In the no-twos subgroup, 17EDT tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written b17&b21.
17EDT is the sixth zeta peak tritave division.
17EDT is closely related to 13EDT, the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13EDT and 17EDT have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13EDT is a calm 2:1, in 17EDT it is a hard 3:1. Thus, the approximation of 5/3 and 7/3 suffers slightly in return for gaining a good approximation of 11/9 (given the context of the weak 5/3 and 7/3), which is in fact the size of the large step. However, by the coincidence of the 11-limit commas 17EDT tempers out, 5/3 and 11/9 are off by practically the same amount in opposite directions (+10.7 cents and -11.8 cents), leading to an excellent approximation of 55/27 (only 1.1 cents flat), as are 11/9 and 9/7 (-11.8 cents and +12.4 cents), leading to an excellent approximation of 11/7 (only .6 cents flat) and these sum to 605/189-1.7 cents, which is also a 16/5 which is only .15 cents sharp (in addition to equaling 256).
|degree||note name||cents value||hekts||cents value |
|1||Db = B#||111.9||76.5|
|2||Eb = C#||223.8||152.9|
|5||F = D#||559.4||382.35|
|6||Gb = E#||671.3||458.8|
|7||Hb = F#||783.2||535.3|
|10||Jb = G#||1118.8||764.7|
|11||Ab = H#||1230.7||841.2||30.7|
|14||Bb = J#||1566.3||1070.6||366.3|
|15||Cb = A#||1678.2||1147.1||478.2|
- Notes named so that C D E F G H J A B C = Lambda mode
It's a weird coincidence how the schemes of 17EDO and 17EDT diatonicism are so similar and how their approximations of 9/7 are off by such similar amounts in opposite directions (17EDO -11.6 cents and 17EDT +12.4 cents).
- Vavoom (118&783)
Below is a plot of the no-twos Z function in the vicinity of 17EDT.