A (roughly) 24PperPoctave eightPfifthsPdown piano design

As the number of keys per octave of a keyboard instrument increases, the=
=0Ademands on the performer tend to increase and the playable pitch range=
of the=0Ainstrument decreases. Performing at the piano itself is somewh=
at "unnatural".=0AThe performer drills many related not=96very=96intuitiv=
e arm, hand, and finger=0Amotions over and over until he or she can perfo=
rm pleasing, natural sounding=0Awell=96paced music. If the keyboard were=
laid out somewhat differently, with=0Amore use being made of different "=
depths" from front=96to=96back - say three=0Adepths rather than the two (=
white keys front, black keys back) currently used,=0Ait might be possible=
to develop a practicable keyboard with from 20 to 24 keys=0Aper octave w=
hich could, with considerable effort by talented, motivated=0Aindividuals=
, be mastered and played with the flexibility and command with=0Awhich tr=
ained pianists and organists perform on current instruments. The=0Aadvan=
tages in harmoniousness - and ability to perform musically meaningful,=0A=
but still difficult=96to=96produce near=96just 7=96 and 11=96 ratio chord=
s might=0Aoutweigh the limitations which such an instrument might have re=
lative to the=0Apresent piano with respect to pitch range, effort needed =
to play it=0Aproficiently, etc.

=09An initial thought regarding the instrument would be to have it based =
on a=0Aspiral of possibly slightly tempered fifths (flat by 0.24 cents to=
produce=0Ajust 5/4 thirds going down eight of these fifths) beginning wi=
th, say, B,=0Agoing down E, A, D, etc. through B=96, E=96, A=96, etc. on =
down to F#- 23 fifths=0Adown from the initial B. With such a keyboard, a=
ssuming 24 notes, there would=0Abe 23 only slightly flat=96tempered fifth=
s, 16 just major thirds, and 22 notes=0Astarting with the A two fifths do=
wn from the initial B having nearly just=0A(flat .5 cents) 9/8 major whol=
e tone notes above them. In addition, ten of=0Athe notes from B down to =
the first G#/Ab would have fairly close harmonic=0Asevenths sharp by abou=
t 7 cents on them. Finally, the six notes from B down=0Ato C would have =
tritone notes forming somewhat close harmonic 11/8 ratios with=0Athem (sh=
arp by about 17 cents) allowing full and there would be four (from A=0Ado=
wn to C) (from MT ear testing with MT 28 cent sharp harmonic 11th=0Aequiv=
alents) to=96an=96appreciable degree musically meaningful 1=963=965=967=
=969=9611 chords=0Aachievable.

=09It would probably be feasible (a lot of work) to do considerable ear=
=96testing=0Aof different tempering schemes with such a keyboard. Would =
it be preferable=0Ato have absolutely just fifths and allow the major thi=
rds to be 2 cents flat,=0Aor would it sound better to have the fifths tem=
pered flat by 0.2 or 0.3 cents?

=09The notes at the lower end of the spiral of fifths, particularly the b=
ottom=0Afour of these are the ones which will be used as harmonic 7ths an=
d 11ths, and=0Ait might prove advantageous to temper these in such a way =
as to yield more=0Aaccurate 7=96 and 11=96 ratio intervals with these not=
es.

=09It also might make sense to make the fifths from B down to Bb just and=
allow=0Aa "miniwolf fifth" narrow by 1.9 cents between Bb and the Eb/D# =
below it (Are=0Athere conventions for use of Eb as against D# when discus=
sing a=0Anot=96heavily=96described tuning scheme?).

=09In order to have introduction of such a keyboard likely to succeed in=
=0Aachieving a durable niche in musical art, it would be necessary to hav=
e=0Aarrangements prepared, and well performed publicly (also widely repor=
ted and=0Adistributed) which would show a model of the instrument off to =
clear and=0Astriking advantage. I believe that quite a few individuals w=
ould immediately=0Asense that well chosen music performed on such an inst=
rument was in every=0Arespect at least equal to that performed on present=
standard instruments, but=0Athat in most ways - clarity, timbral beauty,=
"three=96dimensionality" of its=0Aharmonies, the instrument was in a dif=
ferent class than practically any=0Akeyboard instrument which had ever be=
en heard in present times.

=09Actually, listening results with a current piano tuned to quarter comm=
a mean=0Atone temperament, which yields very close (3 cents flat) 7- rati=
o harmonies on=0Atwo notes and which produces sounds which most who have =
heard them consider=0Aeffective "blues=96piano" chords suggests that the =
proposed instrument could be=0Asuccessful, and go down in history as havi=
ng heralded a radical advance in=0Amusical art when it was introduced. P=
erhaps the stiffest competition to it=0Awould come from many thousands or=
possibly millions of already=96existing pianos=0Atuned in such a way as =
to take fuller advantage of their true, as yet largely=0Aunsuspected beau=
ty as musical instruments.

=09Dave Hill La Mesa, CA