0003. List of superimpositions. Modal control

Mathematical research of superimpositions took a great deal of time. 8 basic types of seventh chord were combined with each other, one of them – static (basic chord), another – varying trough chromatic scale (possible superimposition). In total 768 pairs. Great part of them misfit, some results were rejected because they contained avoid tones.

Here you could see and test a part of final list I`ve got. For full version contact me directly advancedharmonyblog@gmail.com

partial list of superimpositions of 7h chords

Any basic chord could fit with several scales and modes at once, whose have identical 1st, 3rd, 5th and 7th`s. Further list shows what scales / modes and seventh chords have common degrees.

how 7th chords fit with modes

Because superimpositions add modal 2nd`s, 4th`s and 6th`s to arpeggio of basic chord, they could be interpreted as modal. We could list and use them in groups – each group for each mode, with root of basic chord.

For instance, we could define what superimpositions update Cm7 chord up to C dorian #4 mode (add 2, #4 and 6 to basic arpeggio). Let`s see and hear it.

Next is the partial list of superimpositions organized mode by mode. Because some modes have plenty of avoid tones, they are not represented there at all.

If basic chord could not be extended vertically, it may be used in pair with other diatonic chord, which contains missing modal tones. Such one could not be considered as a superimposition.

For instance, Cm7 (C, Eb, G, Bb) has only one stable vertical tension in C phrygian context: it`s 4th (F). Unstable tones (Db and Ab) could be successfully represented by Dbmaj7 chord (Db, F, Ab, C), but this is subject of another study.

Notice that superimpositions also could be extended, according to modal context they belong. Next to each available superimposition, brackets contain the name of diatonically correct mode for it and numbers of degrees – what tones in basic chord are actually hit.

some superimpositions in modal context


0002. Superimpositions – avoid tones avoided

If we are able to define what chord substitutions do not contain avoid tones (modal, but vertically unstable) or chromatics, we could get a great list of harmonic substitutes surely suitable for vertical use. Let`s call them superimpositions.

Superimpositions also should not provoke arpeggio conflicts with basic chords. For instance, there is no place for 7 and b7 or 5 and #5 together (also check alternate spellings).

Every tone of superimposition whether duplicates arpeggio of basic chord, whether works as colorful and stable modal feature – so called tension (2 or 9th, 4 or 11th, 6 or 13th).

Just to be sure: avoid tones are modal upper structures – 9, 11 and 13th`s, – working only as passing or chromatic notes, because of their harmonic instability.

For instance, upper structures of ionian mode are 2, 4, 6; but only 4th (11th) is harmonically unstable. It`s avoid tone. Upper structures of lydian mode are 2, #4, 6; all of them stable, so there`s no avoid tones in lydian mode at all.

Let us hear and compare 4th and #4th vs maj7 chord. Avoids tend to be immediately resolved, until then we feel kind of anxiety.

Most avoid tones meet one basic criteria: they are by minor second (including interval inversions and octave displacement) above the tones of triad (1, 3 and 5). But not always. Perception of harmonic stability is cultural and quite subjective question, therefore some of avoid tones are just recommendable.

There is my personal list of 28 asymmetric scales / modes (suitable for vertical use), with avoid tones marked grey. It will serve as basis for further construction.

avoid tones in 28 modes


001. When and why chord substitutions are not reliable?

Did you ever noticed, when playing in a band or with backing track, that some of traditional chord substitutions do not sound well over original changes? There are reasonable answers why it is so, and what could be done to avoid such irritating effect, without limiting (and even expanding) palette of handy harmonic devices.

At first, let us define what traditional chord substitutions are. They are harmonic devices for creative reconstruction of already known chord changes, without doing any damage to their functional features. Chord substitutions developed gradually, as more and more sophisticated and modern recipes of harmonic variation.

We all know at least few of those:

Diatonic substitutions (Em7 instead of Cmaj7)

Secondary dominants (C C7 | F G7)

Secondary II V`s (C   Gm7 C7 | F G7)

Tritone substitutions (Db7 instead of G7, or Abm instead of Dm)

Sudden change of chord type (Ebmaj7 instead of Eb7 – tritone sub for Am7 or A7)

Passing chords (C C#dim7 | Dm G7)

Coltrane substitutions (Dm7 Eb7 | Abmaj7 B7 | Emaj7 G7 | Cmaj7 instead of Dm7 | G7 | Cmaj7 | Cmaj7)

Root movement by minor third (Bb7 instead of G7 or Db7)

Backcycling (E7 A7 | D7 G7 | C7 | C7 instead of G7 | G7 | C7 | C7)

Side-slipping (Ebm7 Ab7 | Dm7 G7 instead of Dm7 | G7)

Chromatic approach chords (C Bb7 | Am C#m | Dm Ab7 | G7 B7 instead of C | Am | Dm | G7)

You name it…

When using as melodic (arpeggio) devices, chord substitutions could work really well, if played in fast and convincing phrases. Predictably structured series of notes become relatively independent of harmonic context until the point of resolution. They are self content to the listeners` ear, because of very dynamic nature.

Audible conflict between original changes and substitutes occurs in slower tempo, when trying to accent or lean on notes of substitute arpeggio, also in chordal improvisation. It happens because some of chord substitutions have been created foremost as compositional devices and are not really suitable for vertical improvisation, because of avoid tones and chromaticisms (vertically unstable notes) they contain. Riddle of vertically stable and unstable substitutions emerged historically and I will propose clear technical solution for it in progress of series of following articles.

Once more: we could alter original chord changes using any of traditional chord substitutions and still retain the same functional logic, but we could not always do that during spontaneous jam session – original changes and their substitutions sometimes may not sound well, played simultaneously.

Let us analyse and hear few examples, when original chord and common traditional substitute misfit:

Ex. 1:

G7 (V7) ≠ Abm7 (tritone substitution of Dm7 (IIm7), quite common before Db7 (bII7) instead of G7).

Notes of G7: G B D F, it is 1 3 5 b7.

Notes of Abm7: Ab Cb(B) Eb Gb(F#), it is b2, 3, b6, 7, according to G7.

Both summarized: 1, b2, 3, 5, b6, b7, 7. b2 and b6 are avoid tones, b7 and 7 – arpeggio conflict.

Ex. 2:

Am7 (VIm7) ≠ Ebmaj7 (tritone substitution of VIm7, chord type changed, as in common cadence Cmaj7 Ebmaj7 | Abmaj7 Dbmaj7)

Notes of Am7: A C E G, it is 1 b3 5 b7.

Notes of Ebmaj7: Eb G Bb D, it is b5 b7 b2 4, according to Am7.

Both summarized: 1 b2 b3 4 b5 5 b7. b2 is avoid tone, b5 and 5 – arpeggio conflict.

If these examples did hurt your ears (sorry for that), you are ripe for further studies, which will follow here shortly.