42edo: Difference between revisions
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| Line 15: | Line 15: | ||
! | Degree | ! | Degree | ||
! | Size (Cents) | ! | Size (Cents) | ||
!pions | |||
!7mus | |||
! colspan="2" | relative notation | ! colspan="2" | relative notation | ||
! | absolute notation | ! | absolute notation | ||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| style="text-align:center;" | 0 | | colspan="3" style="text-align:center;" | 0 | ||
| style="text-align:center;" | perfect unison | | style="text-align:center;" | perfect unison | ||
| style="text-align:center;" | P1 | | style="text-align:center;" | P1 | ||
| Line 25: | Line 27: | ||
|- | |- | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29.571 | ||
|30.286 | |||
|36.571 (24.925<sub>16</sub>) | |||
| style="text-align:center;" | up 1sn, minor 2nd | | style="text-align:center;" | up 1sn, minor 2nd | ||
| style="text-align:center;" | ^1, m2 | | style="text-align:center;" | ^1, m2 | ||
| Line 31: | Line 35: | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:center;" | 57 | | style="text-align:center;" |57.143 | ||
|60.571 | |||
|73.143 (49.249<sub>16</sub>) | |||
| style="text-align:center;" | double-up 1sn, upminor 2nd | | style="text-align:center;" | double-up 1sn, upminor 2nd | ||
| style="text-align:center;" | ^^1, ^m2 | | style="text-align:center;" | ^^1, ^m2 | ||
| Line 37: | Line 43: | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:center;" | | | style="text-align:center;" |85.714 | ||
|90.857 | |||
|109.714 (6D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | double-up minor 2nd | | style="text-align:center;" | double-up minor 2nd | ||
| style="text-align:center;" | ^^m2 | | style="text-align:center;" | ^^m2 | ||
| Line 43: | Line 51: | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:center;" | 114 | | style="text-align:center;" |114.286 | ||
|121.143 | |||
|146.286 (92.492<sub>16</sub>) | |||
| style="text-align:center;" | downmid 2nd | | style="text-align:center;" | downmid 2nd | ||
| style="text-align:center;" | v~2 | | style="text-align:center;" | v~2 | ||
| Line 49: | Line 59: | ||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:center;" | 143 | | style="text-align:center;" | 143.857 | ||
|151.429 | |||
|182.857 (B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | upmid 2nd | | style="text-align:center;" | upmid 2nd | ||
| style="text-align:center;" | ^~2 | | style="text-align:center;" | ^~2 | ||
| Line 55: | Line 67: | ||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:center;" | 171 | | style="text-align:center;" |171.429 | ||
|181.714 | |||
|219.429 (DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | double-down major 2nd | | style="text-align:center;" | double-down major 2nd | ||
| style="text-align:center;" | vvM2 | | style="text-align:center;" | vvM2 | ||
| Line 62: | Line 76: | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:center;" | 200 | | style="text-align:center;" | 200 | ||
|212 | |||
|256 (100<sub>16</sub>) | |||
| style="text-align:center;" | downmajor 2nd | | style="text-align:center;" | downmajor 2nd | ||
| style="text-align:center;" | vM2 | | style="text-align:center;" | vM2 | ||
| Line 67: | Line 83: | ||
|- | |- | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:center;" | | | style="text-align:center;" |228.571 | ||
|242.286 | |||
|292.571 (124.925<sub>16</sub>) | |||
| style="text-align:center;" | major 2nd | | style="text-align:center;" | major 2nd | ||
| style="text-align:center;" | M2 | | style="text-align:center;" | M2 | ||
| Line 73: | Line 91: | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:center;" | 257 | | style="text-align:center;" |257.143 | ||
