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I've been studying the standard Have You Met Miss Jones and I came across a very interesting chord progression in the B section of the piece. The A section is pretty typical and the key it's in is F major, but once you hit the B section, there's 8 bars of pretty interesting chords.

B section chord progression:

 Cm7 - F7 - BbM7 - Abm7 - Db7 - GbM7 - Em7 - A7 - DM7 - Abm7 - Db7 - GbM7 - Gm7 -C7 - FM7

Now obviously you can chunk out these chords into ii7 - V7 - I7 in several keys including:

  • Bb major (Cm7 - F7 - BbM7)
  • Gb major (Abm7 - Db7 - GbM7)
  • D major (Em7 - A7 - DM7)
  • F major (Gm7 - C7 - FM7)

But there really doesn't seem to be too much to connect these nor does it seem to be very sequence like and it does not seem to be a full modulation away from F major due to you not staying in one tonal center for too long.

So my questions are:

  • What is harmonically going on in the B section of this song?
  • How would we reflect this in Roman Numeral analysis?
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That's Coltrane changes (before Coltrane actually used them in Giant Steps etc.), where the roots of the tonal centers move in (enharmonic) major thirds (either up or down):

[Bb] -> (down M3) [Gb] -> (down M3) [D] -> (up M3) [Gb]

Returning to the key of F is not part of the cycle anymore, it's just going back to the original key.

This is what the wikipedia page says about the relation between "Have You Met Miss Jones" and Coltrane changes (actually, I would claim that the term modulation below is wrong, it's rather tonicization):

The bridge of the Rodgers and Hart song and jazz standard "Have You Met Miss Jones?" (1937) predated Tadd Dameron's "Lady Bird", after which Coltrane named his "Lazy Bird", by incorporating modulation by major third(s).[8] (shown by the * below) "Giant Steps" and "Countdown" may both have taken the inspiration for their augmented tonal cycles from "Have You Met Miss Jones".

Concerning Roman Numeral Analysis you would go about it as is common with tonicizations. However, in my opinion this analysis doesn't give much additional insight.

The following is some additional information on Coltrane changes and on how Coltrane used them for reharmonization. Even though it seems pretty clear that he got the idea for tonal centers moving in major thirds from Rodgers and Hart's song, he was the first to use it for reharmonizing existing chord progressions. A good example is Coltrane's tune Countdown, which is based on Miles Davis' tune Tune Up. The latter mainly consists of ii-V-I progressions in different keys. Coltrane reharmonized these ii-V-I progressions by cycles of major thirds. E.g., if there is a ii-V-I in C major, he would move down in (enharmonic) major thirds starting from Ab major via E major to C major, where each major seventh chord is preceded by its dominant chord. So,

|| Dm 7 | G7 | Cmaj7 | Cmaj7 ||

becomes

|| Dm7 Eb7 | Abmaj7 B7 | Emaj7 G7 | Cmaj7 ||

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    Seems like a sort of backwards tritone, Dm-Eb7, given that Dm is often preceded by its dominant A7, although that's obviously not present. Just a random jotting. – Tim Nov 10 '15 at 8:24
  • @Tim: In this case the Eb7 leads to the Abmaj7. But you're right that an Eb7 before a Dm7 would be a tritone sub for A7. Here it is just an ordinary dominant. – Matt L. Nov 10 '15 at 9:00
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    @Some_Guy: I agree that that way of temporarily shifting tonal centers may seem arbitrary. But does it sound arbitrary to your ears? Not to mine. It's always hard to rationalize about why some things sound better than others, but in this case I think that the symmetry of the cycle of major thirds is appealing to the ears. – Matt L. Nov 11 '15 at 8:24
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    @Some_Guy: Also note that the major 7th chords separated by a major third share two out of their four chord tones. So they are related but there still is sufficient new quality to the following chord to make it sound fresh and surprising in some sense. This and the fact that you cycle instead of arbitrarily moving around make the movement of major thirds a strong device. – Matt L. Nov 11 '15 at 8:24
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    Two tones in common is a very good point, allows the melody to have some continuity, and explains how you get that sort of "wandering" sound rather than feeling like there's been an "abrupt" change to another tonal centre if you know what I mean. Thanks for the clarification :) – Some_Guy Nov 13 '15 at 1:40
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What is harmonically going on in the B section of this song?
Why did the song writer choose rapidly descending major thirds, which will put most listeners off balance, followed by an ascending major 3rd?

The explanation is in the lyrics.

All at once I lost my breath <---Bb then DOWN to the new ii V (also a descending melody)

And all at once was scared to death <---Gb then DOWN to the new ii V (also a descending melody)

And at all once i opened the earth and the sky! <-- D UP to Abm Db7 Gbmaj 7 (ascending melody)

Its like saying no, no , YES! with the words and the harmony

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To other answers that highlight the cycles of thirds here, I'd just note that it's a bit anachronistic to think of these as "Coltrane changes," as Coltrane didn't use them yet. And (as has been well-known for quite a few years) Coltrane himself likely was inspired by Slonimsky's Thesaurus (in one form or another -- the book was very influential on a lot of musicians of the time). The song in this question also feels quite different to me from some of Coltrane's later uses.

But Slonimsky hadn't published his Thesaurus (1947) when "Miss Jones" was written (1937). So where did Richard Rodgers get his major thirds cycles?

And the answer is undoubtedly the same place that Slonimsky did: romantic period (and post-romantic) progressions, which both Rodgers and Slonimsky would have known quite well. Major third key cycles appeared in works going back nearly a century, with prominent examples in composers like Wagner (e.g., the Siegfried Idyll) and Mahler (particularly the Seventh and Ninth symphonies). By the early 20th century, major third cycles of keys were a somewhat common element of post-romantic harmony. Rodgers may not have been a huge fan of opera, but a lot of his training was rather traditional, and he undoubtedly absorbed some of the more wide-ranging harmonic movements that were then-current during his education. (In later life, he reminisced fondly on his theory and harmony classes.) And chromatic third progressions had been seeping into jazz and other popular piano styles for a while (e.g., see some of Joplin's more harmonically adventurous rags).

What's a bit more novel (at least in popular styles) about Rodgers's song is the rapid sequencing through a complete major thirds cycle. But Rodgers had been experimenting with wide-ranging modulations in the 1930s, so this doesn't seem too outlandish for him.

As to how to label it with Roman numerals -- well, Roman numerals are built around the supposition of functional tonal harmony, and they don't make a lot of sense in this sort of rapid key cycling. The best one can do is note the local ii-V-I progressions in each key. If it were me, I'd then just put a big bracket under the whole section and write "major thirds cycle" or something. The Neo-Riemannians and set theorists might have some more complicated nomenclature involving hexatonic systems or something, but I don't think Rodgers was thinking along those lines here. He was just cycling through a sequence by major thirds. (And Bob Wrotenstein's answer that this is likely depicting some element of the lyrics is an insightful analytical observation.)

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On a superficial level it illustrates that a ii7 - V7 - I sequence can take you just about ANY place.

Up or down a major 3rd takes you somewhere that is neither adjacent or closely connected in any of the standard 'Cycle of 5ths' or 'Modal interchange' ways. New territory. Which, in my book, is sufficient reason for exploration! And, of course, repetition in sequence validates even the most unusual changes.

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