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As far as I understand, the main reason why an authentic cadence (i.e. V–I) works well and is so common, is that the dominant chord contains the leading tone, which resolves very strongly to the tonic. It also has a common tone shared with the tonic chord. vii°–I also works well as a cadence owing to the resolution of the leading tone. I presume the main reason why it's less common than an authentic cadence is that the diminished chord is dissonant.

But what about other possible cadences with the leading tone resolving to the tonic? The most obvious one is iii–I, which has a leading tone resolution and two common tones. You might think that iii7–I should be fairly common since iii7 contains V. (Could you consider iii7 to be Vadd13, making iii7–I a kind of colourful authentic cadence?) Another possibility would be Imaj7–I. However, I don't know any examples of these chord sequences being used as a cadence. Is there a reason for this?

I've tried them out and, while they don't sound all that cadential on their own, if you stick a IV at the beginning, they all seem to work, especially IV–Imaj7–I (and if you extend it to vi7–V7–IV–Imaj7–I, it sounds even better). Even if the answer is just that they don't sound as good as an authentic cadence, is there a logical reason why they don't sound as good, or is it just because we're more used to hearing more common cadences?

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    I think IV-Imaj7-I is actually a plagal cadence (IV-I), only that you put the maj7 in there for a while. – Gauthier Jun 25 '15 at 8:03
  • Thanks for the correction. That explains why it sounds more cadential when I add the IV. So I guess that reduces my question to iii(7)–I. – DangerPete Jun 25 '15 at 16:59
  • Personally, I'm completely stormed out by iii-I, iii7-I, and I7-I. Isn't iii-I and iii7-I actually an authentic V13(6th inv.)-I? Plus, I7-5/3 is not a cadence at all! Your IV-I7-5/3 is in fact just a plain plagal cadence. – Maika Sakuranomiya Jul 11 at 10:41
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One important factor that influences how good these progressions sound is the number of common tones between the two successive chords. If we consider vii°-I, there are no common tones between the chords ({B,D,F} vs. {C,E,G}) so all the voices must move, making it a bit rough. On the other hand, if we look at V-I, we see that there is one common tone ({C,E,G} vs. {G,B,D}). This means that one voice (or maybe two, depending on voice doubling) can stay in place while the others move around it. Finally, looking at iii-I (or I7-I, which has the same problem), there are two common tones ({E,G,B} vs {C,E,G}) -- or even three, in the case of I7 -- which diminishes the sense of change, and makes the progression sound too weak, or static. There's not enough of a change from one chord to the next to make an effective cadence.

Put differently, the reason the leading tone makes a good cadence is because it's tendency to resolve to tonic enhances the sense of harmonic motion already inherent in V-I, but it's not the only factor creating that sense of motion. Indeed, that harmonic motion is neutered in iii-I, and essentially removed in I7-I.

As a more general principle, chord progressions from one triad to another will fall into one of these three categories, depending on the root movement.

  • If the root moves up or down by a second/seventh, then there are no common tones, and the resulting progression has a definite sound of motion, sounding strong, and possibly even a bit rough in terms of voice leading. In these progressions, you often have to take extra special care to avoid parallel perfect intervals. A common case of this type of progression is IV-V.

  • If the root moves up or down by a third/sixth, then there are two common tones, and the resulting progression has a rather smooth, static sound, possibly even sounding weak, since there is not much motion involved in the progression and the new chord is barely different from the old one. Progressions where the root falls a third are more common, and sound somewhat stronger, since at least the root is a new note, whereas when the root rises a third, it tends to sound more like an inversion of the previous chord. A common case of a progression by thirds is I-vi-IV.

  • If the root moves up or down by a fourth/fifth, then there is one common tone, which seems to strike a nice sweet spot between the others -- it's not got the potentially awkward voice leading of second-based progressions, but it's got a stronger sense of motion than the placid thirds-based progression. Any progression along the circle of fifths falls into this category, which forms the bread-and-butter of the common practice period. The obvious example here is a V-I cadence, or even a ii-V-I cadence.

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Wikipedia has a nice explanation for what a cadence is:

A harmonic cadence is a progression of (at least) two chords that concludes a phrase, section, or piece of music.

There have to be at least two chords to create a cadence. But in your example Imaj7-I, there is only one chord. Just because you remove the major 7th, the chord doesn't change; it's still the same. It would still be the same if you inverted it, if you added a 9th,11th or 13th etc.

