182 
WEAD. 
Since every intelligent discussion of the scale has involved 
the use of numbers, it is interesting from a historical point of 
view to note that the Greek theorists (how they were led to 
fix on them can only be surmised) were content to work with 
2 and 3, their products and powers; Zarlino broadened the 
tonal foundation by introducing 5, and therefore making 
more use of 6 than the Greeks did. Poole and others have 
insisted on using 7, though it upsets the diatonic scale ; and 
Gevaert, Director of the Brussels Conservatory, asserted in 
1883 that modern composers do use 7, giving the so-called 
natural Seventh, but do not use the next primes, 11 and 13. 
Of course passages for this Seventh must be scored for the 
horn, violin, etc., not for an instrument of fixed tone like the 
piano. 
It may be recalled that a favorite way of defining the Euro- 
pean scale for a century and more has been to consider it as 
made up of three Major Triads F, A, C ; C, E, G ; G, B, D ; the 
vibration-frequencies in each case having the ratios 4:5:0. 
This is the ‘‘Just Diatonic Scale Major" of the theorists, often 
ignorantly and arrogantly spoken of as “the natural scale.” 
A similar operation with the ratios 10 : 12 : 15 gives the 
harmonic minor scale, which does not agree throughout with 
the former scale. The series of Fifths will give a different 
scale ; and modulation with any of those scales will introduce 
numerous new notes, nearly but not quite in unison with 
others. As harmonic music developed the complication be- 
came excessive and the discussions over the possible reforms 
became very acrimonious. In the early books of harpsichord 
music one finds the music confined to four or five keys; F, C, 
G, D, etc. ; but Bach wanted a wider range of keys and large 
freedom for modulation; and as his favorite instrument was 
the clavichord (not piano, as some books say), with a deli- 
cate, short tone he found it practicable to tune this to equal- 
temperament, like our present pianos; so he could play in all 
keys, and in 1722 and 1740 he wrote his famous Fugues and 
Preludes. Later, when the pianoforte came into use, the 
fashion had been set, and as the instrument would not stand 
in tune long any-way, theoretical protests were scorned. If 
