Magic chord

$\relative c {\clef "treble_8" \omit Staff.TimeSignature <e fis a b d e g a >1 }$

Magic chord (as played in The Well-Tuned Piano).^[3]

The Magic Chord is a chord and installation (1984) created by La Monte Young, consisting of the pitches E, F, A, B♭, D, E, G, and A, in ascending order and used in works including his The Well-Tuned Piano and Chronos Kristalla (1990).^[1] The latter was performed by the Kronos Quartet and features all notes of the magic chord as harmonics on open strings.^[1] The quartet has been described as, "offer[ing] perhaps the ultimate challenge in performing in a just environment".^[4]

Described as, "complex and throbbing", the chord does not contain its fundamental (see root chords),^[5] E♭, and is a subset of the Romantic Chord,^[6] G-Dorian in eight octaves, spelled G, A, B, C, D, E, F♯, G.^[7] "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."^[5] The opening chord consists of E♭, B♭, C, E♭, F, B♭ (ratios 4:6:7:8:9:12 Play^ⓘ),^[8] adding C^[9] and E♭ to the magic chord when combined as the magic opening chord (Play^ⓘ).

The Well-Tuned Piano is based on a pitch lattice of perfect fifths and harmonic sevenths, tuned as follows:^[10]^[11]

Note	Note played	(E♭)		E		F		G		A		B♭		(C)		D
	Note sounded relative to E♭ (Ben Johnston notation)	(E♭)		F7++		F+		A7b+		B7b+		Bb		(D7b)		E7b+
	Ratio	(1/1)		567/512		9/8		21/16		189/128		3/2		(7/4)		63/32
	Audio (from C)	(E♭^ⓘ)		E^ⓘ		F^ⓘ		G^ⓘ		A^ⓘ		B♭^ⓘ		(C^ⓘ)		D^ⓘ
Step	Ratio		567/512		64/63		7/6		9/8		64/63		7/6		9/8

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

	P5
H7	49	147	441	1323	(3969)
	B	F♯	C♯	G♯
	7	21	63	189	567
	C	G	D	A	E
	1	3	9	(27)	(81)
	E♭	B♭	F

References

^ ^a ^b ^c 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.
^ Gann 1993, p. 162.
^ Gann 1993, p. 143.
^ Strange, Patricia and Strange, Allen (2001). The Contemporary Violin: Extended Performance Techniques, p. 160. ISBN 978-0-520-22409-4.
^ ^a ^b Duckworth 2009, p. 187
^ Potter 2002, p. 86.
^ Potter 2002, pp. 85–86.
^ Duckworth 2009, p. 168.
^ Potter 2002, p. 87.
^ Gann, Kyle (1997). "La Monte Young's The Well-Tuned Piano"
^ Duckworth 2009, p. 166.

Sources

Duckworth, William (2009). Sound and Light: La Monte Young and Marian Zazeela. Associated University Presse. ISBN 978-0-8387-5738-3.
Gann, Kyle (1993). "La Monte Young's The Well-Tuned Piano". Perspectives of New Music. 31 (1): 134–162. doi:10.2307/833045. JSTOR 833045. (subscription required)
Potter, Keith (2002). Four Musical Minimalists: La Monte Young, Terry Riley, Steve Reich, Philip Glass. Cambridge. ISBN 9780521015011.{{cite book}}: CS1 maint: location missing publisher (link)

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[Grimshaw-1] 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.

[FOOTNOTEGann1993162-2] Gann 1993, p. 162.

[FOOTNOTEGann1993143-3] Gann 1993, p. 143.

[4] Strange, Patricia and Strange, Allen (2001). The Contemporary Violin: Extended Performance Techniques, p. 160. ISBN 978-0-520-22409-4.

[Duckworth-5] Duckworth 2009, p. 187

[FOOTNOTEPotter200286-6] Potter 2002, p. 86.

[FOOTNOTEPotter200285–86-7] Potter 2002, pp. 85–86.

[FOOTNOTEDuckworth2009168-8] Duckworth 2009, p. 168.

[FOOTNOTEPotter200287-9] Potter 2002, p. 87.

[10] Gann, Kyle (1997). "La Monte Young's The Well-Tuned Piano"

[FOOTNOTEDuckworth2009166-11] Duckworth 2009, p. 166.

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