35edo: Difference between revisions
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| Line 9: | Line 9: | ||
! style="text-align:center;" | Degrees | ! style="text-align:center;" | Degrees | ||
! style="text-align:center;" | Cents | ! style="text-align:center;" | Cents | ||
!7mus | !7mus | ||
! colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down]] [[Ups_and_Downs_Notation|Notation]] | ! colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|Up/down]] [[Ups_and_Downs_Notation|Notation]] | ||
|- | |- | ||
| colspan=" | | colspan="3" style="text-align:center;" | 0 | ||
| style="text-align:center;" | unison | | style="text-align:center;" | unison | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| Line 20: | Line 19: | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:center;" | 34.286 | | style="text-align:center;" | 34.286 | ||
|43.886 (2B.E2C<sub>16</sub>) | |43.886 (2B.E2C<sub>16</sub>) | ||
| style="text-align:center;" | up unison | | style="text-align:center;" | up unison | ||
| Line 28: | Line 26: | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:center;" | 68.571 | | style="text-align:center;" | 68.571 | ||
|87.771 (57.C58<sub>16</sub>) | |87.771 (57.C58<sub>16</sub>) | ||
| style="text-align:center;" | double-up unison | | style="text-align:center;" | double-up unison | ||
| Line 36: | Line 33: | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:center;" | 102.857 | | style="text-align:center;" | 102.857 | ||
|131.657 (83.A84<sub>16</sub>) | |131.657 (83.A84<sub>16</sub>) | ||
| style="text-align:center;" | double-down 2nd | | style="text-align:center;" | double-down 2nd | ||
| Line 44: | Line 40: | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:center;" | 137.143 | | style="text-align:center;" | 137.143 | ||
|175.543 (AF.8B<sub>16</sub>) | |175.543 (AF.8B<sub>16</sub>) | ||
| style="text-align:center;" | down 2nd | | style="text-align:center;" | down 2nd | ||
| Line 52: | Line 47: | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:center;" |171.429 | | style="text-align:center;" |171.429 | ||
|219.429 (DB.6DB<sub>16</sub>) | |219.429 (DB.6DB<sub>16</sub>) | ||
| style="text-align:center;" | 2nd | | style="text-align:center;" | 2nd | ||
| Line 60: | Line 54: | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:center;" | 205.714 | | style="text-align:center;" | 205.714 | ||
|263.314 (107.507<sub>16</sub>) | |263.314 (107.507<sub>16</sub>) | ||
| style="text-align:center;" | up 2nd | | style="text-align:center;" | up 2nd | ||
| Line 68: | Line 61: | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:center;" | 240 | | style="text-align:center;" | 240 | ||
|307.2 (133.333<sub>16</sub>) | |307.2 (133.333<sub>16</sub>) | ||
| style="text-align:center;" | double-up 2nd | | style="text-align:center;" | double-up 2nd | ||
| Line 76: | Line 68: | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:center;" | 274.286 | | style="text-align:center;" | 274.286 | ||
|351.086 (15F.15F<sub>16</sub>) | |351.086 (15F.15F<sub>16</sub>) | ||
| style="text-align:center;" | double-down 3rd | | style="text-align:center;" | double-down 3rd | ||
| Line 84: | Line 75: | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:center;" | 308.571 | | style="text-align:center;" | 308.571 | ||
|394.971 (18A.F8B<sub>16</sub>) | |394.971 (18A.F8B<sub>16</sub>) | ||
| style="text-align:center;" | down 3rd | | style="text-align:center;" | down 3rd | ||
| Line 92: | Line 82: | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:center;" |342.857 | | style="text-align:center;" |342.857 | ||
|438.857 (1B6.DB7<sub>16</sub>) | |438.857 (1B6.DB7<sub>16</sub>) | ||
| style="text-align:center;" | 3rd | | style="text-align:center;" | 3rd | ||
| Line 100: | Line 89: | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:center;" | 377.143 | | style="text-align:center;" | 377.143 | ||
|482.743 (1E2.BE3<sub>16</sub>) | |482.743 (1E2.BE3<sub>16</sub>) | ||
