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I asked a question in the past about non-diatonic notes. In the answer I got a progression of the form:

IV Maj | ♯iv dim | I64 | V7 | I Maj
IV Maj | ♯iv dim | V7
| V7 | ♯v dim | vi min
II7 | V7 | I Maj
I Maj | ♭iii dim | ii min | V7
ii min | iv min6 | I64 | V7 | I Maj

This progression was in reference to the guy playing here, which I liked.

My understanding is that non-diatonic chords are usually chords from different modes but I might be wrong. Using the progressions above, I listed the mode followed by what chord degree it is according to the table I found here.

Ionian 4 | Lydian 4 | Ionian 1 | Ionian 5 | Ionian 1
Ionian 4 | Lydian 4 | Ionian 5
Ionian 5 | ??? | Ionian 6
Lydian 2 (?) | Ionian 5 | Ionian 1
Ionian 1 | Aeolian 3 | Ionian 2 | Ionian 5
Ionian 2 | Aeolian 4 | Ionian 1 | Ionian 5 | Ionian 1

So my question is how does one get to the chord "♯v dim", I can't see it in the roman numeral modes table. Also if I'm looking for interesting non-diatonic chord progressions, should I primarily look at mode mixing?

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Modal mixture means borrowing chords from parallel modes. But here, the ♯v dim chord is the leading tone chord to the vi chord (i.e., it's really a vii°/vi). I would suggest not trying to analyze chords as if they are within "other modes" unless they cannot be construed as anything but modal mixture. The reason for this is that many chords (at least in traditional common practice period harmony) can be described as functioning within the given key. In fact, the "II7" chord you have is analyzable as a "V7/V" chord, and is thus given a proper function within the key compared to a "II7". Now obviously this isn't always the case, but the only time I personally would analyze something as ♯v° is if it was unanalyzable as anything else, which I imagine would be a very rare case. (The ♭iii° chord can be analyzed as a diminished passing chord downwards).

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  • I guess either modal mixture or secondary dominants then.
    – user34288
    Feb 5, 2019 at 20:16
  • Try to analyze secondary chords before modal mixture chords as a rule of thumb :)
    – LSM07
    Feb 5, 2019 at 20:28
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    Other way around. First try primary chords (e.g., I, ii, iii, IV, V, vi, vii° in major), then secondary chords (secondary dominants (V7/V), leading tone chords (vii°/V, etc), then modal mixture (♭III, ♭VI, ♭VII, iv, etc), and then possibly modulation. Just loose guidelines here, not solid set-in-stone rules.
    – LSM07
    Feb 5, 2019 at 20:33
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    Not only secondary dominants, chromatic mediants and related chords. Augmented Sixths and Neapolitan Sixths among others.
    – ttw
    Feb 5, 2019 at 22:24
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    In some theory texts primary refers to the I IV V chords and _secondary means ii iii vi, I suppose that leaves viio as a alternative V.
    – Michael Curtis
    Feb 5, 2019 at 22:33
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Also if I'm looking for interesting non-diatonic chord progressions, should I primarily look at mode mixing?

That's one way. But borrowed chords mostly function the same way in the key as the diatonic chords. So they provide colorful, but not necessarily non-functional harmony. It depends on what you really want, but I think the simple comparison is Romantic era harmony versus Impressionism like Debussy where you might have non-diatonic, non-functional dominant seventh chords, etc.

I recently have been exploring this topic myself. I identified the basic diatonic seventh chord types: major seventh, minor seventh, dominant seventh, and half-diminished seventh, and then looked for various non-diatonic harmonic patterns I could apply to them.

One of the first things I took note of was succession of chord qualities within the diatonic realm and then make contrary patterns. For example, diatonically we have two adjacent minor seventh chords a whole step apart: ii and iii, but we do not have similarly adjacent dominant seventh chords. So, I can get a simple non-diatonic, non-functional progression with something like G7 to A7. To avoid that A7 suggesting a V7/ii I could use G7 A7 B7 for an emphatically non-functional progression.

