60edf: Difference between revisions

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== Theory ==

60edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], ~~and as such~~ it inherits ~~some of the~~ properties of both those ~~systems~~. ~~It's~~ very similar to [[205ed4]].

60edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], but it actually inherits few properties from either.

~~{{todo|complete section|inline=1}}~~

It makes available [[dual-n|dual]] versions of [[prime]]s 2 and 3 from both systems. Yet its mappings of primes 5, 7, 11, 13 and up are actually all different from either of those edos. For example mapping prime 5 to the 238th step (not 237 as in 102edo, nor 239 as in 103edo).

60edf is very similar to [[205ed4]].

=== Harmonics ===

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So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.

{{Harmonics in equal|60|3|2|intervals=prime|columns=13|title=Approximation of primes in 60edf ~~(continued)~~}}

{{Harmonics in equal|60|3|2|intervals=prime|columns=13|title=Approximation of primes in 60edf}}

{{Harmonics in equal|60|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of integers in 60edf ~~(continued)~~}}

{{Harmonics in equal|60|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of integers in 60edf }}

{{Harmonics in equal|60|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of integers in 60edf (continued)}}

=== Subsets and supersets ===

As a highly composite edf, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].

This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos/ed4s) simultaneously.

The relative edos/ed4s of its subsets are: [[7ed4]], [[5edo]], [[9edo]]/[[17ed4]], [[21ed4]], [[31ed4]], [[17edo]], [[21edo]]/[[41ed4]], [[26edo]], [[34edo]] and [[51edo]]/[[103ed4]].

The simplest supersets of 60edf are [[120edf]] and [[180edf]].

== Intervals ==

== Instruments ==

A [[Lumatone mapping for 60edf]] is now available.

== Music ==

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* [[265ed6]] - relative ed6

~~{{Stub}}~~

[[Category:Nonoctave]]

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 == Theory ==
-edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], and as such it inherits some of the properties of both those systems. It's very similar to [[205ed4]].
+edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], but it actually inherits few properties from either.
-{{todo|complete section|inline=1}}
+It makes available [[dual-n|dual]] versions of [[prime]]s 2 and 3 from both systems. Yet its mappings of primes 5, 7, 11, 13 and up are actually all different from either of those edos. For example mapping prime 5 to the 238th step (not 237 as in 102edo, nor 239 as in 103edo).
+edf is very similar to [[205ed4]].
 === Harmonics ===
@@ Line 12: / Line 15: @@
 So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.
-{{Harmonics in equal|60|3|2|intervals=prime|columns=13|title=Approximation of primes in 60edf (continued)}}
+{{Harmonics in equal|60|3|2|intervals=prime|columns=13|title=Approximation of primes in 60edf}}
-{{Harmonics in equal|60|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of integers in 60edf (continued)}}
+{{Harmonics in equal|60|3|2|intervals=integer|columns=11|collapsed=true|title=Approximation of integers in 60edf }}
 {{Harmonics in equal|60|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of integers in 60edf (continued)}}
 === Subsets and supersets ===
-{{todo|complete section|inline=1}}
+As a highly composite edf, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].
+This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos/ed4s) simultaneously.
+The relative edos/ed4s of its subsets are: [[7ed4]], [[5edo]], [[9edo]]/[[17ed4]], [[21ed4]], [[31ed4]], [[17edo]], [[21edo]]/[[41ed4]], [[26edo]], [[34edo]] and [[51edo]]/[[103ed4]].
+The simplest supersets of 60edf are [[120edf]] and [[180edf]].
+== Intervals ==
+{{Interval table}}
+== Instruments ==
+A [[Lumatone mapping for 60edf]] is now available.
 == Music ==
@@ Line 29: / Line 45: @@
 * [[265ed6]] - relative ed6
-{{Stub}}
+[[Category:Nonoctave]]