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13-リミットマジックのジェネレーター列のヴァルは {{val| 0 5 1 12 -8 18 }} であるので、ジェネレーター 5 つで 3、12 個で 7×2、-8 つで 11/64、そして 18 個で 13×4 を近似する。
13-リミットマジックのジェネレーター列のヴァルは {{val| 0 5 1 12 -8 18 }} であるので、ジェネレーター 5 つで 3、12 個で 7×2、-8 つで 11/64、そして 18 個で 13×4 を近似する。
</div>
== Chords ==
{{main| Chords of magic }}
{{see also| Magic Tetrachords }}
== Scales ==
; MOS scales
* [[Magic7]] - improper [[3L 4s]]
* [[Magic10]] - improper [[3L 7s]]
* [[Magic13]] - improper [[3L 10s]]
* [[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.
; Transversal scales
* [[Magic19trans37]]
* [[Magic19trans37ex]]
* [[Magic22trans37]]
* [[Magic22trans37ex]]
; Others
* [[Paulsmagic]]
== Tuning spectra ==
=== Magic ===
Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
Gencom mapping: [{{map| 1 0 2 -1 6 -2 }}, {{map| 0 5 1 12 -8 18 }}]
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 14/13
| 378.617
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 15/13
| 379.355
|
|-
|
| 18/13
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 10/9
| 379.733
|
|-
|
| 13/12
| 379.890
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 16/13
| 380.029
|
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| 13/11
| 380.354
| 13 and 15-odd-limit minimax
|-
|
| <span style="font-size:0.75em">{{monzo| 0 56 -31 46 -94 88 }}</span>
| 380.377
| 13-odd-limit least squares
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 58 -29 52 -108 100 }}</span>
| 380.389
| 15-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| 11/9
| 380.700
| 11-odd-limit minimax
|-
|
| <span style="font-size:0.9em">{{monzo| 0 85 -14 52 -68 }}</span>
| 380.714
| 11-odd-limit least squares
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
|
| 12/11
| 380.818
|
|-
|
| 14/11
| 380.875
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 16/15
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
|
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}
=== Necromancy ===
Gencom: [2 5/4; 100/99 225/224 245/243 275/273]


</div>
Gencom mapping: [{{map| 1 0 2 -1 6 11 }}, {{map| 0 5 1 12 -8 -23 }}]
 
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 10/9
| 379.733
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| 11/9
| 380.700
| 11-odd-limit minimax
|-
|
| 18/13
| 380.709
| 13 and 15-odd-limit minimax
|-
|
| <span style="font-size:0.9em">{{monzo| 0 85 -14 52 -68 }}</span>
| 380.714
| 11-odd-limit least squares
|-
|
| 13/11
| 380.719
|
|-
|
| 8/7
| 380.735
|
|-
|
| 13/12
| 380.765
|
|-
| 33\104
|
| 380.769
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -179 -10 -87 53 158 }}</span>
| 380.785
| 13-odd-limit least squares
|-
|
| 14/13
| 380.809
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -222 -53 -93 67 187 }}</span>
| 380.817
| 15-odd-limit least squares
|-
|
| 12/11
| 380.818
|
|-
|
| 16/13
| 380.847
|
|-
|
| 14/11
| 380.875
|
|-
| 20\63
|
| 380.952
|
|-
|
| 15/13
| 380.957
|
|-
|
| 7/6
| 380.982
|
|-
|
| 13/10
| 381.074
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 16/15
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
|
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}
 
=== Sorcery ===
Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
 
Gencom mapping: [{{map| 1 0 2 -1 6 4 }}, {{map| 0 5 1 12 -8 -1 }}]
 
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 16/13
| 359.472
|
|-
|
| 13/10
| 372.893
|
|-
|
| 13/12
| 376.905
|
|-
|
| 15/13
| 378.249
|
|-
|
| 18/13
| 378.489
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 14/13
| 379.100
|
|-
|
| 10/9
| 379.733
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -113 12 -65 75 26 }}</span>
| 380.427
| 13-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 134 9 71 -89 -33 }}</span>
| 380.457
| 15-odd-limit least squares
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| 11/9
| 380.700
| 11, 13 and 15-odd-limit minimax
|-
|
| <span style="font-size:0.9em">{{monzo| 0 85 -14 52 -68 }}</span>
| 380.714
| 11-odd-limit least squares
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
|
| 12/11
| 380.818
|
|-
|
| 14/11
| 380.875
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 11/8
| 381.085
|
|-
|
| 15/11
| 381.211
|
|-
|
| 16/15
| 381.378
|
|-
|
| 11/10
| 381.666
|
|-
| 7\22
|
| 381.818
|
|-
|
| 9/7
| 382.458
|
|-
|
| 13/11
| 384.173
|
|-
|
| 5/4
| 386.314
|
|}
 
