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So, I've been writing a book on music theory and I'm getting ever closer to the place where I will go in depth on the common chord progressions of Classical Music including:

  • Circle of Fifths(here, I will mainly be talking about the full octave Circle of Fifths, although I will mention that subsets of this progression like ii-V-I and vi-ii-V-I are found all over the place)
  • La Folia
  • Descending Thirds aka the chord progression of Pachelbel's Canon in D
  • Quiescenza
  • Lament Bass
  • Omnibus Progression

including variants that are seen upon some of these progressions. And I already know that I will have to include Mozart's K 545 Sonata when I talk about the Circle of Fifths Progression because of this section from the exposition of the first movement:

Mozart K 545, mvmt 1, mm. 18–24

and the analogous section of the recapitulation. However, I see what looks like yet another instance of the circle of fifths in the development section of that same movement, here:

Mozart K 545, mvmt 1, mm. 36–41

Starting in bar 2 of this second example, look at the final quarter note of each 16th note scalar run that makes up this melodic sequence and you can see a bass line of C-F-B-E-A-D-G#-Cwhich is an instance of the circle of fifths. However, would this count as the Circle of Fifths Progression or just a Circle of Fifths sequence? I mean, in the exposition's Circle of Fifths sequence, there's a clear harmonic outline because of the arpeggios. I don't see such a clear harmonic outline in the development's Circle of Fifths sequence. In fact, I'm not sure that there is any harmony to speak of in this part of the development.

So, would this part of the development section count as an instance of the Circle of Fifths Progression or is it just a melodic sequence going around the circle of fifths without any harmony to speak of?

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  • 1
    The implied harmony (starting in bar 2) is Am Dm G C F Bdim E Am Bb C7 F - but the letter names you picked out are the third degrees of those chords not the roots. To analyse the harmony you'd normally consider the roots, not the thirds. Feb 8, 2022 at 13:20
  • wiki says In practice, compositions rarely make use of the entire circle of fifths. More commonly, composers make use of "the compositional idea of the 'cycle' of 5ths, when music moves consistently through a smaller or larger segment of the tonal structural resources which the circle abstractly represents."[11] The usual practice is to derive the circle of fifths progression from the seven tones of the diatonic scale, rather from the full range of twelve tones present in the chromatic scale… Feb 8, 2022 at 13:42
  • …In this diatonic version of the circle, one of the fifths is not a true fifth: it is a tritone (or a diminished fifth), e.g. between F and B in the "natural" diatonic scale (i.e. without sharps or flats). Feb 8, 2022 at 13:42
  • @BrianTHOMAS Yes, I know the full circle of fifths is rare. In fact, I can't think of a single piece that uses all 12 notes in the chromatic circle of fifths. I've seen modulation chains around the circle of fifths of various lengths, and I've seen the diatonic progression of I-IV-vii°-iii-vi-ii-V-I or in minor i-iv-VII-III-VI-ii°-V-I(which is what I mean by the full octave Circle of Fifths Progression), subsets of this progression like vi-ii-V-I and even variants that are all seventh chords in works by Vivaldi and other Baroque composers.
    – Caters
    Feb 8, 2022 at 21:50
  • @Caters - Report is that Widor's famed Toccata (for organ) goes through all 12 major keys in the circle of 5ths in order (and starts and ends in F major).
    – Dekkadeci
    Feb 9, 2022 at 3:17

3 Answers 3

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TL;DR

The passage is a circle of fifths progression.

Analysis

It's tempting to analyze this passage in terms of scales, being so obviously scalar. And it's also tempting to analyze this passage in terms of the endpoints of those scales, coming on the metrically strongest points of each measure.

However, the passage is best analyzed by looking at the first three notes in each half of the measure (i.e., the first three notes of beats 1 and 3, respectively). Doing so gives the following reduction:

X: 1
T: Mozart K 545
T: Reduction 1
M: none
L: 1/2
K: none
%%score V1 | V2
[V:V1] [ae'] f | [gd'] e | [fc'] d | [eb] c |
[V:V2 clef=bass] C, [K:none clef=treble] [DA] | B, [CG] | A, [K:none clef=bass] [B,F] | ^G, [A,C] |

Re-voicing the chords in root, close position gives:

X: 1
T: Mozart K 545
T: Reduction 2
M: none
L: 1/2
K: none
"_Am"[Ace] "_Dm"[DFA] "_G"[GBd] "_C" [CEG] "_F" [FAc] "_Bdim"[B,DF] "_E" [E^GB] "_Am" [A,C] |

Thus, a circle of fifths progression diatonic to A minor: a d g c f b e a. This can be easily confirmed by playing the chord progression, which clearly retains the character of the passage. Playing chords rooted on the endpoints of each scale, for example, clearly sounds wrong.

