New-York tribune., 1909-12-12

mathematics. The practical difficulty of a
piano maker NAV be apprehended in an un-
technical way by an examination of the KEY
board of Your piano This YOU will fnd Is
divided of into alternating groups of four
white KEYS inclOSing three black KEYS. and three
white keys IncloSIng two black KEYS. y combi-
nation OF these two groups makes what Is
rightly known IS a septavc- But the more
usual expression Is % include the first note Of
the next group and call the notes included be-
tween any note and its octave above OF below
an octave. Each Septdve contains seven white
keys and hve black KEYS, each key representing
musical note.
In the key of c major the white KEYS in re-
latlon 10 one another represent perfect whole
intervals OF tone and the black KEYS perfect
half intervals OF semitones. But when we get
away from the KEY of & our troubles begin
For instance, II We 20 10 the kew Of d. We hear
only semltone between + and + natural
where in the KEY of G We heard a full interval
and between natural and F sharp we hear a
tull interval where in the kew of we heard
only a Semitone.
Us We pass into other KEYS. We begin 10 tind
that piano KEYS have a double Significance
The same piano KEY viii represent sharp in
one signature and g. flat in another. In like
manner, the next black KEY above il NAV be
either q sharp OF y flat. the next \ sharp OF b
Hat. Even the white KEYS b and & and r and
r interchange. Now a scientific fact any
two OF these notes represented bv the same kev
nearly alike; but not quite
Now We begin to see the piano makers prob
lem. II he was To undertake To build an instr,l-
ment capable OF giving perfect reproduction L.
every tone IN everyone OF the twelve scale KEYS
IN which music can be written. ne would have
% put hity-three KEYS IN each octave and his
keyboard instead of being comfortably inside
OF hve feet would stretch out over twenty feet
No one but a millionaire could own such an
instrument and only Marathon runner could
play IT,
some practical compromise was necessary
and the problem was tackled in a Crue, WY
dS soon aS the hrSt keyboard was constructed L.
M the system OF notation perfected bv Guido
ID Arezzo. NTginaS, spinets. clavicrs. and
hdrpSlchords antedated the piano a great MANY
wears. and the makers of these instruments IN
Whch the musical tone Is produced hv strik-
my a WIRE began 10 have their troubles about
tuning Organ builders had even greater trou-
uie>' as the prolongation Of the tone IN that in
strumcnt makes the dSSonanccs due to m.
limitations ot The keyboard more apparent
IMAM IN the instruments of percussion
t'uIdo himself Is sand 10 baVe b,rn s,,.,rs.,r
Tor a system OF tuning which has not added any
u ms glory. His idea was to tune th,. rest of
ms instrument in perfect octaves from tb.
SeP'dNe OF middle 4. This sounds rtasonab abl.
ON ON paper but quite otherwise in actual prac-
uVT- me reason underlying this Is intricate
ana technical. but Is practically demonstrabI.
III piano was SO tuned TODAY. II would not
require musical ear 10 detect that II was de
cidcdly of pitch
Naiiists, an organIst IN the cathedral of Bur
S"S IN SPAN invented what Is known as the
Il0'n'"he system OF tuning As early as 1913
~ SVhcidl way, ms ann was 10 make an the.