Kyle Gann: The Aardvarks' Parade (2009)

I have always been fascinated by aardvarks. As a junior high kid I wrote a comic strip about a superhero called Super-Aardvark. His sidekick was a komodo dragon.

The idea I had for this piece was to write a simple, memorable melody conventional in every way except for its tuning, which would weave back and forth between familiar intervals and quarter- and sixth-tones. As in Ravel's Bolero, the melody repeats (four times) without alteration, with changes of only tone color and intensity. The plodding march time seemed appropriate for a procession of aardvarks. It is one of those comic pieces I write from time to time. The realization is electronic except for the chorus at the end, which I made by overdubbing my voice singing the melody, and the bass drum and tambourine, which I played in a studio. Here is the melody, with the number of cents above C# over each note, in Ben Johnston's notation (explained below). The melody starts at 0:14, 2:45, 5:16, and 7:47 in the recording if you want to follow it:

Another impetus was to reuse the wonderfully elegant tuning I had arrived at in my virtual piano piece Triskaidekaphonia, one whose possibilities I had only begun to explore. The tuning is superlatively simple: it consists of merely all the ratios formed by the whole numbers from 1 to 13, of which there are 29:

13/12, 13/11, 13/10, 13/9, 13/8, 13/7 (13/6, 13/5, and so on, are octaves of those already mentioned)

12/11, 12/7 (12/10 is the same as 6/5, 12/9 = 4/3, and so on)

11/10, 11/9, 11/8, 11/7, 11/6

10/9, 10/7 (10/8 = 5/4, 10/6 = 5/3)

9/8, 9/7, 9/5

8/7, 8/5

7/6, 7/5, 7/4


5/4, 5/3




The resulting scale (given in Ben Johnston's notation) is as follows:

Pitch:C#D13-D#vD^- D#-D#D#L-E7E13vE E^-E#E#LF13F#
Ratio:1/113/1212/1111/10 10/99/88/77/613/11 6/511/95/49/713/104/3
Cents:0138.6150.6165 182.4203.9231.2266.9289.2 315.6347.4386.3435.1454.2498

F#^G7FxLG13-G# G#^L-AA13A#A#LB7 BB^-B13L-
11/87/5 10/713/93/211/78/5 13/85/312/77/49/511/613/7
551.3582.5 617.5636.6702782.5813.7840.5 884.4933.1968.81017.61049.41071.7

(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, v lowers it by 32/33, 13 raises it by 65/64, and F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.

I had figured out in Triskaidekaphonia that I could make different scales within this network by taking all notes expressible by the form 13/X, or 11/X, or X/7, and the scales with the smallest numbers would be closest to simple tonality, while the larger-numbered scales will have a much more oblique relationship. Thus the scales that run through the piece are:

13/X:1/1 13/1213/1113/1013/913/8 13/7
12/X:1/1 12/116/54/33/212/7
11/X:1/1 11/1011/911/811/711/6
10/X:1/1 10/95/410/75/3
9/X:1/1 9/89/73/29/5
8/X:1/1 8/74/38/5
7/X:1/1 7/67/57/4
X/9:1/1 10/911/94/313/95/3
X/7:1/1 8/79/710/711/712/7 13/7
X/5:1/1 11/106/513/107/58/5 9/5
X/3:1/1 13/127/64/33/25/3 11/6
X/2:1/1 9/85/411/83/213/8 7/4

Of course, the scales with X in the numerator are overtone series, and those with X in the denominator are undertone series. (Harry Partch called them otonalities and utonalities.) Since all the pitches have a simple relationship to 1/1 C#, a rhythmicized drone on that pitch runs throughout. The piece, then, moves "in and out of focus" depending on which scale is used at a given moment.

Kyle Gann

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