Xenharmonic Wiki

Magic: Difference between revisions

← Older edit
VisualWikitext
Misc. improvements in the intro
Overthink (talk | contribs)
autopatrolled
2,726 edits
→Scales: 13-limit interpretations
 
(6 intermediate revisions by 3 users not shown)
Line 28: Line 28:
Magic has certain properties that commend it as a step up in complexity from traditional harmony:
Magic has certain properties that commend it as a step up in complexity from traditional harmony:
* It is the simplest mapping capable of tuning every [[9-odd-limit]] interval better than in [[12edo]].
* It is the simplest mapping capable of tuning every [[9-odd-limit]] interval better than in [[12edo]].
* It is only slightly more complex than [[meantone]] (both work well with a 19-note gamut).
* It is only slightly more complex than [[septimal meantone]] (both work well with a 19-note gamut).
* 5-limit intervals are generally simpler than 7-limit intervals.
* 5-limit intervals are generally simpler than 7-limit intervals.


Line 35: Line 35:
* It is more complex than meantone (higher [[complexity]] and [[badness]]).
* 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.
* 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]].  
For technical information, see [[Magic family #Magic]]. For a discussion on alternative 11- and 13-limit extensions, see [[Magic extensions]].  
Line 66: Line 60:
| 3
| 3
| 1141.4
| 1141.4
| 27/14
| 27/14, 35/18, 48/25
|-
|-
| 4
| 4
Line 86: Line 80:
| 8
| 8
| 643.7
| 643.7
| (13/9, '''16/11''')
| 35/24, (13/9, '''16/11''')
|-
|-
| 9
| 9
Line 106: Line 100:
| 13
| 13
| 145.9
| 145.9
| (12/11, 13/12)
| 35/32, (12/11, 13/12)
|}
|}
<nowiki/>* In 7-limit CWE tuning
<nowiki/>* In 7-limit CWE tuning
Line 124: Line 118:
{{See also| Magic Tetrachords }}
{{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]], as well as [[33/32]] and [[27/26]] in tridecimal magic.
* [[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 represents [[12/11]]~[[13/12]] in tridecimal magic.
=== Scala files ===
; Mos scales
; 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.
* [[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
; Transversal scales
Line 217: Line 218:
! Comments
! Comments
|-
|-
|[[16edo|5\16]]
| [[16edo|5\16]]
|
|  
|375.000
| 375.000
|Major thirds slightly flatter than this fall under [[submerged]]
| Flatter tunings may be analysed as [[submerged]]
|-
|-
|
|
|[[25/24]]
| [[25/24]]
|376.443
| 376.443
|1/3-comma
| 1/3-comma
|-
|-
|
|
|[[125/72]]
| [[125/72]]
|377.853
| 377.853
|2/7-comma
| 2/7-comma
|-
|-
|  
|  
Line 297: Line 298:
|  
|  
|-
|-
|
|  
|[[45/32]]
| [[45/32]]
|380.929
| 380.929
|
| 2/11-comma
|-
|-
| [[63edo|20\63]]
| [[63edo|20\63]]
|  
|  
Line 324: Line 324:
|-
|-
|
|
|[[75/64]]
| [[75/64]]
|382.083
| 382.083
|1/7-comma
| 1/7-comma
|-
|-
|  
|  
Line 333: Line 333:
|  
|  
|-
|-
|[[25edo|8\25]]
| [[25edo|8\25]]
|
|  
|384.000
| 384.000
|
| Sharper tunings may be analysed as [[anthoine]]
|-
|-
|  
|  
| [[5/4]]
| [[5/4]]
| 386.314
| 386.314
| Untempered, major thirds slightly sharper than 5/4 fall under 25&28 or [[würschmidt]]
| Untempered
|}
|}
<nowiki/> * Besides the octave
<nowiki/> * Besides the octave
Retrieved from "https://en.xen.wiki/w/Magic"