 981.818
|-
|-
|E fa ut
|E fa mi
|M
|M
|23\15, 1061.538
|23\15, 1061.538
Line 1,262: Line 1,262:
|27\17, 1117.241
|27\17, 1117.241
|16\10, 1129.412
|16\10, 1129.412
|21\9, 1145.{{Overline|45}}
|21\9, 1145.455
|-
|-
|E fa ut#
|E fa mi#
|M#
|M#
|24\15, 1107.923
|24\15, 1107.923
Line 1,272: Line 1,272:
|30\17, 1241.379
|30\17, 1241.379
|18\10, 1270.588
|18\10, 1270.588
| 24\13, 1309.{{Overline|09}}
| 24\13, 1309.091
|-
|-
|F sol re utb
|F sol fa utb
| Nbb, Nee
| Nbb, Nee
|25\15, 1153.846
|25\15, 1153.846
Line 1,281: Line 1,281:
|26\17, 1075.862
|26\17, 1075.862
|15\10, 1058.824
|15\10, 1058.824
|19\13, 1036.{{Overline|36}}
|19\13, 1036.364
|-
|-
|'''F sol re ut'''
|'''F sol fa ut'''
|'''Nb, Ne'''
|'''Nb, Ne'''
|'''26\15,''' '''1200'''
|'''26\15,''' '''1200'''
Line 1,293: Line 1,293:
|'''22\13,''' '''1200'''
|'''22\13,''' '''1200'''
|-
|-
|F sol re ut#
|F sol fa ut#
|N
|N
|27\15, 1246.154
|27\15, 1246.154
Line 1,303: Line 1,303:
|25\13, 1363.{{Overline|63}}
|25\13, 1363.{{Overline|63}}
|-
|-
| F sol re utx
| F sol fa utx
|N#
|N#
|28\15, 1292.308
|28\15, 1292.308
Line 1,313: Line 1,313:
|28\13, 1527.{{Overline|27}}
|28\13, 1527.{{Overline|27}}
|-
|-
|G la mi reb
|G la sol reb
| Pb, Pe
| Pb, Pe
|29\15, 1338.462
|29\15, 1338.462
Line 1,322: Line 1,322:
|23\13, 1254.{{Overline|54}}
|23\13, 1254.{{Overline|54}}
|-
|-
!G la mi re
!G la sol re
!P
!P
!30\15, 1384.615
!30\15, 1384.615
Line 1,332: Line 1,332:
!26\13, 1418.{{Overline|18}}
!26\13, 1418.{{Overline|18}}
|-
|-
|G la mi re#
|G la sol re#
|P#
|P#
|31\15, 1430.769
|31\15, 1430.769
Line 1,342: Line 1,342:
|29\13, 1581.{{Overline|81}}
|29\13, 1581.{{Overline|81}}
|-
|-
|A fab
|A la mibb
|Qbb, Qee
|Qbb, Qee
|32\15, 1476.923
|32\15, 1476.923
Line 1,351: Line 1,351:
| 24\13, 1309.{{Overline|09}}
| 24\13, 1309.{{Overline|09}}
|-
|-
|A fa
|A la mib
| Qb, Qe
| Qb, Qe
|33\15, 1523.077
|33\15, 1523.077
Line 1,361: Line 1,361:
|27\13, 1472.{{Overline|72}}
|27\13, 1472.{{Overline|72}}
|-
|-
|'''A mi'''
|'''A la mi'''
|'''Q'''
|'''Q'''
|'''34\15,''' '''1569.231'''
|'''34\15,''' '''1569.231'''
Line 1,371: Line 1,371:
|'''30\13,''' '''1636.{{Overline|36}}'''
|'''30\13,''' '''1636.{{Overline|36}}'''
|-
|-
|A mi#
|A la mi#
|Q#
|Q#
|35\15, 1615.385
|35\15, 1615.385
Line 1,381: Line 1,381:
|33\13, 1800
|33\13, 1800
|-
|-
|B sol fa utb
|B fa utb
|Rb, Re
|Rb, Re
|37\15, 1707.692
|37\15, 1707.692
Line 1,390: Line 1,390:
|31\13, 1690.{{Overline|90}}
|31\13, 1690.{{Overline|90}}
|-
|-
| B sol fa ut
| B fa ut
|R
|R
|38\15, 1753.846
|38\15, 1753.846
Line 1,400: Line 1,400:
|34\13, 1854.{{Overline|54}}
|34\13, 1854.{{Overline|54}}
|-
|-
|B sol fa ut#
|B fa ut#
|R#
|R#
|39\15, 1800
|39\15, 1800
Line 1,410: Line 1,410:
|37\13, 2018.{{Overline|18}}
|37\13, 2018.{{Overline|18}}
|-
|-
|C la sol reb
|C sol reb
|Sbb, See
|Sbb, See
|40\15, 1846.154
|40\15, 1846.154
Line 1,419: Line 1,419:
|32\13, 1745.{{Overline|45}}
|32\13, 1745.{{Overline|45}}
|-
|-
|'''C la sol re'''
|'''C sol re'''
|'''Sb, Se'''
|'''Sb, Se'''
|'''41\15,''' '''1892.308'''
|'''41\15,''' '''1892.308'''
Line 1,429: Line 1,429:
|'''35\13,''' '''1909.{{Overline|09}}'''