|282.571 | |||
|329.143 (149.249<sub>16</sub>) | |||
| style="text-align:center;" | minor 3rd | | style="text-align:center;" | minor 3rd | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
| Line 79: | Line 99: | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:center;" | | | style="text-align:center;" |285.714 | ||
|302.857 | |||
|365.714 (16D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | ^m3 | | style="text-align:center;" | ^m3 | ||
| Line 85: | Line 107: | ||
|- | |- | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:center;" | 314 | | style="text-align:center;" | 314.286 | ||
|333.143 | |||
|402.286 (192.492<sub>16</sub>) | |||
| style="text-align:center;" | double-up minor 3rd | | style="text-align:center;" | double-up minor 3rd | ||
| style="text-align:center;" | ^^m3 | | style="text-align:center;" | ^^m3 | ||
| Line 91: | Line 115: | ||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:center;" | | | style="text-align:center;" |342.857 | ||
|363.429 | |||
|438.857 (1B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | downmid 3rd | | style="text-align:center;" | downmid 3rd | ||
| style="text-align:center;" | v~3 | | style="text-align:center;" | v~3 | ||
| Line 97: | Line 123: | ||
|- | |- | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:center;" | 371 | | style="text-align:center;" | 371.429 | ||
|393.714 | |||
|475.429 (1DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | upmid 3rd | | style="text-align:center;" | upmid 3rd | ||
| style="text-align:center;" | ^~3 | | style="text-align:center;" | ^~3 | ||
| Line 104: | Line 132: | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:center;" | 400 | | style="text-align:center;" | 400 | ||
|424 | |||
|512 (200<sub>16</sub>) | |||
| style="text-align:center;" | double-down major 3rd | | style="text-align:center;" | double-down major 3rd | ||
| style="text-align:center;" | vvM3 | | style="text-align:center;" | vvM3 | ||
| Line 109: | Line 139: | ||
|- | |- | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:center;" | | | style="text-align:center;" |428.571 | ||
|454.286 | |||
|548.571 (224.925<sub>16</sub>) | |||
| style="text-align:center;" | downmajor 3rd | | style="text-align:center;" | downmajor 3rd | ||
| style="text-align:center;" | vM3 | | style="text-align:center;" | vM3 | ||
| Line 115: | Line 147: | ||
|- | |- | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:center;" | 457 | | style="text-align:center;" |457.143 | ||
|484.571 | |||
|585.143 (249.249<sub>16</sub>) | |||
| style="text-align:center;" | major 3rd, down 4th | | style="text-align:center;" | major 3rd, down 4th | ||
| style="text-align:center;" | M3, v4 | | style="text-align:center;" | M3, v4 | ||
| Line 121: | Line 155: | ||
|- | |- | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| style="text-align:center;" | | | style="text-align:center;" | 485.714 | ||
|514.857 | |||
|621.714 (26D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | perfect 4th | | style="text-align:center;" | perfect 4th | ||
| style="text-align:center;" | P4 | | style="text-align:center;" | P4 | ||
| Line 127: | Line 163: | ||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| style="text-align:center;" | | | style="text-align:center;" |51<span style="line-height: 1.5;">4.286</span> | ||
|545.143 | |||
|658.286 (292.492<sub>16</sub>) | |||
| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| style="text-align:center;" | ^4 | | style="text-align:center;" | ^4 | ||
| Line 133: | Line 171: | ||
|- | |- | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:center;" | 543 | | style="text-align:center;" | 543.857 | ||
