Before you read any further, please be aware that none of this post will make sense unless you've read this first.
The minor 7th chord consists of a stack of alternating major and minor thirds: min 3rd, maj 3rd, min 3rd, maj 3rd. It's always been my favorite chord, and at the time of writing the post linked above I was even vaguely aware that there was some connection between this chord and the chord progression I was analysing. However, I was so new to harmonic analysis at that time that I was happy to leave the analysis at a series of chords.
It's only very recently that I've been able to piece together and understand some of the connections I've always sensed existed between a handful of musical patterns and elements. This post is an attempt to explain these connections, with the aid of some examples. I still have much to learn about this topic, and I'm sure there will be many more blog posts to write as I make new discoveries.
Let's say we're in the key of B flat minor. In this key, the notes which correspond to the degrees of the scale that form the Chord Progression of Resignation are B flat, D flat, E flat and G flat, from the bottom up:
Let's now invert this chord to the 2nd inversion, so it starts on E flat (note that the dominant of E flat is B flat...) The resulting chord is E flat minor 7th:
The notes used in the examples above are 4 of the 5 notes of the pentatonic scale. If we were still in B flat minor (which we're not, since E flat is our new tonic), the missing note (an A flat) would form the 7th degree of the scale - a fairly common addition to the 'pure' chord progression of resignation.
The pentatonic scale is the mode you get from playing only the black keys of the piano (although it can be transposed into any key). It's an interesting scale in that it's very pure sounding - you can combine any of its 5 notes, or play them all at once, and as long as you stay within that mode nothing will ever sound jarringly dissonant.
It's also quite tonally ambiguous - shifting from major to minor and between keys is effortless. I've yet to figure out what gives the pentatonic scale this ambiguous quality, as - depending on which note you begin it on - the degrees of the scale that are 'missing' vary.
The pentatonic scale is prevalent in the traditional music of many vastly different and geographically separated cultures. This can hardly be attributed to coincidence, and the discovery of its relationship to the 'chord of resignation', and by assosciation the chord progression of resignation, has only reinforced my impression that there's something fundamentally significant about the pentatonic scale.
Below are some examples of the 'chord of resignation'. As with the chord prog list, I'll add to this over time, so check back! (Quite a few examples I could easily include here would double with ones already in the chord prog
list, so I'm leaving some - though not all - of them out.)
To make collecting examples easier, I'm attempting to group them by harmonic structure a little.
The following examples simply use the minor 7th chord in its purest form:
1. Leo Ornstein - Piano Sonata No. 4, 2nd mvt (see 0:07, and probably most prominently 0:14) Aside from the timecodes noted, the opening of this appears to make use of the minor 7th constantly in other ways too complex for me to try to analyse yet. This piece already appears on the chord prog examples list, but I had to repeat it here because it has such a wealth of interesting harmony.
2. Ravel - Le Gibet (see 13:42 and several times again until the end)
3. Gershwin - Summertime (see 9:11)
4. Leo Ornstein - Piano Sonata No. 4, 4th mvt The opening of this is practically built out of minor 7th chords (or stacks of 3rds, in any case).
5. Steve Reich - Six Marimbas (see 6:15 onwards) The uppermost note of this chord shifts constantly between the 7th and
8th degree of the scale, while the underlying 3rds remain 'fixed'. Interestingly, the tonic doesn't appear in the bass until 6:32, and it dissappears again at 13:42. The inversion of the minor 7th created by this is the one shown in the first image above - the degrees of the chord prog of resignation stacked on top of each other in order: I, III, IV, VI.
6. Ravel - Une barque sur l'ocean (see 4:47)
7. Ravel - Noel des Jouets (see 2:26)
8. Ravel - Ondine (see 5:20) This example is really in a class of its own, as the chord is not only broken into a myriad of semiquavers and tuplets with a scattering of arbitrary notes in between, but it also isn't even a minor 7th. Nevertheless, a Chord of Resignation it undoubtedly is. A far more conventional example can be found at 5:49.
A very common way in which the minor 7th chord manifests - especially in minimalism - is where a particular interval or combination of intervals are maintained over the top of a changing base chord progression, resulting in the 'Chord of Resignation' seeming to grow naturally out of a pure tonic triad. The following examples demonstrate this.
9. Stellardrone - In Time This is a fairly simple example - harmonically and texturally - so well suited for explanatory purposes. The bass is progressing as follows: I, [V], VI, VII. To start with the...er, constellation of notes being repeated over the top is simply part of the tonic triad, but as it remains the same while the bass changes, it forms a minor 7th over the VI chord.
10. Porcupine Tree - Trains As with the previous example, the upper notes in the harmony here remain constant over a changing bassline,
resulting in a minor 7th forming over the VI chord. However, there are other relevant complexities to the harmony which you can read about in the chord prog examples list.
11. Steve Reich - Electric Counterpoint III This is an interesting example because the underlying chord progression consists only of the degrees of the scale that form the minor 7th - IV, VI, Im. As a result, in this instance it's impossible to say that a minor 7th is only formed over, say, the VI chord, as was the case with the previous 2 examples. The harmony just morphs organically, an effect intensified the gradual introduction of each degree of the scale in the bass at the start of the piece (you have to listen to the whole thing to get what I'm talking about). PS in case you're curious what happens when it briefly modulates, the progression is III, IV, V, but effectively that III chord becomes the new tonic.
12. Steve Reich - Music for large ensemble Initially, the uppermost note of the chord is simply the 3rd degree of the tonic triad (i.e. the dominant), but each time the bass plunges down a third it becomes a minor 7th.
Yes, there is a lot of Ravel on this list. :P