Techniques of Polytempic Polymicrotonal Composition: Microtonal Intervals, part XIIa

 Microtonal Intervals and Harmony




Figures 1-3. J. Murray Barbour's Superparticular Ratios from octave to schisma (added by me.)

fig. 2

fig. 3

I am deliberately using an old textbook (Tuning and Temperament: A Historical Survey, by J. Murray Barbour) list of superparticular ratios converted into cents values for a semi-comprehensive list of intervals for the effect of tabula rasa vis-à-vis the wealth of tuning and microtonal information available today. 

Between Ellis-Helmholtz's On the Sensations of Tone, 1875, and today, a good deal of literature exists concerning tuning and microtones by hundreds of writers on the subject. This rather simple list of Barbour's helps me gain perspective on what I am attempting to convey about pitch relations and intervals without the extra baggage of thoughts, opinions, and tuning inventions since 1953, when this book was published. 

What I have found myself doing in my own music is that I have made a mental separation between the categories of standard common practice intervals for musical functioning and chord spelling for triads, and other chords, and for the linear, narrow line of tiny intervallically compressed microtonal voice-leading. Although I am not tonal, there are "tonal" elements I call centricity, and elements of atonal functioning regarding the microtonality of the particular system at hand. My usage gravitates towards a holistic omnivorous approach, neither favoring nor disfavoring tonality or atonality. Depending on what I am hearing, I will assert the prevalence of a tone based on its interactions with other lines. Repetition of pitches will occur, and this, though not tonal nor atonal, becomes centric. The tones never last for long, so the repeated centric tone never becomes king. Perhaps centricity, as I see it, is between tonality and atonality, where the latter advocates a strict dictum of non-repetition as primary, to avoid tonality. 

Tonality is the ordered natural overtones at the bottom of the spectrum, with the octave, restated, and then the P5, followed by the octave again and a major third. This has been established by Pythagoras and rediscovered by Mersenne and Descartes simultaneously in the Renaissance. Zarlino attributed all Occidental harmony to the senarius, which is the first 6 overtones. This is nature's law. I love nature. But I want to do my own thing. This makes me a mannerist. I am a modern mannerist in the 21st century, exaggerating the non-natural, while most of my colleagues are naturalists and are droning on the fundamental, while retuning the senarius away from equal temperament back to just intonation, which is pure: pure fifths and pure major thirds. Beatless. So, while Cowell based his tempo relationships on the overtone series, and my colleagues today are re-embracing the bottom senarius and septanarius, droning on the fundamental for hours, I would rather occupy the upper portions of the overtone series without referring to the bottom portion all the time. I have even thought of a Schönbergian approach to microtonal rows. So has my friend Joel Grant Taylor, a very interesting composer. 

Am I flouting nature by using harsh intervals from inharmonic or tempered tunings? Is ^13 root 2, at 92.3 cents a crime against the natural order? Figure 2 shows the 19/18 overtone at 93 cents....This means that the 13-tone temperament is well within the range of nature herself. I guess I'm not mannerist. 

I rather like beats. I also like inharmonic timbres produced by idiophones and drums. I like wolf fifths, and I love the ultimate dissonance of the quartertone. So did Ives. Also similar to Ives, I am, too, omnivorous and, to quote Ives: "why tonality should be thrown out, I can't see; why tonality should be kept, I can't see." 

This subject will occupy several blogs.

Comments

  1. Joel TaylorJuly 31, 2025 at 4:33 PM

    Thanks for the mention, Dr. Thoegersen. On this post my addition is that centricity can arise in a micro chromatic music not only through repetitions, be also by using other ways to emphasize a particular tone. Placement at the top and the bottom of the gamut used will help a tone stand out, as will instrumental and dynamic accent. Microchromatic voice leading may be constructed that favors certain "cadential" or "tendency" tones. I know that you know this from listening to your music, but for your readers, add this note to clarify how centricity might arise in that in-between tonality and atonality space you refer to here.

    ReplyDelete
    Replies
    1. peter alexander thoegersenJuly 31, 2025 at 4:40 PM

      You just did. Readers read comments, too. Thanks for the add!

      Delete

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