Kyle Gann: New Aunts

Recording here
CAUTION: Score is meaningless as to pitch without retuning, key given at bottom of this page

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:AA^Bb^-B- BC7CC#C#+C#L D7-D-D^-D#
Ratio:1/133/3211/1010/9 9/87/66/55/481/64 9/735/274/311/845/32
Cents:053.3165182.4 203.9266.9315.6386.3407.8 435.1449.3498551.3590.2

D#LE7EF7F E#LF#F#+G7G#G#LA7A7+
81/5635/24 3/214/98/545/285/3 27/167/415/827/1435/1863/32
639653.2 702764.9813.7821.4884.4905.9 968.81088.311371151.21172.7

(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#1F714/9F2 - 35.1 cents
B1EL45/28F2 + 21.4 cents
C2F8/5F2 + 13.7 cents
C#2F#5/3F#2 - 15.6 cents
D2F#+27/16F#2 + 5.9 cents
D#2G77/4G2 - 31.2 cents
E2G#15/8G#2 - 11.7 cents
F2C77/3C3 - 33.1 cents
F#2C12/5C + 15.6 cents
G2C#5/2C#3 - 13.7 cents
G#2C#L18/7C#3 + 35.1 cents
A2D7-140/27C#3 + 49.3 cents
A#2D#45/16D#3 - 9.8 cents
B2E3/1E3 + 2 cents
C3G#L27/7G#3 + 37 cents
C#3A735/9A3 - 48.8 cents
D3A7+63/16A3 - 27.3 cents
D#3A4/1A3 + 0 cents
E3A^33/8A#3 - 46.7 cents
F3Bb^-22/5B3 - 35 cents
F#3B-40/9B3 - 17.6 cents
G3B9/2B3 + 3.9 cents
G#3C714/3C4 - 33.1 cents
A3C24/5C4 + 15.6 cents
A#3C#5/1C#4 - 13.7 cents
B3C#+81/16C#4 + 7.8 cents
C4C#L36/7C#4 + 35.1 cents
C#4D7-140/27C#4 + 49.3 cents
D4D-16/3D4 - 2 cents
D#4D^-11/2D#4 - 48.7 cents
E4D#45/8D#4 - 9.8 cents
F4D#L81/14D#4 + 39 cents
F#4E735/6E4 - 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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