|'''35\13,''' '''1909.{{Overline|09}}'''
|-
|-
|C la sol re#
|C sol re#
|S#
|S#
|42\15, 1938.462
|42\15, 1938.462
Line 1,439: Line 1,439:
|38\13, 2072.{{Overline|72}}
|38\13, 2072.{{Overline|72}}
|-
|-
| C la sol rex
| C sol rex
| Sx
| Sx
|43\15, 1984.615
|43\15, 1984.615
Line 1,468: Line 1,468:
!39\13, 2127.{{Overline|27}}
!39\13, 2127.{{Overline|27}}
|-
|-
|D la mib
|D la mi#
|T#
|T#
|46\15, 2123.077
|46\15, 2123.077
Line 1,478: Line 1,478:
|42\13, 2090.{{Overline|90}}
|42\13, 2090.{{Overline|90}}
|-
|-
|E fa utb
|E fab
|Ub, Ue
|Ub, Ue
|48\15, 2215.385
|48\15, 2215.385
Line 1,487: Line 1,487:
|40\13, 2181.{{Overline|81}}
|40\13, 2181.{{Overline|81}}
|-
|-
|'''E fa ut'''
|'''E fa'''
|'''U'''
|'''U'''
|'''49\15, 2261.538'''
|'''49\15, 2261.538'''
Line 1,497: Line 1,497:
|'''43\13,''' '''2345.{{Overline|45}}'''
|'''43\13,''' '''2345.{{Overline|45}}'''
|-
|-
|E fa ut#
|E mi fax
|U
|U
|50\15, 2307.692
|50\15, 2307.692
Line 1,507: Line 1,507:
| 46\13, 2509.{{Overline|09}}
| 46\13, 2509.{{Overline|09}}
|-
|-
|F sol re utb
|F sol fa utb
|Vb, Ve
|Vb, Ve
|52\15, 2400
|52\15, 2400
Line 1,516: Line 1,516:
|44\13, 2400
|44\13, 2400
|-
|-
|F sol re ut
|F sol fa ut
|V
|V
|53\15, 2446.154
|53\15, 2446.154
Line 1,526: Line 1,526:
|47\13, 2563.{{Overline|63}}
|47\13, 2563.{{Overline|63}}
|-
|-
|F sol re ut#
|F sol fa ut#
| V#
| V#
|54\15, 2492.308
|54\15, 2492.308
Line 1,575: Line 1,575:
|54\13, 2945.{{Overline|45}}
|54\13, 2945.{{Overline|45}}
|-
|-
|A fab
|A fa mibb
|Xbb, Xee
|Xbb, Xee
|42\11, 2652.632
|42\11, 2652.632
Line 1,584: Line 1,584:
|46\13, 2509.{{Overline|09}}
|46\13, 2509.{{Overline|09}}
|-
|-
|A fa
|A fa mib
|Xb, Xe
|Xb, Xe
|59\15, 2723.077
|59\15, 2723.077
Line 1,594: Line 1,594:
| 49\13, 2672.{{Overline|72}}
| 49\13, 2672.{{Overline|72}}
|-
|-
!A mi
!A fa mi
!X
!X
!60\15, 2769.231
!60\15, 2769.231
Line 1,604: Line 1,604:
!52\13, 2836.{{Overline|36}}
!52\13, 2836.{{Overline|36}}
|-
|-
|A mi#
|A fa mi#
|X#
|X#
|61\15, 2815.385
|61\15, 2815.385
Line 1,868: Line 1,868:
|-
|-
|0
|0
|Do, Sol
|Do, Fa, Sol
|perfect unison
|perfect unison
|0
|0
|Do, Sol
|Do, Fa, Sol
|sesquitave (just fifth)
|sesquitave (just fifth)
|-
|-
|1
|1
|Fa, Do
|Fa, Sib, Do
|perfect fourth
|perfect fourth
| -1
| -1
|Re, La
|Re, Sol, La
|perfect second
|perfect second
|-
|-
|2
|2
|Mib, Sib
|Mib, Lab, Sib
|minor third
|minor third
| -2
| -2
|Mi, Si
|Mi, La, Si
|major third
|major third
|-
|-
|3
|3
|Reb, Lab
|Reb, Solb, Lab
|diminished second
|diminished second
| -3
| -3
|Fa#, Do#
|Fa#, Si, Do#
|augmented fourth
|augmented fourth
|-
|-
Line 1,898: Line 1,898:
|-
|-
|4
|4
|Dob, Solb
|Dob, Fab, Solb
|diminished sesquitave
|diminished sesquitave
| -4
| -4
|Do#, Sol#
|Do#, Fa#, Sol#
|augmented unison (chroma)
|augmented unison (chroma)
|-
|-
|5
|5
|Fab, Dob
|Fab, Sibb, Dob
| diminished fourth
| diminished fourth
| -5
| -5
|Re#, La#
|Re#, Sol#, La#
|augmented second
|augmented second
|-
|-
|6
|6
|Mibb, Sibb
|Mibb, Labb, Sibb
|diminished third
|diminished third
| -6
| -6
|Mi#, Si#
|Mi#, La#, Si#
|augmented third
|augmented third
|}  
|}  
Line 1,924: Line 1,924:
{| class="wikitable"
{| class="wikitable"
|Mibb
|Mibb
Labb
   