| style="text-align:center;" | up 3rd | | style="text-align:center;" | up 3rd | ||
| Line 108: | Line 96: | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:center;" | 411.429 | | style="text-align:center;" | 411.429 | ||
|526.629 (20E.A0F<sub>16</sub>) | |526.629 (20E.A0F<sub>16</sub>) | ||
| style="text-align:center;" | double-up 3rd | | style="text-align:center;" | double-up 3rd | ||
| Line 116: | Line 103: | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:center;" | 445.714 | | style="text-align:center;" | 445.714 | ||
|570.514 (23A.83A8<sub>16</sub>) | |570.514 (23A.83A8<sub>16</sub>) | ||
| style="text-align:center;" | double-down 4th | | style="text-align:center;" | double-down 4th | ||
| Line 124: | Line 110: | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:center;" | 480 | | style="text-align:center;" | 480 | ||
|614.4 (266.666<sub>16</sub>) | |614.4 (266.666<sub>16</sub>) | ||
| style="text-align:center;" | down 4th | | style="text-align:center;" | down 4th | ||
| Line 132: | Line 117: | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:center;" |514.286 | | style="text-align:center;" |514.286 | ||
|658.286 (292.492<sub>16</sub>) | |658.286 (292.492<sub>16</sub>) | ||
| style="text-align:center;" | 4th | | style="text-align:center;" | 4th | ||
| Line 140: | Line 124: | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:center;" | 548.571 | | style="text-align:center;" | 548.571 | ||
|702.171 (2BE.2BE<sub>16</sub>) | |702.171 (2BE.2BE<sub>16</sub>) | ||
| style="text-align:center;" | up 4th | | style="text-align:center;" | up 4th | ||
| Line 148: | Line 131: | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| style="text-align:center;" | 582.857 | | style="text-align:center;" | 582.857 | ||
|746.057 (2EA.0EA<sub>16</sub>) | |746.057 (2EA.0EA<sub>16</sub>) | ||
| style="text-align:center;" | double-up 4th | | style="text-align:center;" | double-up 4th | ||
| Line 156: | Line 138: | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| style="text-align:center;" | 617.143 | | style="text-align:center;" | 617.143 | ||
|789.943 (315.F16<sub>16</sub>) | |789.943 (315.F16<sub>16</sub>) | ||
| style="text-align:center;" | double-down 5th | | style="text-align:center;" | double-down 5th | ||
| Line 164: | Line 145: | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:center;" | 651.429 | | style="text-align:center;" | 651.429 | ||
|833.829 (341.D42<sub>16</sub>) | |833.829 (341.D42<sub>16</sub>) | ||
| style="text-align:center;" | down 5th | | style="text-align:center;" | down 5th | ||
| Line 172: | Line 152: | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| style="text-align:center;" |685.714 | | style="text-align:center;" |685.714 | ||
|877.714 (36D.B6E<sub>16</sub>) | |877.714 (36D.B6E<sub>16</sub>) | ||
| style="text-align:center;" | 5th | | style="text-align:center;" | 5th | ||
| Line 180: | Line 159: | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| style="text-align:center;" | 720 | | style="text-align:center;" | 720 | ||
|921.6 (399.99A<sub>16</sub>) | |921.6 (399.99A<sub>16</sub>) | ||
| style="text-align:center;" | up 5th | | style="text-align:center;" | up 5th | ||
| Line 188: | Line 166: | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| style="text-align:center;" | 754.286 | | style="text-align:center;" | 754.286 | ||
|965.486 (3C5.7C58<sub>16</sub>) | |965.486 (3C5.7C58<sub>16</sub>) | ||
| style="text-align:center;" | double-up 5th | | style="text-align:center;" | double-up 5th | ||
| Line 196: | Line 173: | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| style="text-align:center;" | 788.571 | | style="text-align:center;" | 788.571 | ||
|1009.371 (3F1.5F1<sub>16</sub>) | |1009.371 (3F1.5F1<sub>16</sub>) | ||
| style="text-align:center;" | double-down 6th | | style="text-align:center;" | double-down 6th | ||
| Line 204: | Line 180: | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| style="text-align:center;" | 822.857 | | style="text-align:center;" | 822.857 | ||