|575.429 | |||
|694.857 (2B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | double-up 4th | | style="text-align:center;" | double-up 4th | ||
| style="text-align:center;" | ^^4 | | style="text-align:center;" | ^^4 | ||
| Line 139: | Line 179: | ||
|- | |- | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| style="text-align:center;" | 571 | | style="text-align:center;" |571.429 | ||
|605.714 | |||
|731.429 (2DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | triple-up 4th | | style="text-align:center;" | triple-up 4th | ||
| style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span>4 | | style="text-align:center;" | ^<span style="font-size: 90%; vertical-align: super;">3</span>4 | ||
| Line 146: | Line 188: | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| style="text-align:center;" | 600 | | style="text-align:center;" | 600 | ||
|6 | |||
|768 (300<sub>16</sub>) | |||
| style="text-align:center;" | triple-down aug 4th, triple-up dim 5th | | style="text-align:center;" | triple-down aug 4th, triple-up dim 5th | ||
| style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>A4, ^<span style="font-size: 90%; vertical-align: super;">3</span>d5 | | style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>A4, ^<span style="font-size: 90%; vertical-align: super;">3</span>d5 | ||
| Line 151: | Line 195: | ||
|- | |- | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| style="text-align:center;" | | | style="text-align:center;" |628.571 | ||
|666.286 | |||
|804.571 (324.925<sub>16</sub>) | |||
| style="text-align:center;" | triple-down 5th | | style="text-align:center;" | triple-down 5th | ||
| style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>5 | | style="text-align:center;" | v<span style="font-size: 90%; vertical-align: super;">3</span>5 | ||
| Line 157: | Line 203: | ||
|- | |- | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| style="text-align:center;" | 657 | | style="text-align:center;" | 657.143 | ||
|696.571 | |||
|841.143 (349.249<sub>16</sub>) | |||
| style="text-align:center;" | double-down 5th | | style="text-align:center;" | double-down 5th | ||
| style="text-align:center;" | vv5 | | style="text-align:center;" | vv5 | ||
| Line 163: | Line 211: | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| style="text-align:center;" | | | style="text-align:center;" |685.714 | ||
|726.857 | |||
|877.714 (36D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| style="text-align:center;" | v5 | | style="text-align:center;" | v5 | ||
| Line 169: | Line 219: | ||
|- | |- | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| style="text-align:center;" | 714 | | style="text-align:center;" | 714.286 | ||
|757.143 | |||
|950.286 (392.492<sub>16</sub>) | |||
| style="text-align:center;" | perfect 5th | | style="text-align:center;" | perfect 5th | ||
| style="text-align:center;" | P5 | | style="text-align:center;" | P5 | ||
| Line 175: | Line 227: | ||
|- | |- | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| style="text-align:center;" | | | style="text-align:center;" |742.857 | ||
|787.429 | |||
|950.857 (3B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | up 5th, minor 6th | | style="text-align:center;" | up 5th, minor 6th | ||
| style="text-align:center;" | ^5, m6 | | style="text-align:center;" | ^5, m6 | ||
| Line 181: | Line 235: | ||
|- | |- | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| style="text-align:center;" | 771 | | style="text-align:center;" |771.429 | ||
|817.714 | |||
|987.429 (3DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | upminor 6th | | style="text-align:center;" | upminor 6th | ||