I also looked at all the chord qualities for the fundamental root progression by descending fifth. Going through the whole diatonic circle of fifths I listed the two chord pairs (which I called bi-grams after a linguistic analysis term) and compared that with the 16 possible bi-grams of chord qualities. I eliminated the bi-grams that were diatonic and selected the others. A diatonic root progression by descending fifth from viiø7 goes to iiim7. I could alter the iiim7 chord by lowering the fifth and get a succession of chord qualities that isn't diatonic: Bø7 to Eø7.

Instead of using a circle of fifths I tried a circle of chromatic mediants. I tried both root progression by ascending minor third and ascending major third. One thing I thought was interesting is how when diatonic seventh chords move through a circle of fifths each progression has two common tones and two tones changing by step. With a circle of chromatic mediants - ascending minor third, using any of the four seventh chord qualities - the smoothest voice leading resulted in two common tones and two tones changing by half step. Both of these sequential progressions had similar voice leading re. common tones.

Finally some interesting progression can be found by holding the chord root while changing the chord quality and then moving sequentially by ascending or descending half step. Something like: start with a minor seventh chord, lower the fifth to create a half diminished seventh on the same root, then drop the root a half step and form a minor seven chord above it by dropping the root, third, and seventh, then continue that sequence. Like this Cm7 Cø7|Bm7 Bø7|.... There are many other possibilities ascending and descending.

Some rules of thumb emerge:

  • multiple successions of the same chord quality are mostly non-diatonic
  • changing chord quality on a shared root is non-diatonic
  • number of common tones in voice leading helps determine harmonic 'pull'

I don't really know how to word that last point concisely. Basically, it seems that regardless of the pitches being diatonic or chromatic, if the number of voices changing is only one the progression is 'weak' or 'gentle', if about half the voices change the progression is 'strong' or 'dynamic', if all the voices change, the progression is 'emphatic' maybe even 'abrupt.'

This was my approach. I was aiming for a fairly traditional sound. Most of it sounds jazz-ish or Impressionistic. You could do something different. I mostly want to say you can try to create your own tonal logic. When you dispense with diatonic+secondary+borrowed harmony there really aren't established conventions.

Another thing to try is progressions and voice leading through any non-diatonic scale. Try the double harmonic as an example. It has all kinds of interesting options with simple triads and seventh chords. By definition all of the progressions will be non-diatonic.

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  • thinking of the chromatic mediants as a circle is helpful, thank you! ascending roots of chromatic minor third mediants is: C, D#, F#, A, C. major third mediants is a bit smaller with: C, E, G#, C.
    – user34288
    Feb 6, 2019 at 2:12
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For me, I think the question of "getting to" a another step in the scale (For ex. IV to #v0 or V7 to a #vo ) is really a question of functional harmony not modes. The idea of functional harmony is that the music develops away from and back to the home key in a way that creates some tension and release.

In the case of the video the guy is using very traditional harmonic concepts with a lot of V7 dominant (on C dominant back to the key of F major). It is somewhere between neo romantic/classical and popular song (e.g. Hammerstein). He is using a traditional hummable melodic theme with development towards the dominant via vi and II7 (aka Vof V). He gets there by using Vof III (E7 to A- which gets to G7 to C7 which creates a strong motion back to F. I'm reminded of a slowed down "Surrey with the Fringe on the Top" in its harmonic feeling

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  • thanks for your answer, this is great stuff. so you're saying he uses a bunch of secondary dominants. What does #v0 or #vo mean?
    – user34288
    Feb 15, 2019 at 22:35
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    \Yes he uses secondary dominants. He uses I7 (V of IV) to get to Bb as well. I was a little sloppy there in my notation, sorry. I meant to notate #ivo and #vo as you had done with the o. o is the same as dim (diminished).
    – Jon Raney
    Feb 16, 2019 at 13:05

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