|1053.257 (40B.21B<sub>16</sub>) | |1053.257 (40B.21B<sub>16</sub>) | ||
| style="text-align:center;" | down 6th | | style="text-align:center;" | down 6th | ||
| Line 212: | Line 187: | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| style="text-align:center;" |857.143 | | style="text-align:center;" |857.143 | ||
|1097.143 (449.249<sub>16</sub>) | |1097.143 (449.249<sub>16</sub>) | ||
| style="text-align:center;" | 6th | | style="text-align:center;" | 6th | ||
| Line 220: | Line 194: | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| style="text-align:center;" | 891.429 | | style="text-align:center;" | 891.429 | ||
|1141.029 (475.073<sub>16</sub>) | |1141.029 (475.073<sub>16</sub>) | ||
| style="text-align:center;" | up 6th | | style="text-align:center;" | up 6th | ||
| Line 228: | Line 201: | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| style="text-align:center;" | 925.714 | | style="text-align:center;" | 925.714 | ||
|1184.914 (1A0.EA1<sub>16</sub>) | |1184.914 (1A0.EA1<sub>16</sub>) | ||
| style="text-align:center;" | double-up 6th | | style="text-align:center;" | double-up 6th | ||
| Line 236: | Line 208: | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| style="text-align:center;" | 960 | | style="text-align:center;" | 960 | ||
|1228.8 (4CC.CCD<sub>16</sub>) | |1228.8 (4CC.CCD<sub>16</sub>) | ||
| style="text-align:center;" | double-down 7th | | style="text-align:center;" | double-down 7th | ||
| Line 244: | Line 215: | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| style="text-align:center;" | 994.286 | | style="text-align:center;" | 994.286 | ||
|1272.686 (4F8.AF9<sub>16</sub>) | |1272.686 (4F8.AF9<sub>16</sub>) | ||
| style="text-align:center;" | down 7th | | style="text-align:center;" | down 7th | ||
| Line 252: | Line 222: | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| style="text-align:center;" |1028.571 | | style="text-align:center;" |1028.571 | ||
|1316.571 (524.925<sub>16</sub>) | |1316.571 (524.925<sub>16</sub>) | ||
| style="text-align:center;" | 7th | | style="text-align:center;" | 7th | ||
| Line 260: | Line 229: | ||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| style="text-align:center;" | 1062.857 | | style="text-align:center;" | 1062.857 | ||
|1360.467 (550.73<sub>16</sub>). | |1360.467 (550.73<sub>16</sub>). | ||
| style="text-align:center;" | up 7th | | style="text-align:center;" | up 7th | ||
| Line 268: | Line 236: | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
| style="text-align:center;" | 1097.143 | | style="text-align:center;" | 1097.143 | ||
|1404.343 (57C.57C<sub>16</sub>) | |1404.343 (57C.57C<sub>16</sub>) | ||
| style="text-align:center;" | double-up 7th | | style="text-align:center;" | double-up 7th | ||
| Line 276: | Line 243: | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
| style="text-align:center;" | 1131.429 | | style="text-align:center;" | 1131.429 | ||
|1448.229 (5A8.3A8<sub>16</sub>) | |1448.229 (5A8.3A8<sub>16</sub>) | ||
| style="text-align:center;" | double-down 8ve | | style="text-align:center;" | double-down 8ve | ||
| Line 284: | Line 250: | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
| style="text-align:center;" | 1165.714 | | style="text-align:center;" | 1165.714 | ||
|1492.114 (5D4.1D4<sub>16</sub>) | |1492.114 (5D4.1D4<sub>16</sub>) | ||
| style="text-align:center;" | down 8ve | | style="text-align:center;" | down 8ve | ||
| Line 292: | Line 257: | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
| style="text-align:center;" | 1200 | | style="text-align:center;" | 1200 | ||
|1536 (600<sub>16</sub>) | |1536 (600<sub>16</sub>) | ||
| style="text-align:center;" | 8ve | | style="text-align:center;" | 8ve | ||
Revision as of 13:51, 12 December 2019
35-tET or 35-EDO refers to a tuning system which divides the octave into 35 steps of approximately 34.29¢ each.
