A SIMPLE DEVICE FOR DEMONSTRATING THE TEM- 
PERED SCALE. 
L. B. SPINNEY. 
The diatomic scale consisting of 
a succession of eight tones and con- 
taining three intervals known as 
major second intervals,’^ two 
known as ‘‘minor second intervals” 
and two “half-tones,” is not 
adapted to musical instruments of 
“fixed pitch” (e.g. the piano, harp, 
etc.) for the reason that it does not 
without a multiplicity of keys 
(strings) allow of transposition or 
change of keys. 
For fixed-pitch instruments, 
therefore, the scale is modified in 
the following manner. First, an 
additional tone is inserted in each 
of the larger intervals (major and 
minor seconds) of the scale — thus 
breaking the octave into twelve in- 
stead of seven intervals, and sec- 
ond, the pitches of the various 
tones are so altered as to make the 
interval between any two succes- 
sive tones the same. This scale is 
known as the scale of “equal tem- 
perament” or briefiy, the tem- 
pered scale. 
The “interval” between two 
tones, as the term is here used, is 
the ratio of the pitch of the higher 
tone to that of the lower. It fol- 
lows that on the tempered scale 
this ratio is the same for any two 
adjacent tones. The numerical 
value of this interval is 1.05946, 
since the sum of twelve such in- 
tervals is 2, the numerical value of 
the octave interval. 
Pig. 26, — Diagram for demonstrating the tempered scale. 
