97ed12: Difference between revisions

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== Theory ==

97ed12 is ~~very nearly identical~~ to [[27edo]], but with the [[12/1]] ~~rather than the 2/1~~ being just. This [[stretched and compressed tuning|compresses the octave]] by about 2.45{{c}}.

97ed12 is closely related to [[27edo]], but with the 12th harmonic rather than the [[2/1|octave]] being just. This [[stretched and compressed tuning|compresses the octave]] by about 2.45{{c}}. The harmonics that 27edo approximates accurately—3, 5, 7, 13, and 19—are all tuned significantly sharper than just, and 97ed12 improves these approximations.

=== Harmonics ===

{{Harmonics in equal|97|12|1|~~start~~=12|~~columns~~=12|collapsed=true|title=Approximation of harmonics in 97ed12 (continued)}}

{{Harmonics in equal|97|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 97ed12 (continued)}}

=== Subsets and supersets ===

97ed12 is the 25th [[prime equal division|prime ed12]], following 89ed12 and before 101ed12.

97ed12 is the 25th [[prime equal division|prime ed12]], following 89ed12 and before 101ed12, so it does not contain any nontrivial subset ed12's.

== See also ==

* [[16edf]] – relative edf

* [[27edo]] – relative edo

* [[43edt]] – relative edt

* [[70ed6]] – relative ed6

* [[90ed10]] – relative ed10

[[Category:27edo]]

@@ Line 3: / Line 3: @@
 == Theory ==
-ed12 is very nearly identical to [[27edo]], but with the [[12/1]] rather than the 2/1 being just. This [[stretched and compressed tuning|compresses the octave]] by about 2.45{{c}}.
+ed12 is closely related to [[27edo]], but with the 12th harmonic rather than the [[2/1|octave]] being just. This [[stretched and compressed tuning|compresses the octave]] by about 2.45{{c}}. The harmonics that 27edo approximates accurately—3, 5, 7, 13, and 19—are all tuned significantly sharper than just, and 97ed12 improves these approximations.
 === Harmonics ===
-{{Harmonics in equal|97|12|1}}
+{{Harmonics in equal|97|12|1|intervals=integer|columns=11}}
-{{Harmonics in equal|97|12|1|start=12|columns=12|collapsed=true|title=Approximation of harmonics in 97ed12 (continued)}}
+{{Harmonics in equal|97|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 97ed12 (continued)}}
 === Subsets and supersets ===
-ed12 is the 25th [[prime equal division|prime ed12]], following 89ed12 and before 101ed12.
+ed12 is the 25th [[prime equal division|prime ed12]], following 89ed12 and before 101ed12, so it does not contain any nontrivial subset ed12's.
 == See also ==
+* [[16edf]] – relative edf
 * [[27edo]] – relative edo
 * [[43edt]] – relative edt
 * [[70ed6]] – relative ed6
+* [[90ed10]] – relative ed10
+[[Category:27edo]]