36edo: Difference between revisions
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=== Zeta peak index === | |||
{| class="wikitable center-all" | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[155zpi]] | |||
| 35.9823877000425 | |||
| 33.3496490006021 | |||
| 6.027497 | |||
| 1.028887 | |||
| 14.706508 | |||
| 36edo | |||
| 1200.58736402167 | |||
| 8 | |||
| 8 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
| Line 1,046: | Line 1,045: | ||
833 Cent Golden Scale MOS [11]: '''3 1 3 3 1 3 1 3 3 1 3''' | 833 Cent Golden Scale MOS [11]: '''3 1 3 3 1 3 1 3 3 1 3''' | ||
== Tuning by | == Tuning by ear == | ||
After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way its purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals. | After [[9edo]] and [[19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way its purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6]]'s with a comma of less than 2 cents) connected by [[3/2]]'s, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo]] and obviously a much smaller absolute error. It's a good system to use on large organs that have three manuals. | ||