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic macrotonal edos: 5edo and 7edo. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 subgroup and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among whitewood tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore 22edo's more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for greenwood and secund temperaments, as well as 11-limit muggles, and the 35f val is an excellent tuning for 13-limit muggles.
Notation
| Degrees | Cents | 7mus | Up/down Notation | ||
|---|---|---|---|---|---|
| 0 | unison | 1 | D | ||
| 1 | 34.286 | 43.886 (2B.E2C16) | up unison | ^1 | D^ |
| 2 | 68.571 | 87.771 (57.C5816) | double-up unison | ^^1 | D^^ |
| 3 | 102.857 | 131.657 (83.A8416) | double-down 2nd | vv2 | Evv |
| 4 | 137.143 | 175.543 (AF.8B16) | down 2nd | v2 | Ev |
| 5 | 171.429 | 219.429 (DB.6DB16) | 2nd | 2 | E |
| 6 | 205.714 | 263.314 (107.50716) | up 2nd | ^2 | E^ |
| 7 | 240 | 307.2 (133.33316) | double-up 2nd | ^^2 | E^^ |
| 8 | 274.286 | 351.086 (15F.15F16) | double-down 3rd | vv3 | Fvv |
| 9 | 308.571 | 394.971 (18A.F8B16) | down 3rd | v3 | Fv |
| 10 | 342.857 | 438.857 (1B6.DB716) | 3rd | 3 | F |
| 11 | 377.143 | 482.743 (1E2.BE316) | up 3rd | ^3 | F^ |
| 12 | 411.429 | 526.629 (20E.A0F16) | double-up 3rd | ^^3 | F^^ |
| 13 | 445.714 | 570.514 (23A.83A816) | double-down 4th | vv4 | Gvv |
| 14 | 480 | 614.4 (266.66616) | down 4th | v4 | Gv |
| 15 | 514.286 | 658.286 (292.49216) | 4th | 4 | G |
| 16 | 548.571 | 702.171 (2BE.2BE16) | up 4th | ^4 | G^ |
| 17 | 582.857 | 746.057 (2EA.0EA16) | double-up 4th | ^^4 | G^^ |
| 18 | 617.143 | 789.943 (315.F1616) | double-down 5th | vv5 | Avv |
| 19 | 651.429 | 833.829 (341.D4216) | down 5th | v5 | Av |
| 20 | 685.714 | 877.714 (36D.B6E16) | 5th | 5 | A |
| 21 | 720 | 921.6 (399.99A16) | up 5th | ^5 | A^ |
| 22 | 754.286 | 965.486 (3C5.7C5816) | double-up 5th | ^^5 | A^^ |
| 23 | 788.571 | 1009.371 (3F1.5F116) | double-down 6th | vv6 | Bvv |
| 24 | 822.857 | 1053.257 (40B.21B16) | down 6th | v6 | Bv |
| 25 | 857.143 | 1097.143 (449.24916) | 6th | 6 | B |
| 26 | 891.429 | 1141.029 (475.07316) | up 6th | ^6 | B^ |
| 27 | 925.714 | 1184.914 (1A0.EA116) | double-up 6th | ^^6 | B^^ |
| 28 | 960 | 1228.8 (4CC.CCD16) | double-down 7th | vv7 | Cvv |
| 29 | 994.286 | 1272.686 (4F8.AF916) | down 7th | v7 | Cv |
| 30 | 1028.571 | 1316.571 (524.92516) | 7th | 7 | C |
| 31 | 1062.857 | 1360.467 (550.7316). | up 7th | ^7 | C^ |
| 32 | 1097.143 | 1404.343 (57C.57C16) | double-up 7th | ^^7 | C^^ |
| 33 | 1131.429 | 1448.229 (5A8.3A816) | double-down 8ve | vv8 | Dvv |
| 34 | 1165.714 | 1492.114 (5D4.1D416) | down 8ve | v8 | Dv |
| 35 | 1200 | 1536 (60016) | 8ve | 8 | D |
Ups and downs for chords
Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.
