Problems of Harmony
by Arnold Schoenberg
online version © 1999 by Joseph L. Monzo
Modern music has centered interest on two problems: that of tonality, and that of dissonance. It cannot be said that the conflict regarding these questions is new, nor that it is waged with new weapons. On the contrary: just as all the battlefields of world history are constantly the scene of renewed strife, so, too, is this one; this also is a bettlefield in the historic sense.
Of course, it is not necessary for me to cite as proof the well-known precendents from the musical past. It is enough to recall the "Dissonance" -Quartet of Mozart and Hans Sachs' lines:
Ihr schlosset nicht im gleichen Ton,
Das macht den Meistern Pein;
Doch nimmt Hans Sachs die Lehr' davon;
Im Lenz wohl Mu¨ss' es so sein.[Your closing key is not the same,
This gives the masters pain;
But Hans Sachs draws a rule from this;
In Spring it must be so, 'tis plain.]
In Spring!
We can say that in the development of art, it must always be as it is in Spring! One does what is necessary, tho it cause somebody else pain; one does what the situation demands, unconcerned about the approval or disapproval of others.
And the cause of music demands, as the history of art-battles shows, that the secret of the sounding tone be always pursued anew. The development of music is more dependent than any other art upon the development of its technique. A truly new idea - at least as musical history reveals - is hardly imaginable without significant changes in musical technique. The material of music offers inexhaustible possibilities; but every new possibility in turn demands a new kind of treatment, because it presents new problems or at any rate demands a new solution of the old one. Every tonal progreassion, every progression of even two tones, raises a problem which requires a special solution. Yet the further such tones are brought into relation and contrast with each other and with rhythm, the greater is the number of possible solutions to the problem, and the more complex are the demands made on the carrying out of the musical idea.
In no art, properly speaking, can one say "the same thing", the same thing which has been said once before, least of all in music.
An idea in music consists principally in the relation of tones to one another. But every relation that has been used too often, no matter how extensively modified, must finally be regarded as exhausted; it ceases to have power to convey a thought worthy of expression. Therefore every composer is obliged to invent, to invent new things, to present new tone relations for discussion and to work out their consequences. It is for this reason that the technique of music must develop so quickly and so peristently. In a methodic progresssion from the more simple to the more complex, one would hardly be aware of the inevitable changes in technique. But imagination does not ask about method, nor does it invent according to a graduated scale. Differences in technique therefore appear far more abrupt than they are in reality. When we realize that today the difference in the technique of the early Beethoven from that of the later is apparent only to the connoisseur, we can no longer understand the cry from the gallery at the premiere of Beethoven's 8th Symphony: "Es fällt ihm schon wieder nichts ein".1
Let us first examine the concept of tonality.
To elucidate the relationship between tones one must first of all recall that every tone is a compound sound, consisting of a fundamental tone (the strongest sounding one) and a series of overtones.2 We may now make the statement, and to a great extent test and prove it, that all musical phenomena can be referred to the overtone series, so that all things appear to be the application of the more simple and more complex relationships of that series.
Considered singly these relations are as follows:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||
C | C | |G| | c | e | g | bb | c | d | e | f# | g | ab | ||
F | F | |C| | f | a | c | eb | f | g | a | b | c | db | ||
G | G | |D| | g | b | d | f | g | a | b | c# | d | eb |
bb | as the | 7th | overtone of | C | ||
f# | as the | 11th | overtone of | C | ||
eb | as the | 7th | overtone of | F | and 13th of | G |
db | as the | 13th | overtone of | F | and 11th of | G |
ab | as the | 13th | overtone of | C |
But let us bear in mind [... TO BE CONTINUED!]
NOTES
1"It falls it already again nothing." in my bad German translation. (back to text)
2Modern psychoacoustical research has shown that even when the fundamental tone itself does not exist, the existence of higher sine tones in an arrangement according to any segment of the harmonic series, will cause a listener to perceive that fundamental anyway. (back to text)
REFERENCES
Harmonielehre: my introduction, Chapter 1, Chapter 2, Chapter 3, Chapter 4.
or try some definitions. |
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