10edf: Difference between revisions

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== Theory ==

10edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is about 6.68 ~~cents compressed~~. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.

10edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.

=== Harmonics ===

{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}}

=== Subsets and supersets ===

Since 10 factors into primes as {{nowrap| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs.

== Intervals ==

{| class="wikitable center-all right-2"

|-

! #

! Cents

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 == Theory ==
-edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is about 6.68 cents compressed. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.
+edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.
 === Harmonics ===
 {{Harmonics in equal|10|3|2|intervals=integer|columns=11}}
 {{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}}
+=== Subsets and supersets ===
+Since 10 factors into primes as {{nowrap| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs.
 == Intervals ==
 {| class="wikitable center-all right-2"
+|-
 ! #
 ! Cents