Kyle Gann: New Aunts

The title New Aunts appealed to me because the homonymous relation among "new aunts" (British/New England pronunciation), "new ants" (Midwestern pronunciation), and "naunce" is analogous to the slight melodic changes the piece is based around. I googled "nuance," and the most common noncommercial uses had to do with the need for more nuance in our political discourse, so perhaps listening to this piece will encourage that. Or perhaps not. There are 27 pitches to the octave here, in an 11-limit just-intonation system, though the entire melody takes place within barely more than a perfect fifth.

The scale (given in a typographical approximation of Ben Johnston's notation) is as follows:

Pitch:	A	A^	Bb^-	B-	B	C7	C	C#	C#+	C#L	D7-	D-	D^-	D#
Ratio:	1/1	33/32	11/10	10/9	9/8	7/6	6/5	5/4	81/64	9/7	35/27	4/3	11/8	45/32
Cents:	0	53.3	165	182.4	203.9	266.9	315.6	386.3	407.8	435.1	449.3	498	551.3	590.2

D#L E7 E F7 F E#L F# F#+ G7 G# G#L A7 A7+

81/56 35/24 3/2 14/9 8/5 45/28 5/3 27/16 7/4 15/8 27/14 35/18 63/32

639 653.2 702 764.9 813.7 821.4 884.4 905.9 968.8 1088.3 1137 1151.2 1172.7

(If you don't have enough experience with just intonation to make sense of this chart, try reading the step-by-step Just Intonation Explained section.) In Johnston's notation, + raises a pitch by 81/80, - lowers it by 80/81, # raises it by 25/24, b lowers it by 24/25, 7 lowers it by 35/36, L raises it by 36/35, ^ raises it by 33/32, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.

The score (available here as a PDF) uses conventional notation that does not indicate pitch, but merely tells the keyboardist which keys to play. The keyboard is tuned as follows, with respect to A 110 hz defined as 1/1:

Key: Pitch: Ratio: Tuning (relative to normal 12tet):

A#1 F7 14/9 F2 - 35.1 cents

B1 EL 45/28 F2 + 21.4 cents

C2 F 8/5 F2 + 13.7 cents

C#2 F# 5/3 F#2 - 15.6 cents

D2 F#+ 27/16 F#2 + 5.9 cents

D#2 G7 7/4 G2 - 31.2 cents

E2 G# 15/8 G#2 - 11.7 cents

F2 C7 7/3 C3 - 33.1 cents

F#2 C 12/5 C + 15.6 cents

G2 C# 5/2 C#3 - 13.7 cents

G#2 C#L 18/7 C#3 + 35.1 cents

A2 D7- 140/27 C#3 + 49.3 cents

A#2 D# 45/16 D#3 - 9.8 cents

B2 E 3/1 E3 + 2 cents

C3 G#L 27/7 G#3 + 37 cents

C#3 A7 35/9 A3 - 48.8 cents

D3 A7+ 63/16 A3 - 27.3 cents

D#3 A 4/1 A3 + 0 cents

E3 A^ 33/8 A#3 - 46.7 cents

F3 Bb^- 22/5 B3 - 35 cents

F#3 B- 40/9 B3 - 17.6 cents

G3 B 9/2 B3 + 3.9 cents

G#3 C7 14/3 C4 - 33.1 cents

A3 C 24/5 C4 + 15.6 cents

A#3 C# 5/1 C#4 - 13.7 cents

B3 C#+ 81/16 C#4 + 7.8 cents

C4 C#L 36/7 C#4 + 35.1 cents

C#4 D7- 140/27 C#4 + 49.3 cents

D4 D- 16/3 D4 - 2 cents

D#4 D^- 11/2 D#4 - 48.7 cents

E4 D# 45/8 D#4 - 9.8 cents

F4 D#L 81/14 D#4 + 39 cents

F#4 E7 35/6 E4 - 46.8 cents

Enough information is given here to facilitate a performance - kindly contact the composer if this is contemplated. The piece is performable on a four-octave keyboard.

Kyle Gann

Return to Just Intonation Explained

Return to List of Compositions

return to the home page