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I'm working through "Guide to the Practical Study of Harmony" by Tchaikovsky and I had a question about this section on triads (he's working with a C Major scale):

The whole mass of major and minor triads may be grouped into three sets of two triads each: One, the tonic group viz: the triads on the 1st and the 6th degrees. Two, the dominant group viz: the triads on the 5th and the 3rd degrees. Three, the subdominant group viz: the triads on the 4th and 2nd degrees.

Now, I get why the 1st and 6th triad are in the tonic group. I also get why the 5th triad is in the dominant group and why the 4th triad is in the subdominant group. But, I'm having a hard time understanding why the 3rd triad is dominant and the 2nd triad is subdominant.

I'm not sure how I'd categorize them, and I suppose they have to placed somewhere, but I'm not sure why they're being placed here.

I Googled around some and found some conflicting information on Open Music Theory which has muddied the water further:

If you are already comfortable with Roman numerals, you can generally think of I, III, and VI as tonic, II and IV as subdominant, and V and VII as dominant. (Though, as you will see below, there is more to it than that.)

I suppose I'm just looking for some clarity here. It's important that I understand why Tchaikovsky is placing the 3rd and 2nd triad where he is as I keep plowing through the book. Thanks for the help!

  • The only thing I can think of is that, if you're creating a group of minor triads, that, in that case, the 3rd triad would take the same place that the 5th triad does in a grouping of major triads. I'm not sure that this is right, though, and I don't know how to reconcile that with the Open Music Theory entry. – krebshack Jun 3 '18 at 22:51
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The chord built on the sixth degree of the major scale is closely related to the I chord, and similarly the chord built on the second degree is closely related to the IV chord, and the chord built on the third degree is closely related to the V chord. The I, IV, and V chords have tonic, subdominant, and dominant functions, respectively, and the vi, ii, and iii chords (sometimes called parallel chords) are sometimes called tonic-parallel, subdominant-parallel, and dominant-parallel, respectively.

In the key of C Major, the I chord contains C-E-G, and the vi chord contains C-E-A; that is, the vi chord can be formed by raising the 5th a whole step. Since the vi chord shares the root and the third of the I chord, it can function as a tonic chord. The fifth of the I chord is relatively unimportant, so you might think of the vi chord as a I6 chord. There are no other triads in the key that share the root and third of the tonic chord.

The same considerations can be applied to the ii and iii chords. In the key of C Major, the ii chord contains D-F-A, and the IV chord contains F-A-C; these share the root and third of the IV chord, so the ii chord can function as a subdominant chord. The iii chord contains E-G-B, and the dominant V chord contains G-B-D; these share the root and third of the V chord, so the iii chord can function as a dominant chord.

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    I thought the parallel chord of C maj was Cm, parallel of F maj was Fm, and parallel of G maj. was Gm. Relative might be a more appropriate term, as the relative of C is Am., relative of F is Dm., and relative of G is Em. – Tim Jun 4 '18 at 5:57
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    @Tim -- in this usage parallel chord and relative chord have the same meaning; the terms come from Riemannian theory. There is a link in my answer to a Wikipedia page about this. But I think the bottom line is that the I chord and the iii chord are the only two chords that share the root and 3rd of the tonic. – ex nihilo Jun 4 '18 at 6:17
  • I=CEG, iii=EGB. Sharing three and five of the tonic? The only one sharing the root of the tonic is IV. I find it strange that the term parallel can be used here, regardless of who came up with a theory. It just sounds confusing - to me. When terms already exist, and have specific, different meanings, where's the mileage in making them both mean the same? – Tim Jun 4 '18 at 6:37
  • @Tim -- sorry, it's late and my brain is shutting down. I meant the I chord and the vi chord both share the root and third of the tonic chord, as I wrote in the answer above. – ex nihilo Jun 4 '18 at 6:38
  • @Tim -- I don't see the terminology as confusing; it connects the I chord to the vi chord, the IV chord to the ii chord, and the V chord to the iii chord with a name that underscores their relatedness. There are loads of overlapping terms in music anyway; I think that these date from the late 1800's. The Wikipedia page suggests that the "relative" and "parallel" conflation has to do with translation from the original German. – ex nihilo Jun 4 '18 at 6:47
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Why is the third triad dominant?

It is not. The third triad is the mediant. The triad on the fifth degree is the dominant.

The selected answer is misleading about the substitute nature of the mediant triad. Apparently the answer take a Riemannian view without pointing out the ambiguous nature of the chord. The mediant chord shares two tones with the dominant chord, but it also shares two tones with the tonic. There is no clear way to simply say the mediant chord substitutes one or the other chords.

This definition from the Harvard Dictionary of Music summarizes the point well...

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It should be understood that such substitutions lead toward ambiguous tonality. That is not a problem per se, but cadences won't have their proper function if chords are substituted. V iii, iii I, etc. won't work as perfect cadences.

  • I did not take a Riemannian point of view, and we did discuss this in the comment thread under my answer. I specifically took the point of view that the iii chord can (not must) function as a dominant because it contains the root and third of the V chord. I only mentioned dominant-parallel as an existing term (which happens to come from Riemannian Theory) that describes this relationship, providing a link for anyone who would like to read more about that. – ex nihilo Feb 21 at 18:08
  • My point is to make clear the ambiguity. – Michael Curtis Feb 21 at 18:15
  • I agree that there is some ambiguity, as there is likely to be with substitutions, but the iii chord contains the root and third of the V chord, yet contains only the third and fifth of the I chord. This would seem to make it less likely that the iii would find itself in the role of the tonic. – ex nihilo Feb 21 at 18:25
  • ...and if we return to the Harvard Dictionary article we see that kind of isolated determination is a problem. The substitute character of either tonic or dominant isn't about those chord tone comparisons, but about the mediant chord's use in the surrounding harmonic context. Basically, it's problematic to simply say iii subs for V – Michael Curtis Feb 21 at 19:33
  • Probably the best example I can think of now is a deceptive progression like V4/2 iii, if the iii was indeed simply a sub for V that kind of deceptive progression wouldn't be sensible. In that harmonic context iii clearly isn't acting as a dominant. – Michael Curtis Feb 21 at 19:39

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