Understanding the Fundamentals of Music (2006), by Robert Greenberg, B.A. in music (magna cum laude) from Princeton, Ph.D. in music composition from the University of California, Berkeley. p. 27 of the Lecture Transcript.

Apologies! I scanned the whole page just for context and to ward off rude comments asking for more context. I'm not asking anyone to read all of it.

  1. What's the tonic in the first half of "Dance of the Girls" in The Rite of Spring (1912)? Greenberg doesn't say what it is. I listened to it the first time 15 years ago, and I always thought this movement was bitonal and had no tonic.

  2. How is this tonic asserted, "sustained and/or repeated for so long that it becomes, by sheer dint of tis assertion, the gravitational center"?

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    I think it would be better to type in the relevant quotes rather than scan. Also you don’t have to put all of Dr. Greenberg’s credentials in your questions. Finally, it won’t always be possible for anyone other than Dr. Greenberg himself to explain the concepts he presents in his book. – Todd Wilcox Jul 2 '19 at 2:09
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    I'm not editing any more of this. – Your Uncle Bob Jul 2 '19 at 2:11
  • @YourUncleBob Thanks for antecedent help. You don't need to this time! The questions are standalone. – Lai M.Mus. Jul 2 '19 at 2:12
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    I mean type in his words yourself and don’t scan. – Todd Wilcox Jul 2 '19 at 2:17
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    From all the quotes you've put up from this author, I pretty much assume everything he's written is somewhat dodgy. – Todd Wilcox Jul 2 '19 at 2:53

In my opinion, the author is unclear here. (I'm beginning to get suspicious about Dr. Greenberg's book...)

Here is the excerpt in question:

enter image description here

This portion is, famously, an F♭-major triad with an E♭ dominant seventh above it. With no overlap between the two harmonies, this means that seven individual pitches are sounding simultaneously. (The non-sounding pitches are C, D, F, G♭, and A.)

So Greenberg is unclear because he says that "Tonality via assertion is when a single pitch is sustained and/or repeated for so long" (emphasis added), and yet this is obviously seven pitches. I would prefer to think of this polychord as a reference sonority than as a single tonic. In any event, coming to this sonority later definitely gives the listener a sense of returning home, much like coming back to tonic does in a tonal piece (albeit it in a very different way).

It's possible he's not claiming that there's a tonic here, just showing an example of something that's repeated many times. But in a section on tonality, that would be pretty poor pedagogy.

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