The Riemann zeta function and tuning: Difference between revisions

Alternatively (as [[groundfault]] has found), if we do not allow octave detuning and only look at the record |Z(x)| zeta scores corresponding to exact edos with pure octaves, we get {{EDOs| 1, 2, 3, 5, 7, 10, 12, 19, 22, 31, 41, 53, 87, 118, 130, 171, 224, 270, 311, 472, 494, 742, 1065, 1106, 1395, 1578, 2460, 2684, 3566, 4231, 4973, 5585, 8269, 8539, 14124, 14348, 16808, 28742, 30631, 34691, 36269, 57578, 58973,}} … of '''zeta peak integer edos''', Edos in this list not included in the previous are {{EDOs| 87, 311, 472, 1065, 3566, 4231, 4973, 14124, 30631,}} … and edos not included in this list but included in the previous are {{EDOs| 4, 27, 72, 99, 152, 217, 342, 422, 441, 764, 935, 954, 1012, 1178, 1236, 1448, 3395, 6079, 7033, 11664,}} … with 72's removal perhaps being the most surprising, showing the strength of 53 in that 72 does not improve on the peak of 53. This definition may be better for measuring how accurate the edo itself is without stretched octaves, whereas the previous list assumes that the octave is tempered along with all other intervals. This list can thus also be thought of as "pure-octave zeta peak edos." Similarly, we can look at pure-tritave EDTs, etc.

{| class="wikitable"

|+ style="font-size: 105%;" | Zeta peak EDOs under 1000

| 1 || 2 || 3 || 4 || 5 || 7 || 10 || 12 || 19 || 22 || 27 || 31 || 41 || 53 || 72 || 87 || 99 || 118 || 130 || 152 || 171 || 217 || 224 || 270 || 311 || 342 || 422 || 472 || 494 || 742 || 764 || 935 || 954

| ★ || ★ || ★ || ★ || ★ || ★ || ★

| ★ || ★ || ★ || || ★ || ★ || ★