magic chord

{{Short description|Musical chord}}

File:Magic chord on E.pnges sounded, A=440{{sfn|Gann|1993|page=162}})File:Magic chord MIDI.mid]]

{{Image frame|width=150|content=\relative c {\clef "treble_8" \omit Staff.TimeSignature 1 }|caption=Magic chord (as played in The Well-Tuned Piano).{{sfn|Gann|1993|p=143}}}}

The Magic Chord is a chord and installation (1984) created by La Monte Young, consisting of the pitches E, F, A, B{{music|b}}, D, E, G, and A, in ascending order and used in works including his The Well-Tuned Piano and Chronos Kristalla (1990).Grimshaw, Jeremy (2011). Draw A Straight Line and Follow It: The Music and Mysticism of La Monte Young, p. 176. {{ISBN|978-0-19-974020-8}}. The latter was performed by the Kronos Quartet and features all notes of the magic chord as harmonics on open strings. The quartet has been described as, "offer[ing] perhaps the ultimate challenge in performing in a just environment".Strange, Patricia and Strange, Allen (2001). The Contemporary Violin: Extended Performance Techniques, p. 160. {{ISBN|978-0-520-22409-4}}.

Described as, "complex and throbbing", the chord does not contain its fundamental (see root chords),{{harvnb|Duckworth|2009|p=187}} E{{music|b}}, and is a subset of the Romantic Chord,{{sfn|Potter|2002|p=86}} G-Dorian in eight octaves, spelled G, A, B, C, D, E, F{{music|#}}, G.{{sfn|Potter|2002|pp=85–86}} "When the Magic Opening Chord is obtained by playing the Opening Chord at one end of a room while the Magic Chord is played at the other (as Young set it up for me), the feeling-changes of the stereo effect as you move back and forth[-]are dazzling." The opening chord consists of E{{music|b}}, B{{music|b}}, C, E{{music|b}}, F, B{{music|b}} (ratios 4:6:7:8:9:12 {{audio|La Monte Young - Opening chord on E-flat.mid|Play}}),{{sfn|Duckworth|2009|p=168}} adding C{{sfn|Potter|2002|p=87}} and E{{music|b}} to the magic chord when combined as the magic opening chord ({{audio|La Monte Young - Magic opening chord.mid|Play}}).

The Well-Tuned Piano is based on a pitch lattice of perfect fifths and harmonic sevenths, tuned as follows:Gann, Kyle (1997). [http://www.kylegann.com/wtp.html "La Monte Young's The Well-Tuned Piano"]{{sfn|Duckworth|2009|p=166}}

class="wikitable" style="text-align: center;" ! rowspan="4" | Note ! style="width:20em;" | Note played ! colspan="2" style="width: 3em;" | (E{{music|b}}) ! colspan="2" style="width: 3em;" | E ! colspan="2" style="width: 3em;" | F ! colspan="2" style="width: 3em;" | G ! colspan="2" style="width: 3em;" | A ! colspan="2" style="width: 3em;" | B{{music|b}} ! colspan="2" style="width: 3em;" | (C) ! colspan="2" style="width: 3em;" | D
Note sounded relative to E{{music|b}} (Ben Johnston notation) ! colspan="2" style="width: 3em;" | (E{{music|b}}) ! colspan="2" style="width: 3em;" | F7++ ! colspan="2" style="width: 3em;" | F+ ! colspan="2" style="width: 3em;" | A7b+ ! colspan="2" style="width: 3em;" | B7b+ ! colspan="2" style="width: 3em;" | Bb ! colspan="2" style="width: 3em;" | (D7b) ! colspan="2" style="width: 3em;" | E7b+
Ratio | colspan="2" | (1/1) | colspan="2" | 567/512 | colspan="2" | 9/8 | colspan="2" | 21/16 | colspan="2" | 189/128 | colspan="2" | 3/2 | colspan="2" | (7/4) | colspan="2" | 63/32
Audio (from C) | colspan="2" | ({{audio-nohelp|Unison on C.mid|E{{music|b}}}}) | colspan="2" | {{audio-nohelp|Five-hundred-sixty-seventh harmonic on C.mid|E}} | colspan="2" | {{audio-nohelp|Major tone on C.mid|F}} | colspan="2" | {{audio-nohelp|Twenty-first harmonic on C.mid|G}} | colspan="2" | {{audio-nohelp|Hundred-eighty-ninth harmonic on C.mid|A}} | colspan="2" | {{audio-nohelp|Just perfect fifth on C.mid|B{{music|b}}}} | colspan="2" | ({{audio-nohelp|Harmonic seventh on C.mid|C}}) | colspan="2" | {{audio-nohelp|Sixty-third harmonic on C.mid|D}}
Step ! Ratio | style="background-color: white; width: 1.5em;" |   | colspan="2" | 567/512 | colspan="2" | 64/63 | colspan="2" | 7/6 | colspan="2" | 9/8 | colspan="2" | 64/63 | colspan="2" | 7/6 | colspan="2" | 9/8

For example, G (21/16) is the harmonic seventh of the perfect fifth (7/4 * 3/2 = 21/16):

class="wikitable" style="text-align: center;" style="width:6em;" | ! colspan="5"| P5
rowspan="6" | H7 | 49 | 147 | 441 | 1323 | (3969)
B | F{{music|#}} | C{{music|#}} | G{{music|#}} |
7 | 21 | 63 | 189 | 567
C | G | D | A | E
1 | 3 | 9 | (27) | (81)
E{{music|b}} | B{{music|b}} | F | |