0007. Pentatonics as superimpositions – abilities and techniques, part 2

Pentatonic-based chords could be controlled melodically. They behave pretty much as inversions of triads; just have significantly more of chord tones (what makes them supermelodic!).

Let`s pick five three-voiced fragments of the pentatonic, deployed widely, as discussed earlier. Those all have different melodic degrees:

b3 5 1*
4 b7 b3
5 1 4
b7 b3 5
1 4 b7

*Bold digits could be considered as roots of different kinds of “pentatonic triads”.

Notice that tones in columns are deployed narrowly (1 b3 4 5 b7 1 etc.). This could be used for melodic motion, without huge interval leaps.

Tones in rows remain deployed widely, as common chords (1 4 b7 b3 5 1 etc.).

In video this idea should look clearer.

Widely deployed pentatonic triads are always less than octave in range and could be inverted for greater intervalic variety:

4 5 1 4 b7 1
5 b7 b3 5 1 b3
b7 1 4 b7 b3 4
1 b3 5 1 4 5
b3 4 b7 b3 5 b7

Do not get fooled by numerous shapes – they are just the same initial pentatonic, just used with some sense and purpose.

Any tone of inversion also could be displaced by an octave – for even greater range and intervalic variety.

I know all this information might seem puzzling at first, especially when we deal with not only one, but three different kinds of pentatonic and use them as superimpositions over other chords. But proper classification of pentatonic triads and focus on right spots makes the whole system accessible to many. Ask my students.πŸ™‚

If you got the idea and are interested in fully detailed course or want to share your thoughts, contact me directly advancedharmonyblog@gmail.com


0006. Pentatonics as superimpositions – abilities and techniques, part 1

Let`s discuss pentatonics in role of superimpositions, what benefits they give and how we could control them.

First of all, pentatonic (of any kind), built entirely of vertically stable tones, allows us to use pentatonic-based melodic lick in different harmonic contexts, with no modifications. Only condition – avoid tones and chromatics (remaining 7 tones of 12) should be rhythmically passive, unemphasized.

Let`s hear an example.

I think such feature is encouraging (because there`s no chance to fail). Moreover, ear and sense of phrasing are very positively provoked, when one exactly knows what notes are reliable for sure.

And if you are conscious about modal context, when playing pentatonics, they will help you to find the right fingering of modes (because only two modal tones still missing).

Pentatonics are even more powerful and interesting as a vertical structure, chord.

If we organize sounds of pentatonic not in a row, but skip every other one, we would get quite even intervalic pattern where fourths heavily prevail. (Such deployment is perfectly convenient for guitar players, for whom I have special fingering course.)

For example: A C D E G A C D E G A and so on. Bold notes are separated by such intervals: p4, p4, p4, M3, p4.

Wide deployment of pentatonics causes heavy quartal sound. 1 4 b7 b3 5 1 instead of 1 3b 4 5 b7 1.

(to be continued)


0005. Types of chords vs types of pentatonics

Everybody knows that minor pentatonic reflects features of most minor chords, scales or modes (must be with b7 and 4), because of it`s evident structure: 1 b3 4 5 b7.

Measured from b3 (considered as new root), the same tones give structure of major pentatonic: b3 4 5 b7 1 = 1 2 3 5 6. It covers qualities of many major chords, scales or modes.

Following explanation is written with particular letters, to emphasize close relation between pairs of relative pentatonics, which in fact are the same thing.

  1. Minor pentatonic equaly reflects features of m7, maj7 and similar chords:

Am7 fits Cmaj7 as 1 b3 4 5 b7 (A C D E G) fits 1 2 3 5 6 (C D E G A)

Let`s discuss remaining asymmetric seventh chord types: dom7, 7alt, m7b5, m maj7, maj7#5.

  1. Features of dominant seventh chords are well reflected by minor pentatonic with major third (M3). Measured from 3rd degree it also perfectly fits with 7alt (enharmonically = m7b5).

A7 fits C#7alt (= C#m7b5) as 1 3 4 5 b7 (A C# D E G) fits 1 b2 #2(b3) b5 #5(b6) (C# D E G A)

  1. m maj7 features are reflected by minor pentatonic with major seventh (M7). Measured from b3rd degree it also covers maj7#5.

Am maj7 fits Cmaj7#5 as 1 b3 4 5 7 (A C D E G#) fits 1 2 3 #5 6 (A C D E G#)

Newly introduced types of pentatonic contain not only plenty of missing m2, M7 and tritone intervals, but also all four possible kinds of triad: major, minor, diminished and augmented. I dare to state, that three types of pentatonics, shown above, are various and versatile enough to act properly in whole range of musical situations.

That also could be proved by mathematical research, which shows us where pentatonics could be used as superimpositions (five-voiced chords).

pentatonics as superimpositions


0004. Density of vertical texture

Density of chosen harmonic devices (quantity of degrees within) affects few crucial parameters of music: construction of arpeggio based melodic phrases, mix of prevailing intervals and force of functional gravity.

Triads have thinnest texture; prevailing intervals are thirds, fourths and their inversions. Functional gravity is evident (heavily determined by Western cultural environment).

In seventh chords we observe denser texture and greater variety of intervals: seconds and sevenths become common, tritones are much more frequent. Functional gravity is the same, excepting dominant seventh chords – those pull even stronger.

Pentatonics also could be considered as vertical formations, with very dense texture. In such conditions fourths, seconds and their inversions start prevail. Functional gravity becomes weak. Looks like the vertical and horizontal of music got really close to each other. Some modes have no more than five harmonically stable tones (phrygian, for instance), all remaining act like passing or chromatic.

Next list shows how superimpositions could be categorized by density of texture: into triads, seventh chords and pentatonics. Pentatonics are marked in bold font; some of them are not common minor/major type and would be explained in further posts.

superimpositions as triads, 7th chords and pentatonics

Pentatonic is powerful but yet underestimated harmonic device. I think it is because of limited intervalic structure of minor/major pentatonic (which lack some of characteristic intervals: m2, M7, tritone). Musicians are trying to alter pentatonics to fit whole range of musical structures, but they often fail to discover fundamental unifying principle. Hope I found simple and sufficient method how to overcome intervalic limitations of pentatonics and control them vertically. Great deal of upcoming materials would be entirely dedicated to this subject.


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 (CΒ Β  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) β‰  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) β‰  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.