2.3.35 and 2.3.49
2.3.35 and 2.3.49 are two subsets of the 2.3.5.7 (septimal) group that involve many ratios further from 12edo than 2.3.7. The 35th harmonic (5*7) perfectly combines the deviations of the 5th and 7th harmonics to be about as far from 12edo as possible, whereas the 49th harmonic (7*7) overshoots slightly.
Intervals
2.3.35
2.3.35 intervals are the difference between a 5-over and 7-under interval, or vice versa.
36/35 septimal quarter tone
35/32 septimal neutral second
81/70 septimal semifourth
2.3.5.49
2.3.49 intervals are the difference between a 7-over and 7-under interval. 49/5 is further from 12edo.
54/49 larger neutral second
49/45 smaller neutral second
49/40 neutral third
2.3.5.49 tripentatonic 5L2m5s3a (blackdye A Aeolian with added chain of 5/49 offset)
81/80
54/49
9/8
6/5
64/49
4/3
27/20
72/49
3/2
8/5
256/147
16/9
9/5
96/49
2/1
Tempering out 245/243 equates the two smallest steps, leaving 5L2m8s. Tempering out 1029/1024 equates 256/147 to 7/4.
| 3^ | /49 | *245/243 | *1029/1024 |
|---|---|---|---|
| -1 | 256/147 | 1280/729 | 7/4 |
| 0 | 64/49 | 320/243 | 21/16 |
| 1 | 96/49 | 160/81 | 63/32 |
| 2 | 72/49 | 40/27 | 189/128 |
| 3 | 54/49 | 10/9 | 567/512 |
| 4 | 81/49 | 5/3 | 1701/1024 |
| 5 | 243/196 | 5/4 | 5103/4096 |
