8edo: Difference between revisions

Line 28:

=== Octave shrinking ===

8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[~~1ed148.5c~~]].

8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[29ed12]].

Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. ~~1ed148.5c~~ approximates 5 of them.

Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. 29ed12 approximates 5 of them.

Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. ~~1ed148.5c~~ approximates 10 of them.

Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. 29ed12 approximates 10 of them.

In this way, ~~1ed148.5c~~ (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.

In this way, 29ed12 (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.

There are [[zeta peak index]] tunings nearby 8edo as well, however they damage the octave by over 20 cents, rendering them unrecognisable as stretched or compressed 8edo and more like entirely new scales in their own right.

@@ Line 28: / Line 28: @@
 === Octave shrinking ===
-edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[1ed148.5c]].
+edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[29ed12]].
-Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. 1ed148.5c approximates 5 of them.
+Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. 29ed12 approximates 5 of them.
-Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. 1ed148.5c approximates 10 of them.
+Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. 29ed12 approximates 10 of them.
-In this way, 1ed148.5c (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.
+In this way, 29ed12 (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.
 There are [[zeta peak index]] tunings nearby 8edo as well, however they damage the octave by over 20 cents, rendering them unrecognisable as stretched or compressed 8edo and more like entirely new scales in their own right.