| style="text-align:center;" | ^m6 | | style="text-align:center;" | ^m6 | ||
| Line 188: | Line 244: | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| style="text-align:center;" | 800 | | style="text-align:center;" | 800 | ||
|848 | |||
|1024 (400<sub>16</sub>) | |||
| style="text-align:center;" | double-up minor 6th | | style="text-align:center;" | double-up minor 6th | ||
| style="text-align:center;" | ^^m6 | | style="text-align:center;" | ^^m6 | ||
| Line 193: | Line 251: | ||
|- | |- | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| style="text-align:center;" | 829 | | style="text-align:center;" | 829.571 | ||
|878.286 | |||
|1060.571 (424.925<sub>16</sub>) | |||
| style="text-align:center;" | downmid 6th | | style="text-align:center;" | downmid 6th | ||
| style="text-align:center;" | v~6 | | style="text-align:center;" | v~6 | ||
| Line 199: | Line 259: | ||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| style="text-align:center;" | 857 | | style="text-align:center;" |857.143 | ||
|908.571 | |||
|1097.143 (449.249<sub>16</sub>) | |||
| style="text-align:center;" | upmid 6th | | style="text-align:center;" | upmid 6th | ||
| style="text-align:center;" | ^~6 | | style="text-align:center;" | ^~6 | ||
| Line 205: | Line 267: | ||
|- | |- | ||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| style="text-align:center;" | | | style="text-align:center;" | 885.714 | ||
|938.857 | |||
|1133.714 (46D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | double-down major 6th | | style="text-align:center;" | double-down major 6th | ||
| style="text-align:center;" | vvM6 | | style="text-align:center;" | vvM6 | ||
| Line 211: | Line 275: | ||
|- | |- | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
| style="text-align:center;" | 914 | | style="text-align:center;" |914.286 | ||
|969.143 | |||
|1170.286 (492.492<sub>16</sub>) | |||
| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | vM6 | | style="text-align:center;" | vM6 | ||
| Line 217: | Line 283: | ||
|- | |- | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
| style="text-align:center;" | | | style="text-align:center;" |942.857 | ||
|999.429 | |||
|1206.857 (4B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | major 6th | | style="text-align:center;" | major 6th | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
| Line 223: | Line 291: | ||
|- | |- | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
| style="text-align:center;" | 971 | | style="text-align:center;" |971.429 | ||
|1029.714 | |||
|1243.429 (4DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | minor 7th | | style="text-align:center;" | minor 7th | ||
| style="text-align:center;" | m7 | | style="text-align:center;" | m7 | ||
| Line 230: | Line 300: | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
| style="text-align:center;" | 1000 | | style="text-align:center;" | 1000 | ||
|1060 | |||
|1280 (500<sub>16</sub>) | |||
| style="text-align:center;" | upminor 7th | | style="text-align:center;" | upminor 7th | ||
| style="text-align:center;" | ^m7 | | style="text-align:center;" | ^m7 | ||
| Line 235: | Line 307: | ||
|- | |- | ||
| style="text-align:center;" | 36 | | style="text-align:center;" | 36 | ||
| style="text-align:center;" | | | style="text-align:center;" |1028.571 | ||
|1090.286 | |||
|1316.571 (524.925<sub>16</sub>) | |||
| style="text-align:center;" | double-up minor 7th | | style="text-align:center;" | double-up minor 7th | ||
| style="text-align:center;" | ^^m7 | | style="text-align:center;" | ^^m7 | ||
| Line 241: | Line 315: | ||
|- | |- | ||
