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: |
| D | 1/1 | 0 | D + 0 |
| D^ | 33/32 | 53.3 | D# - 47 |
| Ev+ | 12/11 | 150.6 | E - 49 |
| E7+ | 35/32 | 155.1 | E - 45 |
| E | 10/9 | 182.4 | E - 18 |
| E+ | 9/8 | 204 | E + 4 |
| EL | 8/7 | 231.2 | E + 31 |
| F#+ | 5/4 | 386.3 | F# - 14 |
| F#L+ | 9/7 | 435.1 | F# + 35 |
| G7+ | 21/16 | 470.8 | G - 29 |
| G | 4/3 | 498 | G - 2 |
| G^ | 11/8 | 551.3 | G# - 49 |
| G#+ | 45/32 | 590.2 | G# - 10 |
| G#L | 10/7 | 617.5 | G# + 18 |
| Av+ | 16/11 | 648.7 | Ab + 49 |
| A | 40/27 | 680.4 | A - 20 |
| A+ | 3/2 | 702 | A + 2 |
| Bb77+ | 49/32 | 737.7 | A + 38 |
| A^+ | 99/64 | 755.2 | A# - 45 |
| A#+ | 25/16 | 772.6 | A# - 27 |
| Bv+ | 18/11 | 852.6 | B - 47 |
| B | 5/3 | 884.4 | B - 16 |
| B+ | 27/16 | 905.9 | B + 6 |
| BL | 12/7 | 933.1 | B + 33 |
| B^ | 55/32 | 937.6 | B + 38 |
| C7+ | 7/4 | 968.8 | C - 31 |
| C#v+ | 20/11 | 1035 | C + 35 |
| C#+ | 15/8 | 1088.3 | C# - 12 |
| D7+ | 63/32 | 1172.7 | D - 27 |
Clarinet in Bb scale:
| Pitch: | Ratio: | Cents: | Clarinet Notation: |
| D | 1/1 | 0 | E + 0 |
| D^ | 33/32 | 53.3 | F - 47 |
| Ev+ | 12/11 | 150.6 | F# - 49 |
| E7+ | 35/32 | 155.1 | F# - 45 |
| E | 10/9 | 182.4 | F# - 18 |
| E+ | 9/8 | 204 | F# + 4 |
| EL | 8/7 | 231.2 | F# + 31 |
| F#+ | 5/4 | 386.3 | Ab - 14 |
| F#L+ | 9/7 | 435.1 | G# + 35 |
| G7+ | 21/16 | 470.8 | A - 29 |
| G | 4/3 | 498 | A - 2 |
| G^ | 11/8 | 551.3 | Ab - 49 |
| G#+ | 45/32 | 590.2 | Bb - 10 |
| G#L | 10/7 | 617.5 | A# + 18 |
| Av+ | 16/11 | 648.7 | Bb + 49 |
| A | 40/27 | 680.4 | B - 20 |
| A+ | 3/2 | 702 | B + 2 |
| Bb77+ | 49/32 | 737.7 | B + 38 |
| A^+ | 99/64 | 755.2 | C - 45 |
| A#+ | 25/16 | 772.6 | C - 27 |
| Bv+ | 18/11 | 852.6 | C# - 47 |
| B | 5/3 | 884.4 | C# - 16 |
| B+ | 27/16 | 905.9 | C# + 6 |
| BL | 12/7 | 933.1 | C# + 33 |
| B^ | 55/32 | 937.6 | Db + 38 |
| C7+ | 7/4 | 968.8 | D - 31 |
| C#v+ | 20/11 | 1035 | D + 35 |
| C#+ | 15/8 | 1088.3 | D# - 12 |
| D7+ | 63/32 | 1172.7 | E - 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) | 81/80 | raises a pitch by 21.5 cents, or syntonic comma |
| # | (sharp) | 25/24 | raises a pitch by 71 cents |
| 7 | (seven) | 35/36 | lowers a pitch by -49 cents to obtain a seventh harmonic |
| L | (upside-down 7) | 36/35 | raises a pitch by 49 cents |
| ^ | (upward arrow) | 33/32 | raises a pitch by 53 cents to obtain an eleventh harmonic |
| v | (downward arrow) | 36/35 | lowers 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
Return to List of Compositions