   
Sibb
Sibb
|Fab
|Fab
Sibb
   
   
Dob
Dob
|Dob
|Dob
Fab
   
   
Solb
Solb
|Reb
|Reb
Solb
   
   
Lab
Lab
|Mib
|Mib
Lab
   
   
Sib
Sib
|Fa
|Fa
Sib
   
   
Do
Do
|Do
|Do
Fa
   
   
Sol
Sol
|Re
|Re
Sol
   
   
La
La
|Mi
|Mi
La
   
   
Si
Si
|Fa#
|Fa#
Si
   
   
Do#
Do#
|Do#
|Do#
Fa#
   
   
Sol#
Sol#
|Re#
|Re#
Sol#
   
   
La#
La#
|Mi#
|Mi#
La#
   
   
Si#
Si#
Line 2,076: Line 2,089:
|-
|-
|5\19
|5\19
|181.{{Overline|81}}
|181.818
|5
|5
|4
|4
Line 2,111: Line 2,124:
|-
|-
|7\26
|7\26
|186.{{Overline|6}}
|186.667
|7
|7
|5
|5
Line 2,146: Line 2,159:
|-
|-
|14\51
|14\51
|190.{{Overline|90}}
|190.909
|14
|14
|9
|9
Line 2,174: Line 2,187:
|-
|-
|12\43
|12\43
|194.{{Overline|594}}
|194.595
|12
|12
|7
|7
Line 2,188: Line 2,201:
|-
|-
|9\32
|9\32
|196.{{Overline|36}}
|196.364
|9
|9
|5
|5
Line 2,276: Line 2,289:
| 17
| 17
|1.941
|1.941
|
|-
|35\123
|199.009
| 35
|18
|1.944
|
|
|-
|-
|2\7
|2\7
|199.009
|200
| 2
|2
|1
|1
|2.000
|2.000
Line 2,286: Line 2,306:
|-
|-
|17\59
|17\59
| 200
| 201.980
|17
|17
|8
|8
Line 2,293: Line 2,313:
|-
|-
|15\52
|15\52
|201.{{Overline|9801}}
|202.247
|15
|15
|7
|7
Line 2,300: Line 2,320:
|-
|-
|13\45
|13\45
|202.247
|202.597
|13
|13
|6
|6
Line 2,307: Line 2,327:
|-
|-
|11\38
|11\38
|202.597
|203.077
|11
|11
|5
|5
Line 2,314: Line 2,334:
|-
|-
|9\31
|9\31
|203.077
|203.774
|9
|9
|4
|4
Line 2,321: Line 2,341:
|-
|-
|7\24
|7\24
|203.774
|204.878
|7
|7
|3
|3
Line 2,328: Line 2,348:
|-
|-
|12\41
|12\41
|204.878
|205.714
|12
|12
| 5
| 5
Line 2,335: Line 2,355:
|-
|-
|5\17
|5\17
|205.714
|206.897
|5
|5
|2
|2
Line 2,342: Line 2,362:
|-
|-
|18\61
|18\61
|206.897
|207.693
|18
|18
|7
|7
|2.571
|2.571
|
|-
|13\44
|208.000
|13
|5
|2.600
|
|
|-
|-
|8\27
|8\27
|207.693
|208.696
|8
|8
|3
|3
Line 2,356: Line 2,383:
|-
|-
|11\37
|11\37
