Do triads sound strongest in second inversion?
On Mark Levine's Jazz Theory book, on Chapter Five, Slash Chords, it says:
Although triads can sound good in any inversion, all things being equal triads sounds strongest in second inversion.
Then there are some examples of slash chords, with C as the bass and all the major triads that can be played on top of it (1). All of them are in second inversion and then there is the aforementioned quote.
(1):
But why do triads sound strongest in second inversion?
Edit: With slash chords, the author isn't referring just to inversions. The example above shows any major triad that can be played over a C note. For instance, the E/C refers to the Lydian Augmented chord, which can also be written as C maj7 #5 .
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When Levine refers to a chord as being "stronger" is can also be read as "more stable", as in harmonically stable.
Take the C Major Triad as an example (C, E, G). If you analyze what the intervals are for each inversion (first and second) you can see the following:
First inversion; E is root under G and C
E,G = m3
E,C = m6
G,C = P4
Second inversion; G is root under C and E
G,C = P4
G,E = M6
C,E = M3
According to Paul Hindemith the intervals can be ranked from "strong" to "weak" like so:
1 2 3 4 5 6 7 8 9 10 11 12
P8, P5, P4, M3, M6, m3, m6, M2, m7, m2, M7, dim5
The P8 is strong, whereas the dim5 is weak.
Back to our example; first inversion contains intervals 6,7,3 (m3,m6,P4) while second inversion contains intervals 3,4,5 (P4,M3,M6). According to the interval ranking, second inversion is stronger because it contains more intervals that are towards the "strong" side of the ranked intervals.
Note that according to the interval ranking, a P5 is considered stronger than a P4. This means C,G will be more stable than G,C. Even though they are the same notes, the positioning of the notes determines what is called the order of Combination Tones (also known as Resultant Tones). The first resultant tone produced from a P5 is actually different from a P4.
I can't recall exactly what the notes are anymore; Hindemith maps it all out in his book "The Craft of Musical Composition: Book 1" (ISBN 0901938300).
It should be mentioned that throughout the whole book there are three occurrences of the statement that triads sound stronger/strongest in second inversion:
Ex. 1
Ex. 2
Ex. 3
If you look at the context in each of these cases you'll see that Levine always talks about slash chords. In Ex. 1 he talks about a Gsus4 (actually G9sus4) voiced as a F/G chord, where the F triad on top of the G bass note is in second inversion. Ex. 2 is a G/Eb chord, where Levine compares the root position and the second inversion of the G triad. Finally, Ex. 3 is the example stated in the OP with all possible major triads over a C bass note (all of them in second inversion).
So even though it sounds like a general statement, Levine actually always refers to the second inversion as the strongest only in the context of slash chords. And that's a different thing than talking about pure triads, where he might not even agree with that statement. The statement also makes more sense in the context of slash chords because we are already dealing with a different root, so the root position of the top triad does not anymore have its original special significance (as having the chord's root as the lowest note).
Furthermore, looking at the harmonic series for a C root (not bothering about octaves)
1 2 3 4 5 6 ...
C C G C E G ...
we see that the second inversion G C E consists of lower harmonics (3 4 5) than the root position (4 5 6). I'm referring to close voicings here because that's what Levine means when he talks about the second inversion in all three examples. So one could argue that the second inversion in close voicing has some inherent stability IF the root of the triad loses its role due to the existence of another lower root, as is the case with slash chords.
In general, when we say 2nd inversion we mean that the 5th of the chord is in the bass. However, the author is treating these slash chords as independent major chords superimposed over a C bass note. These particular chords are the ones in 2nd inversion regardless of the C note in the bass.
Moreover, in "close chord position" or "keyboard style" such as in the example, the only possibility of a chord in 2nd inversion would be: the 3rd note of the chord over the root, over the 5th.
Since the most characteristic notes of the triad (i.e. the root and the 3rd) are now in the top voices the result is a chord voicing with a "strong" character.
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