0-10-20 = C E G = C = C or C perfect
0-9-20 = C Ev G = C(v3) = C down-three
0-11-20 = C E^ G = C(^3) = C up-three
0-10-19 = C E Gv = C(v5) = C down-five
0-11-21 = C E^ G^ = C(^3,^5) = C up-three up-five
0-10-20-30 = C E G B = C7 = C seven
0-10-20-29 = C E G Bv = C(v7) = C down-seven
0-9-20-30 = C Ev G B = C7(v3) = C seven down-three
0-9-20-29 = C Ev G Bv = C.v7 = C dot down seven
For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.
Intervals
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35-edo interval.)
| Degrees | Cents value | pions | 7mus | Ratios in2.5.7.11.17 subgroup | Ratios with flat 3 | Ratios with sharp 3 | Ratios with best 9 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1/1 | (see comma table) | ||||
| 1 | 34.286 | 36.343 | 43.886 (2B.E2C16) | 50/49 , 121/119 , 33/32 | 36/35 | 25/24 | 81/80 |
| 2 | 68.571 | 72.686 | 87.771 (57.C5816) | 128/125 | 25/24 | 81/80 | |
| 3 | 102.857 | 109.029 | 131.657 (83.A8416) | 17/16 | 15/14 | 16/15 | 18/17 |
| 4 | 137.143 | 145.371 | 175.543 (AF.8B16) | 12/11 , 16/15 | |||
| 5 | 171.429 | 181.714 | 219.429 (DB.6DB16) | 11/10 | 12/11 | 10/9 | |
| 6 | 205.714 | 218.057 | 263.314 (107.50716) | 9/8 | |||
| 7 | 240 | 254.4 | 307.2 (133.33316) | 8/7 | 7/6 | ||
| 8 | 274.286 | 290.743 | 351.086 (15F.15F16) | 20/17 | 7/6 | ||
| 9 | 308.571 | 327.086 | 394.971 (18A.F8B16) | 6/5 | |||
| 10 | 342.857 | 363.429 | 438.857 (1B6.DB716) | 17/14 | 6/5 | 11/9 | |
| 11 | 377.143 | 399.771 | 482.743 (1E2.BE316) | 5/4 | |||
| 12 | 411.429 | 436.114 | 526.629 (20E.A0F16) | 14/11 | |||
| 13 | 445.714 | 472.457 | 570.514 (23A.83A816) | 22/17 , 32/25 | 9/7 | ||
| 14 | 480 | 508.8 | 614.4 (266.66616) | 4/3, 21/16 | |||
| 15 | 514.286 | 545.143 | 658.286 (292.49216) | 4/3 | |||
| 16 | 548.571 | 581.486 | 702.171 (2BE.2BE16) | 11/8 | |||
| 17 | 582.857 | 617.829 | 746.057 (2EA.0EA16) | 7/5 | 24/17 | 17/12 | |
| 18 | 617.143 | 654.171 | 789.943 (315.F1616) | 10/7 | 17/12 | 24/17 | |
| 19 | 651.429 | 690.514 | 833.829 (341.D4216) | 16/11 | |||
| 20 | 685.714 | 726.857 | 877.714 (36D.B6E16) | 3/2 | |||
| 21 | 720 | 763.2 | 921.6 (399.99A16) | 3/2, 32/21 | |||
| 22 | 754.286 | 799.443 | 965.486 (3C5.7C5816) | 17/11 , 25/16 | 14/9 | ||
| 23 | 788.571 | 835.886 | 1009.371 (3F1.5F116) | 11/7 | |||
| 24 | 822.857 | 872.229 | 1053.257 (40B.21B16) | 8/5 | |||
