利用者:Tessyrrh1016/draft/マジックのソースを表示

This is a draft of JP translation of [[:en:Magic]].
<hr>

'''マジック'''は線形音律の一種で、約 380 [[セント|¢]] のジェネレーターが {{en仮リンク|5/4|5/4}} を表し、それが5つで {{en仮リンク|3/1|3/1}} になる。これはつまり、マジックコンマ（{{en仮リンク|3125/3072|3125/3072}}）が[[テンパーアウト]]され、マジックが{{en仮リンク|マジックファミリー|magic family}}のメンバーになるということである。

この記事では、素数7のマッピングも最初から想定している。そのマッピングでは、マーべルコンマ（{{en仮リンク|225/224|225/224}}）がテンパーアウトされ、ジェネレーター2つで {{en仮リンク|14/9|14/9}} に相当する。12個のジェネレーターによって {{en仮リンク|7/4|7/4}} に到達できる。

（{{en仮リンク|マグルズ|Muggles}}として知られる7の代替マッピングがある。これは、ジェネレーターが小さく、小さなステップが少し大きくなり、小さなMOSにおいてL:s比が{{en仮リンク|soft|soft}}寄りになるためメロディー的に優れている可能性があるが、[[19平均律]]を使用していない限り、これを使用する理由はほとんどない。またその場合でも、それはマジックと同じマッピングとなる。）

優れたマジックスケールを含む平均律には、[[19平均律]]・[[22平均律]]・{{en仮リンク|41平均律|41edo}}・{{en仮リンク|60平均律|60edo}}・{{en仮リンク|104平均律|104edo}}などがある。

マジックには、伝統的なハーモニーからさらに複雑さを増したものとしておすすめされる特性がある。

* すべての {{en仮リンク|9-奇数リミット音程|9-odd-limit}}は、[[12平均律]]よりも適切に調律されている。
* これは、上記の特性をもった最も単純なマッピングである。
* これは、ミーントーンよりもわずかに複雑であるだけである（どちらも 19 音域で適切に機能する）。
* 5-リミット音程は他の 7-リミット音程よりも単純。

ただし、以下の理由から「万能薬」にはならない。

* 3音から16音までの{{en仮リンク|適切|proper}}なMOSスケールが無い。
* これは、ミーントーンよりも複雑（より複雑で悪さが大きい）。
* 3/2 近似は 5/4 近似（ジェネレーター）の5倍複雑であるため、5度による転調は通常よりも制限される。

ジェネレーターは 1\3（1オクターヴの3分の1）に非常に近く、従って残りの音程は非常に小さいため、すべての小さなマジックMOSは、3つの大きな音程と小さな音程のグループ3つが交互に並んでいる。具体的には次のようなMOSがあり、sは常に特徴的な小さな間隔を表し、128/125 ~ 36/35 ~ 28/27 ~ 25/24 を同時に表す。

* {{en仮リンク|3L 4s|3L 4s}} : LsLsLss（L は 6/5 を表す）
* {{en仮リンク|3L 7s|3L 7s}} : LssLssLsss（L は 7/6 を表す）
* {{en仮リンク|3L 10s|3L 10s}} : LsssLsssLssss（L は 9/8 を表す）
* {{en仮リンク|3L 13s|3L 13s}} : LssssLssssLsssss（L は中2度で、12/11（マジック音律の場合）または 11/10（関連する{{en仮リンク|テレパシー|telepathy}}音律の場合）を表す。22平均律ではそれらは同一である。

==音程列==
{| class="wikitable center-all"
|-
! Cents<ref>7-リミットの{{en仮リンク|POTE調律|POTE tuning}}における値</ref>
| 0
| 380.352
| 760.704
| 1141.056
| 321.408
| 701.760
| 1082.112
| 262.464
| 642.816
| 1023.168
| 203.520
| 583.872
| 964.224
| 144.576
|-
! Ratios
| 1/1
| 5/4
| 14/9
| 27/14
| 6/5
| 3/2
| 15/8
| 7/6
| (16/11)
| 9/5
| 9/8
| 7/5
| 7/4
| (12/11)
|}
<references />

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。

==和音==
: ''[[:en:Chords of magic]], [[:en:Magic Tetrachords]] なども参照のこと。''

== スケール ==
===MOSスケール===
* [[:en:Magic7]] - improper [[3L 4s]]
* [[:en:Magic10]] - improper [[3L 7s]]
* [[:en:Magic13]] - improper [[3L 10s]]
* [[:en:Magic16]] - improper [[3L 13s]]. The boundary of propriety is 19edo.
* [[:en:Magic19]] - proper [[3L 16s]]. The boundary of propriety is 22edo.
* [[:en:Magic22]] - [[19L 3s]] scale. The boundary of propriety is 41edo.
===Transversalスケール===
* [[:en:Magic19trans37]]
* [[:en:Magic19trans37ex]]
* [[:en:Magic22trans37]]
* [[:en:Magic22trans37ex]]
===Others===
* [[:en: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]

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