Romance Postmoderne is a tuning study, a kind of rewriting of a Romantic genre, on 33 harmonics of Eb. Through the early 2000s, as I wrote microtonal pieces, I found myself inventing scales whose pitches were more and more drawn from a single harmonic series. Finally, in 2012 I decided to try using the harmonic series as my sole resource. I was so happy with the result that I later wrote my magnum opus Hyperchromatica in the same scale. Romance Postmoderne, slightly ironically titled, drifts languidly from harmonic series to harmonic series (all of them harmonics of E-flat) via the smallest of melodic steps.
The scale consists of 33 harmonics of a low E-flat. The 33 pitches result from the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th harmonics being built up on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th harmonics respectively each of those harmonics acting as a secondary tonic. The scale (given in a typographical approximation of Ben Johnston's notation) is as follows, with each harmonic series in a different column, and you can get a sense in this layout for the kinds of microtonal voice-leading I had available:
Pitch: Cents: 1 3 5 7 9 11 13 15 Eb7+ 1172.74 63/32 63/32 Db^^- 1102.64 121/64 D 1088.27 15/8 15/8 15/8 15/8 Db13 1044.44 117/64 117/64 C#+ 976.54 225/128 Db7 968.83 7/4 7/4 C^ 937.63 55/32 55/32 C+ 905.87 27/16 27/16 C7+ 857.09 105/64 105/64 Cb13 840.53 13/8 13/8 B 772.63 25/16 Bb^ 755.23 99/64 99/64 Cb77+ 737.65 49/32 Bb13 728.8 195/128 195/128 Bb 701.96 3/2 3/2 Bb7b13 609.35 91/64 91/64 A+ 590.22 45/32 45/32 45/32 45/32 Ab^ 551.32 11/8 11/8 Ab13b13 481.06 169/128 Ab7+ 470.78 21/16 21/16 G^ 439.59 165/128 165/128 G+ 407.82 81/64 G 386.31 5/4 5/4 Gb13 342.48 39/32 39/32 Gb7^ 320.14 77/64 77/64 F#+ 274.58 75/64 75/64 F+ 203.91 9/8 9/8 9/8 Fb^13 191.85 143/128 143/128 F7+ 155.14 35/32 35/32 E+ 92.18 135/128 135/128 Eb^ 53.27 33/32 33/32 Eb13 26.84 65/64 65/64 Eb 0 1/1 (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, 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.
Kyle Gann
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