Kyle Gann: Love Scene

Tuning for Love Scene for string quartet

Love Scene is a fairly literal arrangement for string quartet of Act III of my opera The Watermelon Cargo. The sung lines describe the scene:

An art school in a box in the late afternoon.
Lazy sunshine pouring through an old style wooden glass window...
Motion and time pass until the two of them are alone...

The piece is in 11-limit just intonation, with tuning instructions as follows:

Tune strings in pure perfect fifths, to cello/viola C, except for violin E strings, which should be 21 cents flatter than pure

ET = Equal-tempered, standard 20th-century tuning

Pitch: Ratio: Cents: Description:

C 1/1 0 reference pitch, normal tuning

C^ 33/32 53.3 (C with quarter-tone-sharp accidental), C 53 cents sharp

C# 25/24 70.7 29 cents flatter than ET

D7 35/32 155.1 45 cents flatter than ET D

D 9/8 203.9 4 cents sharper than ET, 9th harmonic of C, tuned with G

Eb^ 77/64 320.1 (E half-flat) 20 cents sharper than ET Eb

E 5/4 386.3 14 cents flatter than ET, fifth harmonic of C

E+ 81/64 407.8 8 cents sharper than ET E

F7+ 21/16 470.8 29 cents flatter than ET F, 7th harmonic of G

F^ 11/8 551.3 (F with quarter-tone-sharp accidental), halfway between ET F and F#

F# 45/32 590.2 F#+, 10 cents flatter than ET, 5th harmonic of D

G7 35/24 653.2 47 cents flatter than ET G

G 3/2 702 perfectly in tune with C, open string

G^ 99/64 755.2 (G with quarter-tone-sharp accidental), 55 cents sharper than ET G

G# 25/16 772.6 27 cents flatter than ET, 5th harmonic of E

A+ 27/16 905.9 6 cents sharper than ET, tuned perfectly with D, open string

A^ 55/32 937.6 (A with quarter-tone-sharp accidental), 37 cents sharper than ET A

Bb 7/4 968.8 31 cents flatter than ET, always, 7th harmonic of C

B 15/8 1088.3 12 cents flatter than ET

B# 121/64 1102.6 basically an ET B (m. 63)

C7+ 63/32 1172.7 27 cents flatter than C

Kyle Gann

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Pitch:	Ratio:	Cents:	Description:
C	1/1	0	reference pitch, normal tuning
C^	33/32	53.3	(C with quarter-tone-sharp accidental), C 53 cents sharp
C#	25/24	70.7	29 cents flatter than ET
D7	35/32	155.1	45 cents flatter than ET D
D	9/8	203.9	4 cents sharper than ET, 9th harmonic of C, tuned with G
Eb^	77/64	320.1	(E half-flat) 20 cents sharper than ET Eb
E	5/4	386.3	14 cents flatter than ET, fifth harmonic of C
E+	81/64	407.8	8 cents sharper than ET E
F7+	21/16	470.8	29 cents flatter than ET F, 7th harmonic of G
F^	11/8	551.3	(F with quarter-tone-sharp accidental), halfway between ET F and F#
F#	45/32	590.2	F#+, 10 cents flatter than ET, 5th harmonic of D
G7	35/24	653.2	47 cents flatter than ET G
G	3/2	702	perfectly in tune with C, open string
G^	99/64	755.2	(G with quarter-tone-sharp accidental), 55 cents sharper than ET G
G#	25/16	772.6	27 cents flatter than ET, 5th harmonic of E
A+	27/16	905.9	6 cents sharper than ET, tuned perfectly with D, open string
A^	55/32	937.6	(A with quarter-tone-sharp accidental), 37 cents sharper than ET A
Bb	7/4	968.8	31 cents flatter than ET, always, 7th harmonic of C
B	15/8	1088.3	12 cents flatter than ET
B#	121/64	1102.6	basically an ET B (m. 63)
C7+	63/32	1172.7	27 cents flatter than C