|208.000
|209.524
| 11
| 11
| 4
| 4
Line 2,363: Line 2,390:
|-
|-
|14\47
|14\47
|208.696
|210.000
|14
|14
|5
|5
Line 2,370: Line 2,397:
|-
|-
| 3\10
| 3\10
|209.524
|211.765
| 3
| 3
|1
|1
Line 2,377: Line 2,404:
|-
|-
|22\73
|22\73
|210.000
|212.903
|22
|22
|7
|7
Line 2,384: Line 2,411:
|-
|-
|19\63
|19\63
|211.755
|213.084
|19
|19
|6
|6
Line 2,391: Line 2,418:
|-
|-
|16\53
|16\53
|212.903
|213.333
|16
|16
|5
|5
Line 2,398: Line 2,425:
|-
|-
|13\43
|13\43
|213.084
|213.699
|13
|13
|4
|4
Line 2,405: Line 2,432:
|-
|-
|10\33
|10\33
|213.{{Overline|3}}
|214.286
| 10
| 10
|3
|3
Line 2,412: Line 2,439:
|-
|-
|7\23
|7\23
|213.699
|215.385
|7
|7
|2
|2
Line 2,419: Line 2,446:
|-
|-
|11\36
|11\36
|214.286
|216.393
|11
|11
|3
|3
Line 2,426: Line 2,453:
|-
|-
|15\49
|15\49
| 215.385
| 216.867
|15
|15
|4
|4
Line 2,433: Line 2,460:
|-
|-
|19\62
|19\62
| 216.393
| 217.143
|19
|19
|5
|5
Line 2,440: Line 2,467:
|-
|-
|4\13
|4\13
|216.867
|218.182
|4
|4
|1
|1
Line 2,447: Line 2,474:
|-
|-
|13\42
|13\42
|217.143
|219.718
|13
|13
|3
|3
Line 2,454: Line 2,481:
|-
|-
|9\29
|9\29
|218.{{Overline|18}}
|220.408
|9
|9
|2
|2
Line 2,461: Line 2,488:
|-
|-
|14\45
|14\45
|219.718
|221.053
|14
|14
|3
|3
Line 2,468: Line 2,495:
|-
|-
|5\16
|5\16
| 220.408
| 222.222
| 5
| 5
|1
|1
|5.000
|5.000
|Napoli-Archy ends
|Napoli-Archy ends
|-
|16\51
|221.053
|16
| 3
|5.333
|
|-
|-
|11\35
|11\35
|222.{{Overline|2}}
|223.728
|11
|11
|2
|2
Line 2,489: Line 2,509:
|-
|-
|17\54
|17\54
|223.728
|224.176
|17
|17
|3
|3
Line 2,496: Line 2,516:
|-
|-
|6\19
|6\19
|224.176
|225.000
|6
|6
|1
|1
Line 2,502: Line 2,522:
|
|
|-
|-
| 7\22
|1\3
|225.000
|240.000
|1
|1
|0
|0
|→ inf
|→ inf
|Paucitonic
|Paucitonic
|-
|1\3
|240.000
|
|
|
|
|}
|}


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