| style="text-align:center;" | 37 | | style="text-align:center;" | 37 | ||
| style="text-align:center;" | 1057 | | style="text-align:center;" | 1057.143 | ||
|1120.571 | |||
|1353.143 (549.249<sub>16</sub>) | |||
| style="text-align:center;" | downmid 7th | | style="text-align:center;" | downmid 7th | ||
| style="text-align:center;" | v~7 | | style="text-align:center;" | v~7 | ||
| Line 247: | Line 323: | ||
|- | |- | ||
| style="text-align:center;" | 38 | | style="text-align:center;" | 38 | ||
| style="text-align:center;" | | | style="text-align:center;" |1085.714 | ||
|1150.857 | |||
|1389.714 (56D.B6E<sub>16</sub>) | |||
| style="text-align:center;" | upmid 7th | | style="text-align:center;" | upmid 7th | ||
| style="text-align:center;" | ^~7 | | style="text-align:center;" | ^~7 | ||
| Line 253: | Line 331: | ||
|- | |- | ||
| style="text-align:center;" | 39 | | style="text-align:center;" | 39 | ||
| style="text-align:center;" | 1114 | | style="text-align:center;" |1114.286 | ||
|1181.143 | |||
|1426.286 (592.492<sub>16</sub>) | |||
| style="text-align:center;" | double-down major 7th | | style="text-align:center;" | double-down major 7th | ||
| style="text-align:center;" | vvM7 | | style="text-align:center;" | vvM7 | ||
| Line 259: | Line 339: | ||
|- | |- | ||
| style="text-align:center;" | 40 | | style="text-align:center;" | 40 | ||
| style="text-align:center;" | | | style="text-align:center;" |1142.857 | ||
|1211.429 | |||
|1462.857 (5B6.DB7<sub>16</sub>) | |||
| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | vM7 | | style="text-align:center;" | vM7 | ||
| Line 265: | Line 347: | ||
|- | |- | ||
| style="text-align:center;" | 41 | | style="text-align:center;" | 41 | ||
| style="text-align:center;" | 1171 | | style="text-align:center;" | 1171.429 | ||
|1241.714 | |||
|1499.429 (5DB.6DB<sub>16</sub>) | |||
| style="text-align:center;" | major 7th, down 8ve | | style="text-align:center;" | major 7th, down 8ve | ||
| style="text-align:center;" | M7, v8 | | style="text-align:center;" | M7, v8 | ||
| Line 272: | Line 356: | ||
| style="text-align:center;" | 42 | | style="text-align:center;" | 42 | ||
| style="text-align:center;" | 1200 | | style="text-align:center;" | 1200 | ||
|1272 | |||
|1536 (600<sub>16</sub>) | |||
| style="text-align:center;" | perfect 8ve | | style="text-align:center;" | perfect 8ve | ||
| style="text-align:center;" | P8 | | style="text-align:center;" | P8 | ||
Revision as of 21:04, 2 April 2019
The 42 equal division divides the octave into 42 equal parts of 28.571 cents each. It has a 3 (the size of which being coprime to its cardinality, this being a first for a composite equal division of cardinality 7n) and a 5 both over 12 cents sharp, using the same 400 cent interval to represent 5/4 as does 12, which means it tempers out 128/125. In the 7-limit, it tempers out 64/63 and 126/125, making it a tuning supporting augene temperament.
While not an accurate tuning on the full 7-limit, it does an excellent job on the 2.9.15.7.33.39 2*42 subgroup, having the same tuning on it as does 84edo. On this subgroup 42 has the same commas as 84.
42edo is a regular edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. 42edo is one of the most difficult regular edos to notate, because no other regular edo's 5th is as sharp (see 47edo for the opposite extreme). Assuming the natural notes form a chain of fifths, the major 2nd is 8 edosteps and the minor 2nd is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D