=== Telepathy ===
Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
 
Gencom mapping: [{{map| 1 0 2 -1 -1 4 }}, {{map| 0 5 1 12 14 -1 }}]
 
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 16/13
| 359.472
|
|-
|
| 13/10
| 372.893
|
|-
|
| 13/12
| 376.905
|
|-
|
| 15/13
| 378.249
|
|-
|
| 18/13
| 378.489
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 14/13
| 379.100
|
|-
|
| 10/9
| 379.733
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 47 -34 43 57 -48 }}</span>
| 380.676
| 13-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 46 -35 49 65 -55 }}</span>
| 380.691
| 15-odd-limit least squares
|-
|
| 13/11
| 380.719
| 13 and 15-odd-limit minimax
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 16/15
| 381.378
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 19 -36 30 42 }}</span>
| 381.380
| 11-odd-limit least squares
|-
| 7\22
|
| 381.818
|
|-
|
| 11/10
| 381.923
| 11-odd-limit minimax
|-
|
| 11/8
| 382.237
|
|-
|
| 9/7
| 382.458
|
|-
|
| 15/11
| 382.881
|
|-
|
| 12/11
| 383.263
|
|-
|
| 5/4
| 386.314
|
|-
|
| 11/9
| 386.852
|
|-
|
| 14/11
| 391.246
|
|}
 
=== Intuition ===
Gencom: [2 5/4; 55/54 66/65 99/98 105/104]
 
Gencom mapping: [{{map| 1 0 2 -1 -1 -2 }}, {{map| 0 5 1 12 14 18 }}]
 
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 13/11
| 372.302
|
|-
|
| 14/13
| 378.617
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 15/13
| 379.355
|
|-
|
| 18/13
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 10/9
| 379.733
|
|-
|
| 13/12
| 379.890
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
| 19\60
|
| 380.000
|
|-
|
| 16/13
| 380.029
| 13 and 15-odd-limit minimax
|-
|
| 15/14
| 380.093
|
|-
| 32\101
|
| 380.198
|
|-
|
| 7/5
| 380.228
|
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| {{monzo| 0 1 -7 15 }}
| 380.506
| 7-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -30 -73 30 46 78 }}</span>
| 380.562
| 15-odd-limit least squares
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -10 -53 24 38 66 }}</span>
| 380.568
| 13-odd-limit least squares
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 16/15
| 381.378
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 19 -36 30 42 }}</span>
| 381.380
| 11-odd-limit least squares
|-
| 7\22
|
| 381.818
|
|-
|
| 11/10
| 381.923
| 11-odd-limit minimax
|-
|
| 11/8
| 382.237
|
|-
|
| 9/7
| 382.458
|
|-
|
| 15/11
| 382.881
|
|-
|
| 12/11
| 383.263
|
|-
|
| 5/4
| 386.314
|
|-
|
| 11/9
| 386.852
|
|-
|
| 14/11
| 391.246
|
|}
 
=== Witchcraft ===
Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
 
Gencom mapping: [{{map| 1 0 2 -1 -7 -2 }}, {{map| 0 5 1 12 33 18 }}]
 
