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

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