Magic: Difference between revisions

Line 35:

* It is more complex than meantone (higher [[complexity]] and [[badness]]).

* The 3/2 approximation is 5 times as complex as the 5/4 approximation (the generator) so modulation by fifths is more constrained than you may be used to.

Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].

* [[3L 4s]]: LsLsLss, where L represents 6/5

* [[3L 7s]]: LssLssLsss, where L represents 7/6

* [[3L 10s]]: LsssLsssLssss, where L represents 9/8

* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent [[12/11]]~[[13/12]] (in magic temperament) or [[11/10]] (in the related [[telepathy]] temperament). In 22edo they are identical.

For technical information, see [[Magic family #Magic]]. For a discussion on alternative 11- and 13-limit extensions, see [[Magic extensions]].

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Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].

* [[3L 4s]]: LsLsLss, where L represents 6/5;

* [[3L 7s]]: LssLssLsss, where L represents 7/6;

* [[3L 10s]]: LsssLsssLssss, where L represents 9/8;

* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent [[12/11]]~[[13/12]] (in tridecimal magic) or [[11/10]] (in the related [[telepathy]] temperament). In 22edo they are identical.

=== Scala files ===

; Mos scales

* [[Magic7]] – improper [[3L 4s]]

* [[Magic7]] – improper 3L 4s

* [[Magic10]] – improper [[3L 7s]]

* [[Magic10]] – improper 3L 7s

* [[Magic13]] – improper [[3L 10s]]

* [[Magic13]] – improper 3L 10s

* [[Magic16]] – improper [[3L 13s]]. The boundary of propriety is 19edo.

* [[Magic16]] – improper 3L 13s. The boundary of propriety is 19edo.

* [[Magic19]] – proper [[3L 16s]]. The boundary of propriety is 22edo.

* [[Magic22]] – [[19L 3s]] ~~scale~~. The boundary of propriety is 41edo.

* [[Magic22]] – [[19L 3s]]. The boundary of propriety is 41edo.

; Transversal scales

@@ Line 35: / Line 35: @@
 * It is more complex than meantone (higher [[complexity]] and [[badness]]).
 * The 3/2 approximation is 5 times as complex as the 5/4 approximation (the generator) so modulation by fifths is more constrained than you may be used to.
-Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].
-* [[3L 4s]]: LsLsLss, where L represents 6/5
-* [[3L 7s]]: LssLssLsss, where L represents 7/6
-* [[3L 10s]]: LsssLsssLssss, where L represents 9/8
-* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent [[12/11]]~[[13/12]] (in magic temperament) or [[11/10]] (in the related [[telepathy]] temperament). In 22edo they are identical.
 For technical information, see [[Magic family #Magic]]. For a discussion on alternative 11- and 13-limit extensions, see [[Magic extensions]].
@@ Line 124: / Line 118: @@
 {{See also| Magic Tetrachords }}
+Because the generator is so close to 1/3 of an octave, and the interval left over is accordingly so small, all small magic mos scales consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following scales, where s always represents the characteristic small interval, which simultaneously represents [[128/125]], [[36/35]], [[28/27]], and [[25/24]].
+* [[3L 4s]]: LsLsLss, where L represents 6/5;
+* [[3L 7s]]: LssLssLsss, where L represents 7/6;
+* [[3L 10s]]: LsssLsssLssss, where L represents 9/8;
+* [[3L 13s]]: LssssLssssLsssss, where L is a neutral second, which can be taken to represent [[12/11]]~[[13/12]] (in tridecimal magic) or [[11/10]] (in the related [[telepathy]] temperament). In 22edo they are identical.
+=== Scala files ===
 ; Mos scales
-* [[Magic7]] – improper [[3L 4s]]
+* [[Magic7]] – improper 3L 4s
-* [[Magic10]] – improper [[3L 7s]]
+* [[Magic10]] – improper 3L 7s
-* [[Magic13]] – improper [[3L 10s]]
+* [[Magic13]] – improper 3L 10s
-* [[Magic16]] – improper [[3L 13s]]. The boundary of propriety is 19edo.
+* [[Magic16]] – improper 3L 13s. The boundary of propriety is 19edo.
 * [[Magic19]] – proper [[3L 16s]]. The boundary of propriety is 22edo.
-* [[Magic22]] – [[19L 3s]] scale. The boundary of propriety is 41edo.
+* [[Magic22]] – [[19L 3s]]. The boundary of propriety is 41edo.
 ; Transversal scales