Sometimes I like to use microtones in a songlike, almost pop kind of context to bring the tuning weirdness into even greater relief. Charing Cross moves among chords based on the 7th, 9th, 11th, and 13th harmonics, as well as on the tonic and on 15/14 (a virtual 17th harmonic, though actually slightly more exotic). Using software that let me add microtones freely as I went along, I ended up with 39 pitches to the octave. (Only 37 different pitches were used in the realization; when two pitches are closer than five cents I merge them, just to simplify the realization.) The form of the piece is a loose additive process: first the 7th-harmonic and 13th-harmonic tonalities are introduced, later the 9th and 15/14, and the 11th-harmonic tonality is saved for the very end. The opening bass line started ringing in my head as I was sitting on a bench at the Thames near the Charing Cross underground station in London, and I commenced composing the piece on a napkin at the closest outdoor Italian restaurant. That was September 6, 2007. I finished the piece back home in Germantown on the 13th. Hearing the piece always takes me back to that magical moment and spot.

mp3 recording

The total scale is as follows:

Pitch:	C	C+	C13	C^	C#L	D7	Db^13-	D	D^	Eb7^	D#L	Eb13	E	E+	F7+	E#L	F+	F13	F^
Ratio:	1/1	81/80	65/64	33/32	15/14	35/32	143/128	9/8	55/48	77/64	135/112	39/32	5/4	81/64	21/16	75/56	27/20	65/48	11/8
Cents:	0	21.5	26.8	53.3	119.4	155.1	191.8	203.9	235.7	320.1	323.4	342.5	386.3	407.8	470.8	505.8	519.6	524.9	551.3

F#+

G13b7

G7

F#L^

G

G13

Ab77

G^

G#L

Ab13

A

A+

AL

A^

Bb7

A#L

Bb13

B

Bb^^-

C7+

45/32

91/64

35/24

165/112

3/2

195/128

49/32

99/64

45/28

13/8

5/3

27/16

12/7

55/32

7/4

25/14

117/64

15/8

121/64

63/32

590.2

609.4

653.2

670.8

702

728.8

737.7

755.2

821.4

840.5

884.4

905.9

933.1

937.6

968.8

1003.8

1044.4

1088.3

1102.6

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, 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.

Performances:
October 9, 2007 presented by the Karnatic Lab at De Badcuyp in Amsterdam (world premiere)
October 25, 2007, at the Mendelssohnsaal of the Hochschule fŸr Musik und Theater in Hamburg, Germany
November 7, 2007, at Trinity College in Dublin
February 8, 2008, at the University of Kentucky in Lexington

Kyle Gann

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