Kyle Gann:

Tuning for As the Day Is Long (Revisited)

Scored for flute, clarinet, fretless bass, and two keyboard samplers, As the Day Is Long (Revisited) (2005) is written in a 30-pitch scale over eight basic harmonies. The woodwind parts are notated with conventional equal-tempered pitches, with positive or negative numbers above each note showing how sharp or flat the pitch is relative to equal temperament. The 30-pitch scale is given below, first with reference to the flute, then transposed for Bb clarinet:

Pitch:Ratio:Cents:Flute Notation:
D1/10D + 0
D^33/3253.3D# - 47
Ev+12/11150.6E - 49
E7+35/32155.1E - 45
E10/9182.4E - 18
E+9/8204E + 4
EL8/7231.2E + 31
F#+5/4386.3F# - 14
F#L+9/7435.1F# + 35
G7+21/16470.8G - 29
G4/3498G - 2
G^11/8551.3G# - 49
G#+45/32590.2G# - 10
G#L10/7617.5G# + 18
Av+16/11648.7Ab + 49
A40/27680.4A - 20
A+3/2702A + 2
Bb77+49/32737.7A + 38
A^+99/64755.2A# - 45
A#+25/16772.6A# - 27
Bv+18/11852.6B - 47
B5/3884.4B - 16
B+27/16905.9B + 6
BL12/7933.1B + 33
B^55/32937.6B + 38
C7+7/4968.8C - 31
C#v+20/111035C + 35
C#+15/81088.3C# - 12
D7+63/321172.7D - 27

Clarinet in Bb scale:

Pitch:Ratio:Cents:Clarinet Notation:
D1/10E + 0
D^33/3253.3F - 47
Ev+12/11150.6F# - 49
E7+35/32155.1F# - 45
E10/9182.4F# - 18
E+9/8204F# + 4
EL8/7231.2F# + 31
F#+5/4386.3Ab - 14
F#L+9/7435.1G# + 35
G7+21/16470.8A - 29
G4/3498A - 2
G^11/8551.3Ab - 49
G#+45/32590.2Bb - 10
G#L10/7617.5A# + 18
Av+16/11648.7Bb + 49
A40/27680.4B - 20
A+3/2702B + 2
Bb77+49/32737.7B + 38
A^+99/64755.2C - 45
A#+25/16772.6C - 27
Bv+18/11852.6C# - 47
B5/3884.4C# - 16
B+27/16905.9C# + 6
BL12/7933.1C# + 33
B^55/32937.6Db + 38
C7+7/4968.8D - 31
C#v+20/111035D + 35
C#+15/81088.3D# - 12
D7+63/321172.7E - 27

I have notated this scale (as closely as html will allow) in Ben Johnston's excellent microtonal notation, in which accidentals make the following alterations:

Sign:
Ratio:Effect
+(plus)81/80raises a pitch by 21.5 cents, or syntonic comma
#(sharp)25/24raises a pitch by 71 cents
7(seven)35/36lowers a pitch by -49 cents to obtain a seventh harmonic
L(upside-down 7)36/35raises a pitch by 49 cents
^(upward arrow)33/32raises a pitch by 53 cents to obtain an eleventh harmonic
v(downward arrow)36/35lowers a pitch by 53 cents

In addition, F-A-C, C-E-G, and G-B-D are all perfectly tuned 4:5:6 major triads.

(If you don't have enough experience with just intonation to make sense of these charts, try reading the step-by-step Just Intonation Explained section.)

Kyle Gann, 1998

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