Kyle Gann: Romance Postmoderne (2012)

Recording here

Romance Postmoderne is a tuning study, a kind of rewriting of a Romantic genre, on 33 harmonics of Eb. It contains eight harmonics series', each up to the 15th harmonic, based respectively on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th harmonics.

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:13579111315
Eb7+1172.7463/3263/32
Db^^-1102.64121/64
D1088.2715/815/815/815/8
Db131044.44117/64117/64
C#+976.54225/128
Db7968.837/47/4
C^937.6355/3255/32
C+905.8727/1627/16
C7+857.09105/64105/64
Cb13840.5313/813/8
B772.6325/16
Bb^755.2399/6499/64
Cb77+737.6549/32
Bb13728.8195/128195/128
Bb701.963/23/2
Bb7b13609.3591/6491/64
A+590.2245/3245/3245/3245/32
Ab^551.3211/811/8
Ab13b13481.06169/128
Ab7+470.7821/1621/16
G^439.59165/128165/128
G+407.8281/64
G386.315/45/4
Gb13342.4839/3239/32
Gb7^320.1477/6477/64
F#+274.5875/6475/64
F+203.919/89/89/8
Fb^13191.85143/128143/128
F7+155.1435/3235/32
E+92.18135/128135/128
Eb^53.2733/3233/32
Eb1326.8465/6465/64
Eb01/1

(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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