|
Just Keys is a medium upright or console piano that I restrung three times and retuned four times in 1990. The graphic above shows the complete keyboard, with Lexan-covered colored labels, from the first key in the bass to the last key in the treble.
Note that the B-3 key identifies ratio 1/1, which is the fundamental frequency of the tuning. This key sounds G1 at 49.0 cps! Since the G-11 key normally produces this frequency, observe that I eliminated most of the tones that comprise the first octave of the standard piano. Consequently, the A-1 key now sounds frequency ratio 8/5, or a just major third, interval ratio 5/4, below 1/1, which is Eb1 at 39.2 cps; and the A#-2 key now sounds frequency ratio 16/9, or a just major second, interval ratio 9/8, below 1/1, which is F1 at 43.6 cps.
A 10-tone octave, ratios 1/1–2/1, exists from the B-3 key to the A-13 key (two keys with two dark blue labels); a 17-tone octave, ratios 2/1–4/1, from the A-13 key to the D-30 key (two keys with two dark blue labels); and another 17-tone octave, ratios 4/1–8/1, from the D-30 key to the G-47 key (two keys with two dark blue labels). From here, three consecutive 12-tone octaves, ratios 8/1–16/1, ratios 16/1–32/1, and ratios 32/1–64/1 span the distance from the G-47 key to the G-83 key. These 12-tone scales resemble the tuning of a conventional piano. Short string lengths determined by the shape of the cast iron plate and the location of the bridge severely restricted alternate tuning possibilities in the upper treble range. |
