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-[[Magic]] has various competing [[extension]]s to the 11- and 13-limit.
+[[Magic]] has various competing [[extension]]s to the 11- and 13-limit. The following temperaments are discussed in this article:
+* '''Tridecimal magic''' (19 & 22f) – tempering out 100/99, 105/104, 144/143, and 196/195;
+* '''Necromancy''' (19f & 22) – tempering out 100/99, 225/224, 245/243, and 275/273;
+* '''Sorcery''' (19 & 22) – tempering out 65/64, 78/77, 91/90, and 100/99;
+* '''Witchcraft''' (19e & 22ef) – tempering out 105/104, 196/195, 245/243, and 275/273;
+* '''Telepathy''' (19e & 22) – tempering out 55/54, 65/64, 91/90, and 99/98.
+== Interval chain ==
+In the following table, odd harmonics and subharmonics 1–13 are in '''bold'''.
+{| class="wikitable center-1 right-2"
+! rowspan="3" | #
+! rowspan="3" | Cents*
+! colspan="6" | Approximate ratios
+|-
+! rowspan="2" | 7-limit
+! colspan="5" | 13-limit extensions
+|-
+! Magic
+! Necromancy
+! Sorcery
+! Witchcraft
+! Telepathy
+|-
+| 0
+| 0.0
+| '''1/1'''
+|
+|
+|
+|
+|
+|-
+| 1
+| 380.4
+| '''5/4'''
+| 26/21
+|
+| '''16/13'''
+|
+| '''16/13'''
+|-
+| 2
+| 760.9
+| 14/9
+|
+|
+| 20/13
+|
+| 11/7, 20/13
+|-
+| 3
+| 1141.4
+| 27/14
+| 52/27, 64/33
+| 64/33
+| 64/33
+| 52/27
+| 88/45
+|-
+| 4
+| 321.8
+| 6/5
+| 40/33
+| 40/33
+| 40/33
+|
+| 11/9
+|-
+| 5
+| 702.3
+| '''3/2'''
+|
+|
+|
+|
+|
+|-
+| 6
+| 1082.7
+| 15/8, 28/15
+| 13/7
+|
+| 24/13
+| 13/7
+| 24/13
+|-
+| 7
+| 263.2
+| 7/6
+|
+|
+| 13/11
+|
+|
+|-
+| 8
+| 643.7
+| 35/24
+| 13/9, '''16/11'''
+| '''16/11'''
+| '''16/11'''
+| 13/9
+| 22/15
+|-
+| 9
+| 1024.1
+| 9/5
+| 20/11
+| 20/11
+| 20/11
+|
+| 11/6
+|-
+| 10
+| 204.6
+| '''9/8'''
+|
+|
+|
+|
+|
+|-
+| 11
+| 585.0
+| 7/5
+|
+|
+| 18/13
+|
+| 18/13
+|-
+| 12
+| 965.5
+| '''7/4'''
+| 26/15
+|
+|
+| 26/15
+|
+|-
+| 13
+| 146.0
+| 35/32
+| 12/11, 13/12
+| 12/11
+| 12/11, 14/13
+| 13/12
+| 11/10, 14/13
+|-
+| 14
+| 526.4
+| 27/20
+| 15/11
+| 15/11
+| 15/11
+|
+| '''11/8'''
+|-
+| 15
+| 906.9
+| 27/16, 42/25
+|
+| 22/13
+|
+| 22/13
+|-
+| 16
+| 87.3
+| 21/20
+|
+|
+| 27/26
+| 22/21
+| 27/26
+|-
+| 17
+| 467.8
+| 21/16
+| 13/10
+|
+|
+| 13/10
+|
+|-
+| 18
+| 848.2
+| 49/30
+| '''13/8''', 18/11
+| 18/11
+| 18/11, 21/13
+| '''13/8'''
+| 21/13
+|-
+| 19
+| 28.7
+| 49/48, 81/80, 126/125
+| 45/44
+| 45/44
+| 45/44
+|
+| 33/32
+|-
+| 20
+| 409.2
+| 63/50
+| 14/11
+| 14/11
+| 14/11
+|
+|
+|-
+| 21
+| 789.6
+| 63/40
+|
+|
+|
+| 11/7
+|
+|-
+| 22
+| 1170.1
+| 49/25, 63/32
+| 39/20
+|
+|
+| 39/20
+|
+|}
+<nowiki/>* In 7-limit [[CWE tuning]]
 == Tuning spectra ==

Magic extensions: Difference between revisions