[Smt-talk] The Overtone Series

Daniel Wolf djwolf at snafu.de
Tue Jul 22 13:56:43 PDT 2014

On Tue, 22 Jul 2014 20:32:47 +0200, Victor grauer <victorag at verizon.net>  

> Moreover, as I see it the real problem with deriving the triad from the  
> overtone series

Isn't "deriving the triad from the overtone series" both an a-historical  
and unnecessary notion?

The major triad is a local minimum of sensory dissonance (or maximum of  
sensory consonance) in an polyphonic tonal environment in which (1) the  
pitch resources divide the octave in more than five parts and include  
4:5:6 triads or close approximations thereof and (2) the spectra of voices  
and instruments in use are overwhelmingly simple (i.e. the partials are  
integer multiples of the fundamental)harmonic spectra.

This strongly suggests that it is and was possible to derive a tonal  
system that was closely tied to properties of simple harmonic spectra  
without having an explicit theory of the harmonic series at hand. (That  
said, and in full recognition of the absence of historical written  
theoretical evidence, I would be rather circumspect about the state of  
knowledge of the harmonic series, given the practical experience of  
overtone flutes, trumpets, horns, and, possibly, the use of string  
harmonics in instruments. (Unfortunately, we know virtually nothing about  
the prehistory of the tromba marina, a monochordal bowed string instrument  
played by touching harmonic nodes.))

Regarding point (1) above, I offer the counterexample of Central Javanese  
gender playing, which can be understood as a pentatonic counterpoint in a  
maximum of two distinct voices in a tonal system without a functional  
distinction between thirds/fourths or fifths/sixth; regarding the question  
(2) of the relationship between timbral environment and tonal system, I  
heartily recommend William Sethares's Tuning, Timbre, Spectrum, Scale  
(Springer Verlag.))

Daniel Wolf

Dr. Daniel James Wolf
Frankfurt am Main
djwolf at snafu.de

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