Just Keys is a medium upright or console
piano that Cris Forster restrung three times and retuned four times
in 1990. The graphic (left) shows the complete keyboard from the
first key in the bass to the last key in the treble. In the detailed
graphic, we see close-ups of the keyboard divided into two parts:
the upper section spans the distance from the A1-key to the G47-key,
and the lower section, from the G47-key to the C88-key.
Note that the B3-key identifies ratio 1/1, which is the fundamental
frequency of the tuning. This key sounds G1 at 49.0 cps. Since the
G11-key normally produces this frequency, observe that Cris eliminated
most of the tones that comprise the first octave of the standard
piano. Consequently, the A1-key now sounds frequency ratio 8/5,
or a just major third, interval ratio 5/4, below 1/1, which is E
flat at 39.2 cps; and the B flat 2-key now sounds frequency ratio
16/9, or a just major second, interval ratio 9/8, below 1/1, which
is F at 43.6 cps.
The detailed graphic (click here to view
detail) indicates a 10-tone octave, ratios 1/1–2/1, from the
B3-key to the A13-key (two keys with two dark blue labels); a 17-tone
octave, ratios 2/1–4/1, from the A13-key to the D30-key (two keys
with two dark blue labels); and another 17-tone octave, ratios 4/1–8/1,
from the D30-key to the G47-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 G47-key
to the G83-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. |