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  • That sequence is almost cliched now. Wonder when it first appeared.
    – Tim
    Feb 8, 2022 at 10:06
  • Is it still "circle of fifths" despite that movement from F natural to B natural (which isn't a perfect fifth). Feb 8, 2022 at 13:10
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    @BrianTHOMAS I wondered that, too, but yes, it's still considered a circle of fifths progression. A quick Google search will confirm.
    – Aaron
    Feb 8, 2022 at 13:12
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    A diatonic circle of fifths progression would move through the diminished chord ...IV viio iii... nothing at all unusual about that. Feb 8, 2022 at 16:21
  • @Tim Earliest I’ve seen it is in Baroque composers, so like Bach and Vivaldi and many others. The seventh chord variant of the progression is also found in the Baroque(like not just a V7, but the entire progression in seventh chords).
    – Caters
    Feb 8, 2022 at 18:24
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I'm not sure why you didn't include the first bar of the passage. When you include bar 35, carry it through to the first bar of the recapitulation, and make a harmonic reduction you get...

| Dm | E | Am Dm | G C | F Bo | E Am | Bb C | F |

You should make a distinction between a circle of fifth progression, which is a diatonic progression, and the more general root progression by descending fifths. An important distinction being the former is a way to establish/confirm a key, and the latter can be used to modulate. Also, secondary function chords can be inserted into a descending fifths sequence without loosing the basic harmonic design.

The passage is from the development section, which means frequent modulations are expected, and additionally it is the end of the development, which can be called the retransition, and that has the expectation to move to the recapitulation. There shouldn't be any expectation for the passage to fit into one key... and it doesn't.

On a basic level the passage is almost all descending fifths and a large portion of it is diatonic to one key. You can certainly say the portion | Am Dm | G C | F Bo | is a diatonic circle of fifths progression, but the changing and overlapping tonal centers are important and account for the parts that aren't progression by descending fifth.

First it confirms a tonality of Dm, but then Am gets tonicized in E | Am Dm| , that gets overlapped tonally where | Am Dm | G C | F Bo | is all diatonic to C major, the opening tonic, then Am gets tonicized again in | E Am |, then an interesting overlap happens when it continues to | Bb..., where the Bb can be considered a N6 chord in Am but also the subdominant of the next key, F major, arrived at through | Bb C | F |.

 | Dm | E | Am Dm | G C | F  Bo  | E Am | Bb C | F |
                                                    
Dm:i  |           |              |          |      |
------|           |              |          |      |
     Am:V   i  iv |              |          |      |
     -------------|              |          |      |
          C:vi ii   V I   IV viio|          |      |
          -----------------------|          |      |
                                Am:V i    N6|      |
                                ------------|      |
                                   F:iii  IV V   I |
                                   -----------------

Yes, there is a circle of fifth progression in the passage, but it is not only a circle of fifths progression.

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  • I didn’t include the first bar of that passage because 1) the edition I was using would mean having to go further into the D minor part of the development and 2) I was focusing on the circle of fifths part of the passage.
    – Caters
    Feb 8, 2022 at 18:31
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    OK, but you're breaking the phrase structure. If you do that just for the sake of neatly pulling out a diatonic circle of fifths portion, you're missing the larger picture of changing tonal centers. Feb 8, 2022 at 18:56
  • @Caters, if you look at my second chart with Roman numeral analysis, and account for the various overlaps, you would notice a clear pattern V I IV, or more generically to include the N6, dominant-tonic-subdominant. That is of course a segement of the circle of fifths progression, but I think it's more important that it is dominant-tonic-subdominant in several changing tonal centers. Feb 9, 2022 at 15:21
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Just gotta point out that the tendency of the english to call such sequences of descending fifths "circle of fifths" is a bit weird, as the circle of fifths is a different thing altogether. I find the term "sequence of descending fifths" much clearer, also it sounds more impressive.

It is in fact true that your second example follows a descending fifths pattern, but what confuses you is that each sequence ends on the third of the next chord (which is some sort of 7th chord resolution).

So the sequence results in E7 | Am7 Dm7 | Gmaj7 Cmaj7 | Fmaj7 Bdim | E7 Am7 with focussed notes G# B | C F | B E | A D | G# C, which is a full falling fifths sequence on an intemediate A minor tonic.

The first example on the other hand does not follow this scheme. We get G Em7 C | D7 Bdim | Em C7 | D Bm7 G | C which is somewhat similar to a sequence of falling fifths, but it uses a ton of alternative resolutions.

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    – Richard
    Feb 10, 2022 at 19:34

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