source file: m1467.txt Date: Mon, 6 Jul 1998 20:50:37 EDT Subject: A (roughly) 24PperPoctave eightPfifthsPdown piano design From: 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