| 25 | 857.143 | 908.571 | 1097.143 (449.24916) | 28/17 | 5/3 | 18/11 | |
| 26 | 891.429 | 944.914 | 1141.029 (475.07316) | 5/3 | |||
| 27 | 925.714 | 981.257 | 1184.914 (1A0.EA116) | 17/10 | 12/7 | ||
| 28 | 960 | 1017.6 | 1228.8 (4CC.CCD16) | 7/4 | |||
| 29 | 994.286 | 1053.943 | 1272.686 (4F8.AF916) | 16/9 | |||
| 30 | 1028.571 | 1090.286 | 1316.571 (524.92516) | 20/11 | 9/5 | ||
| 31 | 1062.857 | 1126.629 | 1360.467 (550.7316). | 11/6 , 15/8 | |||
| 32 | 1097.143 | 1162.971 | 1404.343 (57C.57C16) | 32/17 | 28/15 | 15/8 | 17/9 |
| 33 | 1131.429 | 1199.314 | 1448.229 (5A8.3A816) | ||||
| 34 | 1165.714 | 1235.657 | 1492.114 (5D4.1D416) | ||||
| 3 | 1200 | 1272 | 1536 (60016) | ||||
Rank two temperaments
| Periods
per octave |
Generator | Temperaments with
flat 3/2 (patent val) |
Temperaments with sharp 3/2 (35b val) |
|---|---|---|---|
| 1 | 1\35 | ||
| 1 | 2\35 | ||
| 1 | 3\35 | Ripple | |
| 1 | 4\35 | Secund | |
| 1 | 6\35 | Messed-up Baldy | |
| 1 | 8\35 | Messed-up Orwell | |
| 1 | 9\35 | Myna | |
| 1 | 11\35 | Muggles | |
| 1 | 12\35 | Roman | |
| 1 | 13\35 | Inconsistent 2.9'/7.5/3 Sensi | |
| 1 | 16\35 | ||
| 1 | 17\35 | ||
| 5 | 1\35 | Blackwood (favoring 7/6) | |
| 5 | 2\35 | Blackwood (favoring 6/5 and 20/17) | |
| 5 | 3\35 | Blackwood (favoring 5/4 and 17/14) | |
| 7 | 1\35 | Whitewood/Redwood | |
| 7 | 2\35 | Greenwood | |
Scales
A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a MOS of 3L2s: 9 4 9 9 4.
Commas
35EDO tempers out the following commas. (Note: This assumes the val < 35 55 81 98 121 130|.)
| Comma | Monzo | Value (Cents) | Name 1 | Name 2 |
|---|---|---|---|---|
| 2187/2048 | | -11 7 > | 113.69 | Apotome | Whitewood comma |
| 6561/6250 | | -1 8 -5 > | 84.07 | Ripple comma | |
| 10077696/9765625 | | 9 9 -10 > | 54.46 | Mynic comma | |
| 3125/3072 | | -10 -1 5 > | 29.61 | Small diesis | Magic comma |
| 405/392 | | -3 4 1 -2 > | 56.48 | Greenwoodma | |
| 16807/16384 | | -14 0 0 5 > | 44.13 | ||
| 525/512 | | -9 1 2 1 > | 43.41 | Avicenna | |
| 126/125 | | 1 2 -3 1 > | 13.79 | Starling comma | Septimal semicomma |
| 99/98 | | -1 2 0 -2 1 > | 17.58 | Mothwellsma | |
| 66/65 | | 1 1 -1 0 1 -1 > | 26.43 |
Music
Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin
Self-Destructing Mechanical Forest by Chuckles McGee (in Secund[9])