Cowell vs. Aldwell & Schachter

In my recent readings I’ve become fond of the idea, presented by Henry Cowell and others, that all musical consonance and dissonance can be explained with relationship to the harmonic series.

It would seem that the overtones should be made the basis of musical theory to a far greater extent than they have been,
- Henry Cowell, New Musical Resources, 1930

But I recently came across this rather passionate rejection of the theory in a text on conventional harmony:

In the past, many theorists went to absurd extremes in their attempt to use the overtone series as a “scientific” basis for music, contorting it in various ways to extract a minor triad from it and making it the basis for arbitrary “rules” of composition - rules that no great composer has ever followed. And even where the series and the tonal system correspond very closely - as with the major triad - there is no proof that the acoustical relationship causes the musical one.
- Aldwell & Schachter, Harmony & Voice Leading 1978

The thing that amused me was the mocking tone of this quote; so alien in the context of a informative text book. One can easily picture the scornful face of the author as they wrote this passage. It also reminded me that Cowell’s justification for minor tonality was to turn the harmonics upside down, looking at the “undertone series”

A very interesting approach to the theoretical explanation of minor is the theory of undertones. Until recently undertones were a theory only. Their existence was contested by scientists on the grounds that a string or vibrating body could not vibrate at a length greater than its complete length…
- Henry Cowell, ibid. 

Perhaps this is exactly the “absurd extreme” that Aldwell & Schachter had in mind? No-one could say for sure but it’s funny to think about. They round off the thought by stating:

Nowadays most musicians would maintain that the foundations for music theory theory should lie in the works of great composers, not in the laboratories of acousticians.
- Aldwell & Schachter, ibid.

I wonder if they considered the chicken-or-egg irony that surrounds this statement. Moreover, I wonder if they are right. I will make a mental note to find some musicians, and ask them.