D# is next to E. The notation requires triple ups and downs, even more if chords are to be spelled correctly. For example, a 1/1 - 5/4 - 3/2 - 9/5 chord with a root on the key or fret midway between G and A would be written either as G#v3 - B#v5 - D#v3 - F#v or as Ab^3 - C^ - Eb^3 - Gb^5. This is a dot-double-down double-up-seven chord, written either as G#v3.vv,^^7 or as Ab^3.vv,^^7.
Intervals of 42edo
| Degree | Size (Cents) | pions | 7mus | relative notation | absolute notation | |
|---|---|---|---|---|---|---|
| 0 | 0 | perfect unison | P1 | D | ||
| 1 | 29.571 | 30.286 | 36.571 (24.92516) | up 1sn, minor 2nd | ^1, m2 | D^, Eb |
| 2 | 57.143 | 60.571 | 73.143 (49.24916) | double-up 1sn, upminor 2nd | ^^1, ^m2 | D^^, Eb^ |
| 3 | 85.714 | 90.857 | 109.714 (6D.B6E16) | double-up minor 2nd | ^^m2 | Eb^^ |
| 4 | 114.286 | 121.143 | 146.286 (92.49216) | downmid 2nd | v~2 | Eb^3 |
| 5 | 143.857 | 151.429 | 182.857 (B6.DB716) | upmid 2nd | ^~2 | Ev3 |
| 6 | 171.429 | 181.714 | 219.429 (DB.6DB16) | double-down major 2nd | vvM2 | Evv |
| 7 | 200 | 212 | 256 (10016) | downmajor 2nd | vM2 | Ev |
| 8 | 228.571 | 242.286 | 292.571 (124.92516) | major 2nd | M2 | E |
| 9 | 257.143 | 282.571 | 329.143 (149.24916) | minor 3rd | m3 | F |
| 10 | 285.714 | 302.857 | 365.714 (16D.B6E16) | upminor 3rd | ^m3 | F^ |
| 11 | 314.286 | 333.143 | 402.286 (192.49216) | double-up minor 3rd | ^^m3 | F^^ |
| 12 | 342.857 | 363.429 | 438.857 (1B6.DB716) | downmid 3rd | v~3 | F^3 |
| 13 | 371.429 | 393.714 | 475.429 (1DB.6DB16) | upmid 3rd | ^~3 | F#v3 |
| 14 | 400 | 424 | 512 (20016) | double-down major 3rd | vvM3 | F#vv |
| 15 | 428.571 | 454.286 | 548.571 (224.92516) | downmajor 3rd | vM3 | F#v |
| 16 | 457.143 | 484.571 | 585.143 (249.24916) | major 3rd, down 4th | M3, v4 | F#, Gv |
| 17 | 485.714 | 514.857 | 621.714 (26D.B6E16) | perfect 4th | P4 | G |
| 18 | 514.286 | 545.143 | 658.286 (292.49216) | up 4th | ^4 | G^ |
| 19 | 543.857 | 575.429 | 694.857 (2B6.DB716) | double-up 4th | ^^4 | G^^ |
| 20 | 571.429 | 605.714 | 731.429 (2DB.6DB16) | triple-up 4th | ^34 | G^3 |
| 21 | 600 | 6 | 768 (30016) | triple-down aug 4th, triple-up dim 5th | v3A4, ^3d5 | G#v3, Ab^3 |
| 22 | 628.571 | 666.286 | 804.571 (324.92516) | triple-down 5th | v35 | Av3 |
| 23 | 657.143 | 696.571 | 841.143 (349.24916) | double-down 5th | vv5 | Avv |
| 24 | 685.714 | 726.857 | 877.714 (36D.B6E16) | down 5th | v5 | Av |
| 25 | 714.286 | 757.143 | 950.286 (392.49216) | perfect 5th | P5 | A |
| 26 | 742.857 | 787.429 | 950.857 (3B6.DB716) | up 5th, minor 6th | ^5, m6 | A^, Bb |
| 27 | 771.429 | 817.714 | 987.429 (3DB.6DB16) | upminor 6th | ^m6 | Bb^ |
| 28 | 800 | 848 | 1024 (40016) | double-up minor 6th | ^^m6 | Bb^^ |
| 29 | 829.571 | 878.286 | 1060.571 (424.92516) | downmid 6th | v~6 | Bb^3 |
| 30 | 857.143 | 908.571 | 1097.143 (449.24916) | upmid 6th | ^~6 | Bv3 |
| 31 | 885.714 | 938.857 | 1133.714 (46D.B6E16) | double-down major 6th | vvM6 | Bvv |
| 32 | 914.286 | 969.143 | 1170.286 (492.49216) | downmajor 6th | vM6 | Bv |
| 33 | 942.857 | 999.429 | 1206.857 (4B6.DB716) | major 6th | M6 | B |
| 34 | 971.429 | 1029.714 | 1243.429 (4DB.6DB16) | minor 7th | m7 | C |
| 35 | 1000 | 1060 | 1280 (50016) | upminor 7th | ^m7 | C^ |
| 36 | 1028.571 | 1090.286 | 1316.571 (524.92516) | double-up minor 7th | ^^m7 | C^^ |
| 37 | 1057.143 | 1120.571 | 1353.143 (549.24916) | downmid 7th | v~7 | C^3 |
| 38 | 1085.714 | 1150.857 | 1389.714 (56D.B6E16) | upmid 7th | ^~7 | C#v3 |
| 39 | 1114.286 | 1181.143 | 1426.286 (592.49216) | double-down major 7th | vvM7 | C#vv |
| 40 | 1142.857 | 1211.429 | 1462.857 (5B6.DB716) | downmajor 7th | vM7 | C#v |
| 41 | 1171.429 | 1241.714 | 1499.429 (5DB.6DB16) | major 7th, down 8ve | M7, v8 | C#, Dv |
| 42 | 1200 | 1272 | 1536 (60016) | perfect 8ve | P8 | D |