The iii works as a dominant. It sounds smooth when the resolution is iii 6 - I . (iii 6 is the first inversion). Because, if we assume we're in the C major scale, the iii would be E-G-B, and iii 6 would have G as a bass. So, it would sound like the V of the scale.

vii°–I also works well as a cadence owing to the resolution of the leading tone. I presume the main reason why it's less common than an authentic cadence is that the diminished chord is dissonant.

V-I isn't the only cadence that is popular. This is only in pop music. In classical, Jazz etc there are many examples of vii o - I, iii 6- I and other. The vii isn't that dissonant. It is a quite common cadence to be honest.

So, to answer your question:

Why aren't unusual leading tone cadences more common?

They are, just not in the popular music.

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    That vii0 happens to be a V7 without a root. So it will naturally progress to a I (or i). – Tim Jun 25 '15 at 8:01
  • Thanks for your answer. Could you name some of the examples of iii6–I that you mention, please? I'm not so surprised that it occurs in jazz, and from your answer, it sounds like none of the examples you had in mind are from pop/rock, but I'd be interested to look into some examples from classical music if you have any. – DangerPete Jun 25 '15 at 17:14
  • Sorry, but I don't have any examples right now. I don't study classical music that much, but you can ask a teacher of classical if you know any to provide you with any. The iii6-I might be a bit rarer, but vii o - I (or i) is really really common – Shevliaskovic Jun 25 '15 at 20:28
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Taking C as the key, there's also Bo (inc. Do,Fo and Abo) that leads nicely to the tonic, C. And the triton of G (the dominant), which is C#7.They're probably not so common as they sound a little strange to people who are immersed in only Pop music. V and V7 are obviously far more commonly used, so it's down to familiarity. Which, in jazz players, will often breed contempt...

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The authentic cadence V7 - I actually has several things going for it. One crucial element you're missing is the movement of the bass. Basses going down a fifth or up a fourth are very powerful and is one of the main reason this works. The movement from iii to I however is quite weak.

Another element is the tritone between the 3rd and the 7th of the chord. For G7 these are B and F. Those two notes work quite nicely on their own, resolving to C and E. The bass movement from the leading tone (B to C) is also quite nice (and the basis for the Bdim - C resolution).

So, if you changed the bass of Em to make Em / G, you'd have a resolving feeling. You'd probably end up calling it a G6 though. An even better option is the G13 chord, which also has the 7th in it, creating a strong pull to the tonic.

As others have mentioned, the Bdim chord is the upper structure of the G7 with the leading tone as the bass. The Bdim7 chord is and even stronger cadence and is the upper structure of the G7b9 chord - which a very powerful chord resolution, especially in a minor key (it also works in major key, with some chromatic color added, since the b9 of the chord is the b6 of the scale).

Some variations on the authentic cadence are common in jazz, such as the tritone substitution, where you'd have Db7 - C (or Cm), in the key of C. It has the same tritone as G7 (i.e. the notes F and B) and has a jazzy bass movement down a half step.

You can play around with those elements and see what you can come up with. Some cadences don't even contain the leading tone at all, like the "backdoor progression", Fm - Bb7 - C, in the key of C (although the b9, i.e. B natural, is often added to the Bb7 as an extension). Some weaker bass movements can probably be made to work with clever chord progressions and voice-leading, but they will be harder to pull off and thus less common.

Tl; dr: It's all about that bass!

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The root movement of dominant to tonic in an authentic cadence is very powerful -- even more, it could be argued, than the leading tone movement. No other cadential formula has this.

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Cadences articulate structure; the stronger the cadence, the more important that structural point. You'll never find a composer employing an inverted V or a vii moving to chord to a root position I at a point in a piece that requires the great structural clarity, such as the end of a period, a section, a modulation etc. Root movement = strength.

iii-I is not as convincing as V-I because it doesn't not contain the supertonic. So what? V contains the closest scale degrees to the tonic triad. Think of a tonic as the centre of gravity. Chord V has the strongest pull. A seventh on top of that adds yet a stronger pull because a) the seventh is a semitone from the third (of the tonic) and b) the third and seventh (of the dominant) create a strong dissonance - aug 4 - which demands resolution to the tonic and third (of the tonic). Resolve it any other way, it won't be as "convincing" especially if you do it in context i.e. in an actually key and not just as an isolated interval.

Sometimes composers use V with a substituted 6th...looks like a iii in first inversion. But you will find however that to ensure the V still has its 'dominance' the 6th always falls to the tonic (3-1) in the melody. Gaurantee you won't ever here that V subs 6 as iii.

My sources include Oxford Music Online; Harmony and Voice Leading (4th ed, Aldwell et al), Theories and Practices of Harmony (Cho), Classical Form (Caplin) among others.

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