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The values of the [Fibonacci] series
may be applied to intonations as well. . . .
. My own applications of the various summation series to design as well as music (not only to pitch, but also to the development of durations) show that such groups of lines or durations or pitches affect us as organic formations. . Many other forms of the harmonic arrangement of numbers produce an organic effect upon the listener when such harmonic relations underlie the structure of melodic intervals. Among such harmonic relations I will mention only the most fundamental ones:
Thus we see that the forms of organic growth associated with life, well-being, self-preservation and evolution appeal to us as a form of beauty when expressed through an art medium. Intuitive artists of great merit are usually endowed with great sensitiveness and intuitive knowledge of the underlying scheme of things. This is why a composer like Wagner is capable of projecting spiral formations through the medium of musical intonations without any analytical knowledge of the process involved. On the other hand, scientific analysis shows that the efforts of greatly endowed and creative persons could have been accomplished without any waste of time, introspection, or over-sensitiveness. Once the laws underlying certain structures have been disclosed, anyone can develop any number of structures in a class through the use of a formula. This does not prevent an artist, who makes an individual selection (whatever the value of such selection may be), from operating under the illusion of as great a freedom as that he imagines he possesses when he creates through the channels of vague intuition and nebulous notions.
Joseph Schillinger
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