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<span style="display: block; text-align: right;">[[de:Magische_Temperaturen-x-7-Limit-magisch|Deutsch]]</span>
<span style="display: block; text-align: right;">[[de:Magische_Temperaturen-x-7-Limit-magisch|Deutsch]]</span>


'''Magic''' is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic_comma|magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic_family|Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic_family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo|19edo]], in which case it's identical to magic anyway.)
'''Magic''' is a linear temperament in which the ~380 cent generator represents [[5/4]], and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[magic family]]. This article also assumes the default mapping for the prime 7, which tempers out [[225/224]] and makes two generators equivalent to [[14/9]]. [[7/4]] can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family #Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.)


EDOs that contain good magic scales include [[19edo|19edo]], [[22edo|22edo]], [[41edo|41edo]], [[60edo|60edo]] and [[104edo|104edo]].
EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]].


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:


<ul><li>Every non-trivial 7-limit interval is better tuned than in [[12edo|12edo]].</li><li>It is the simplest mapping with the above property.</li><li>It is only slightly more complex than meantone (both work well with a 19 note gamut).</li><li>5-limit intervals are simpler than other 7-limit intervals.</li></ul>
* Every non-trivial 7-limit interval is better tuned than in [[12edo]].
* It is the simplest mapping with the above property.
* It is only slightly more complex than meantone (both work well with a 19 note gamut).
* 5-limit intervals are simpler than other 7-limit intervals.


It fails to be a panacea because:
It fails to be a panacea because:


<ul><li>It has no proper MOS scales of between 3 and 16 notes.</li><li>It is more complex than meantone</li><li>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.</li></ul>
* It has no proper MOS scales of between 3 and 16 notes.
* It is more complex than meantone
* 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 (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.


<ul><li>[[3L_4s|3L 4s]]: LsLsLss where L = 6/5</li><li>[[3L_7s|3L 7s]]: LssLssLsss where L = 7/6</li><li>[[3L_10s|3L 10s]]: LsssLsssLssss where L = 9/8</li><li>[[3L_13s|3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic_family#Magic-Telepathy|telepathy]] temperament). In 22edo they are identical.</li></ul>
* [[3L 4s]]: LsLsLss where L = 6/5
* [[3L 7s|3L 7s]]: LssLssLsss where L = 7/6
* [[3L 10s]]: LsssLsssLssss where L = 9/8
* [[3L 13s]]: LssssLssssLsssss where L is a neutral second, which can be taken to represent 12/11 (in magic temperament) or 11/10 (in the related [[Magic family #Telepathy|telepathy]] temperament). In 22edo they are identical.


==Interval chain==
== Interval chain ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | 0.
| 0.
| | 380.352
| 380.352
| | 760.704
| 760.704
| | 1141.056
| 1141.056
| | 321.408
| 321.408
| | 701.76
| 701.76
| | 1082.112
| 1082.112
| | 262.464
| 262.464
| | 642.816
| 642.816
| | 1023.168
| 1023.168
| | 203.52
| 203.52
| | 583.872
| 583.872
| | 964.224
| 964.224
| | 144.576
| 144.576
|-
|-
| | 1/1
| 1/1
| | 5/4
| 5/4
| | 14/9
| 14/9
| | 48/25~125/64
| 48/25~125/64
| | 6/5
| 6/5
| | 3/2
| 3/2
| | 15/8
| 15/8
| | 7/6
| 7/6
| | (16/11)
| (16/11)
| | 9/5
| 9/5
| | 9/8
| 9/8
| | 7/5
| 7/5
| | 7/4
| 7/4
| | (12/11)
| (12/11)
|}
|}


The generator chain val for 13-limit magic is &lt;0 5 1 12 -8 18|, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.
The generator chain val for 13-limit magic is {{val| 0 5 1 12 -8 18 }}, so that five generators give an approximate 3, twelve 14, minus eight 11/64, and eighteen 52.


=Spectrum of Magic Tunings by Eigenmonzos=
== Spectrum of Magic Tunings by Eigenmonzos ==


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Major Third
! Major Third
|-
|-
| | 6/5
| 6/5
| | 378.910
| 378.910
|-
|-
| | 10/9
| 10/9
| | 379.733
| 379.733
|-
|-
| | 7/5
| 7/5
| | 380.228
| 380.228
|-
|-
| | 4/3
| 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| 380.391 (5, 7 and 9 limit minimax)
|-
|-
| | 11/9
| 11/9
| | 380.700 (11 limit minimax)
| 380.700 (11 limit minimax)
|-
|-
| | 8/7
| 8/7
| | 380.735
| 380.735
|-
|-
| | 12/11
| 12/11
| | 380.818
| 380.818
|-
|-
| | 14/11
| 14/11
| | 380.875
| 380.875
|-
|-
| | 7/6
| 7/6
| | 380.982
| 380.982
|-
|-
| | 11/8
| 11/8
| | 381.085
| 381.085
|-
|-
| | 11/10
| 11/10
| | 381.666
| 381.666
|-
|-
| | 9/7
| 9/7
| | 382.458
| 382.458
|-
|-
| | 5/4
| 5/4
| | 386.314
| 386.314
|}
|}


=[[Chords_of_magic|Chords of magic]]=
== Chords of magic ==
{{main| Chords of magic }}
{{see also| Magic Tetrachords }}


=[[Magic_Tetrachords|Magic Tetrachords]]=
== Music ==
 
=Music=
''[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16]''
''[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16]''


[[magic16|magic16]]
[[magic16]]


''[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 A Piece in Paulsmagic]''
''[http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 A Piece in Paulsmagic]''


[[paulsmagic|paulsmagic]]
[[paulsmagic]]


''[http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 The Magic of Belief]'' Magic[19] in 41et tuning
''[http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 The Magic of Belief]'' Magic[19] in 41et tuning
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[http://www.chrisvaisvil.com/ Chris Vaisvil]
[http://www.chrisvaisvil.com/ Chris Vaisvil]


''[https://soundcloud.com/jdfreivald/little-magical-object Little Magical Object]'' [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] Magic[19] in 41et tuning by [[Jake_Freivald|Jake Freivald]]
''[https://soundcloud.com/jdfreivald/little-magical-object Little Magical Object]'' [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] Magic[19] in 41et tuning by [[Jake Freivald]]


''[http://micro.soonlabel.com/gene_ward_smith/Others/Milne/Magic%20Traveller.mp3 Andrew Milne; magic with 379.8 cent generator]''
''[http://micro.soonlabel.com/gene_ward_smith/Others/Milne/Magic%20Traveller.mp3 Andrew Milne; magic with 379.8 cent generator]''
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''[http://x31eq.com/music/jitter.ogg Gene's Jitterbug] 9-limit harmony, may not require magic.''
''[http://x31eq.com/music/jitter.ogg Gene's Jitterbug] 9-limit harmony, may not require magic.''
[[Category:Temperament]]
[[Category:Magic]]
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