21edf: Difference between revisions

(6 intermediate revisions by 2 users not shown)

Line 2:

21EDF is related to [[36edo]], but with the 3/2 rather than the 2/1 being ~~jus~~, which stretches the octave by about 3.3514 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.

21EDF is related to [[36edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by about 3.3514 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.

~~Lookalikes: [[36edo]], [[57edt]], [[93ed6]], [[101ed7]]~~

Lookalikes: [[36edo]], [[57edt]], [[93ed6]], [[101ed7]], [[129ed12]]

== Theory ==

21edf acts as a stretched version of 36edo, though under most circumstances the stretch is more than ideal. If used as a fifth-based system, the chord 6:7:8(:9) may act as the fundamental chord of the system. The most important comma tempered out by this system is [[1029/1024]], and the related temperament is a fifth-based version of [[slendric]] with a 1/3-fifth period representing [[8/7]] and a generator of about a sixth-tone. One generator up or down from this period gives [[7/6]] and [[9/8]] respectively. Other edfs supporting this temperament include [[24edf]] and [[45edf]].

== Approximations ==

=== Harmonics ===

Line 78:

Line 79:

! Additional ratios<br />of 2.3.7.13.17

|-

| colspan="2" 0

| colspan="2" | 0

| 1/1

|

Line 292:

Line 293:

|

|}

== See also ==

* [[36edo]] – relative edo

* [[57edt]] – relative edt

* [[93ed6]] – relative ed6

* [[101ed7]] – relative ed7

* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo

[[Category:36edo]]

@@ Line 2: / Line 2: @@
 {{ED intro}}
-EDF is related to [[36edo]], but with the 3/2 rather than the 2/1 being jus, which stretches the octave by about 3.3514 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.
+EDF is related to [[36edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by about 3.3514 cents. Unlike 36edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.
-Lookalikes: [[36edo]], [[57edt]], [[93ed6]], [[101ed7]]
+Lookalikes: [[36edo]], [[57edt]], [[93ed6]], [[101ed7]], [[129ed12]]
+== Theory ==
+edf acts as a stretched version of 36edo, though under most circumstances the stretch is more than ideal. If used as a fifth-based system, the chord 6:7:8(:9) may act as the fundamental chord of the system. The most important comma tempered out by this system is [[1029/1024]], and the related temperament is a fifth-based version of [[slendric]] with a 1/3-fifth period representing [[8/7]] and a generator of about a sixth-tone. One generator up or down from this period gives [[7/6]] and [[9/8]] respectively. Other edfs supporting this temperament include [[24edf]] and [[45edf]].
 == Approximations ==
 === Harmonics ===
@@ Line 78: / Line 79: @@
 ! Additional ratios<br />of 2.3.7.13.17
 |-
-| colspan="2" 0
+| colspan="2" | 0
 | 1/1
 |
@@ Line 292: / Line 293: @@
 |
 |}
+== See also ==
+* [[36edo]] – relative edo
+* [[57edt]] – relative edt
+* [[93ed6]] – relative ed6
+* [[101ed7]] – relative ed7
+* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo
 {{todo|expand}}
+[[Category:36edo]]