| The
first intervals between the overtones are farther apart, but the distance
between the notes grows less and less as one progresses up the series. The
first notes we readily class as concords and the latter ones as dissonants,
but there is no definite point at which we can say that concord stops and
dissonance begins. . . . The important truth which is demonstrated scientifically
by acoustics, is this: that the intervals which have been accepted have
been accepted in the order in which they occur in the overtone scale--first
the octave, then the perfect fifth, then the fourth, then the third, and
so on. The innovations in harmony which time has refused, were out of that
order. . . . The great masters who have developed our music step-by-step,
have done so because their ears were keen enough to hear the harmony of
the overtones and to play in outward notes the combinations which they heard.[Cowell,
Henry, "The Impasse of Modern Music," in Essential Cowell,
Edited by Dick Higgins, Document Text, McPherson & Co., 2001, p292] |
|
. . . Each
step in historical progress was marked by an innovation--the use of one
or more overtone relationships in combination with the tone combinations
already accepted. Each innovation was felt at the time to be both radical
and daring, and as such it was resisted until the musical ear of the period,
grown accustomed to the new combination, accepted it as essentially consonant
or "harmonious." . . . From these beginnings music has proceeded
steadily in the same direction. Many increasingly complex intervals have
been added, at first as passing or auxiliary tones, then as part of a
chord demanding resolution, and finally, as the ear became more and more
used to them, as independent chord tones, without specific obligation.
Each one of these intervals was, when it was added, the one formed by
the next highest members of the overtone series, following those already
in use. [Cowell, Henry, New Musical Resources, Cambridge University
Press, 1996, pp13-14]
|
| It
is interesting to observe that as musicians became accustomed to reach into
the higher ranges of the overtone series for their harmonic material, there
was a corresponding tendency to reject the simplest ratios, . . . . [Cowell,
Henry, New Musical Resources, Cambridge University Press, 1996, p16] |