{| class="wikitable center-all left-4"
|-
! ET<br>generator
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval)]]
! generator<br>(¢)
! comments
|-
|
| 14/13
| 378.617
|
|-
|
| 6/5
| 378.910
|
|-
| 6\19
|
| 378.947
|
|-
|
| 15/13
| 379.355
|
|-
|
| 18/13
| 379.577
|
|-
|
| 13/10
| 379.660
|
|-
|
| 10/9
| 379.733
|
|-
|
| 27/20
| 379.968
| 5-odd-limit least squares
|-
|
| 13/12
| 379.890
|
|-
| 19\60
|
| 380.000
|
|-
|
| 16/13
| 380.029
|
|-
|
| 15/14
| 380.093
|
|-
|
| 15/11
| 380.113
| 15-odd-limit minimax
|-
|
| 14/11
| 380.119
| 13-odd-limit minimax
|-
|
| 11/10
| 380.156
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -106 -111 11 179 59 }}</span>
| 380.193
| 15-odd-limit least squares
|-
| 32\101
|
| 380.198
|
|-
|
| <span style="font-size:0.75em">{{monzo| 0 -67 -72 5 152 47 }}</span>
| 380.218
| 13-odd-limit least squares
|-
|
| 7/5
| 380.228
|
|-
|
| <span style="font-size:0.9em">{{monzo| 0 -38 -55 11 137 }}</span>
| 380.278
| 11-odd-limit least squares
|-
|
| 11/9
| 380.322
|
|-
|
| 12/11
| 380.334
|
|-
|
| 11/8
| 380.343
| 11-odd-limit minimax
|-
|
| {{monzo| 0 36 -23 32 }}
| 380.384
| 9-odd-limit least squares
|-
|
| 4/3
| 380.391
| 5, 7 and 9-odd-limit minimax
|-
| 13\41
|
| 380.488
|
|-
|
| 13/11
| 380.719
|
|-
|
| 8/7
| 380.735
|
|-
| 33\104
|
| 380.769
|
|-
| 20\63
|
| 380.952
|
|-
|
| 7/6
| 380.982
|
|-
|
| 16/15
| 381.378
|
|-
| 7\22
|
| 381.818
|
|-
|
| 9/7
| 382.458
|
|-
|
| 5/4
| 386.314
|
|}
 
== Music ==
; [[Andrew Milne]]
* [https://soundcloud.com/andrew-j-milne/magic-traveller ''Magic Traveller''] (2008) – magic[10] with 379.8-cent generator
 
; [[Cameron Bobro]]
* [https://web.archive.org/web/20201127015243/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/Magical_Daydream_CBobro.mp3 ''Magical Daydream''] ''A brief demonstration of the near-Just musical temperament which flattens the pure major third of 5:4 by a few cents, such that 5 major thirds does not exceed 3:1 (a pure fifth + 1 octave), but meets it precisely. In a purely tuned system, the thirds would exceed 3:1 by what is known as the small diesis, (a ratio 3125/3072, about thirty cents). This temperament, then, brings (almost) pure thirds and pure fifths together.''
* [https://web.archive.org/web/20201127014810/http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3 ''Evening Horizon''] ''The earliest implementation (by happy accident, it seems) of this temperament was, to my knowledge, by Paul von Janko over a century ago. More recently, an online tuning community has elaborated many precise variations, calling the temperament "magic". This piece is a demonstration of the array of pitches created by using 22 generators (the slightly tempered 5:4) within the octave, an approach which creates a "moment of symmetry", with all pitches separated by the same two intervals. This has many curious repercussions, creating some musical possibilities and restricting others.''
 
; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site])
* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] (2012) – magic[16] in 145edo tuning (→ [[magic16]])
* [http://micro.soonlabel.com/22-ET/daily20120128-pauls-magic.mp3 ''A Piece in Paulsmagic''] (2012) – in [[paulsmagic]]
* [http://micro.soonlabel.com/41edo/20130910_magic%5b19%5dor_41_the_magic_of_belief.mp3 ''The Magic of Belief''] (2013) – magic[19] in 41edo tuning
 
; [[Graham Breed]]
* [http://x31eq.com/music/dingsheng.mp3 ''Golden Age''] – disco involving magic comma pumps.
* [http://x31eq.com/music/dingshi.mp3 ''Extravagant Food''] – a single magic comma pump in under 60 seconds in 60edo.
* [http://x31eq.com/music/jitter.ogg ''Gene's Jitterbug''] – 9-odd-limit harmony, may not require magic.
 
; [[Jake Freivald]]
* ''Little Magical Object'' (2013) – [https://web.archive.org/web/20201127014655/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/little-magical-object.mp3 play] | [https://soundcloud.com/jdfreivald/little-magical-object SoundCloud] – magic[19] in 41edo tuning
 
; [[User:Xenllium|Xenllium]]
* [https://m.youtube.com/watch?v=5iBXKRWE-_U ''Magical life''] (2023) – in 19-tone pure-fifth magic scale
 
== See also ==
* [[Kite Guitar]]
* [[Lumatone mapping for magic]]
 
== External links ==
* [http://x31eq.com/magic/ Magic Temperament] – Graham Breed's documents
Retrieved from "https://en.xen.wiki/w/User:Triethylamine/draft:_マジック"