Schoenberg – Modern Music Theory Improvisation and Application

Jared E Davis: “Atonal Improvisation and Jazz” Techniques Explained

Posted on August 11, 2026August 11, 2026 by Modern Music Theory and Application

Jared E Davis Atonal Improvisation and Jazz music examples and analysis

Please watch video above for detailed info:

Hi Guys,

Today, a quick look at “Atonal improvisation and jazz” book by Jared E Davis.

Atonal Jazz analysis with examples from webpage — Jared E Davis Atonal Improvisation and Jazz

Please note: This Blog won’t contain a Pdf download due to any copyright infringement.

PART 1:

Jared’s book, is similar in some ways to John ‘O’ Gallagher’s book 12 tone improvisation

Screenshot 2026-08-07 at 18.34.23 — 12 tone improvisation book John ‘O’ Gallagher

But, also differs due to being atonal [interval pairs] and not 12 tone.

BASIC PROCEDURE:

This concept works with the 12 chromatic notes.

So, for example if we were to start on the note C it would be,

C=O C#=1 D=2 D#/Eb=3 E=4 F=5 etc.

Resulting in a minor 3rd =3 or a Major 7th = 11 or Unison = 0 etc.

We are just counting the minor 2nds/semitones as in the chart below:

CHART:

Jared E Davis Atonal Improvisation and Jazz

What to be aware of:

If we were to have singular intervals like 11111 etc, we would end up with a chromatic scale:

Or, for example, 3333 we would end up with Diminished 7ths:

Below, is a list of techniques explained:

In this blog in order to avoid any copyright infringements I am going to look at interval pairs in the main.

Etude 1-6

Exercise in “Interval Pairs”

In order to get really fluid with this it’s a great idea to write an etude.

But, before we can do this we need to learn/practice an etude already prepared.

So, in this case I am going to take one from the book which consists of the interval pair 1-6

In this example we will master 1= minor 2nd and 6= Tritone

EXAMPLE:

From the example above we can see our interval pair of 1-6 in action.

Notice also, where there =1 it can be inverted to/create octave displacement.

Example of Atonal Improvisation and jazz book by Jared E Davis. Musical examples and demos with music theory analysis. Complete lesson for atonal improvisational music techniques.

Below, is the full etude that I have starting on a down stroke for strict alternate picking.

Full Etude:

An example of tonal Improvisation and jazz book by Jared E Davis. Musical examples and demos with music theory analysis. Complete lesson for atonal improvisational music techniques.

Atonal Improvisation and jazz book by Jared E Davis. Musical examples and demos with music theory analysis. Complete lesson for atonal improvisational music techniques.

TRI-CHORDS

We can also build some amazing chords from atonal techniques.

I am going to look at a couple of Tri-Chords. [Although, we can create, tetrachords and pentachords etc].

EXAMPLE 1: “016“

Below we have the “Retrograde” of the above: “056”

ii V7 I Example

Let’s now apply this to a ii V7 I cadence:

Again, sticking to our minor 2nd and tritone 1-6 interval pairs from our Etude:

ii V7 I Atonal Improvisation and jazz book by Jared E Davis. Musical examples and demos with music theory analysis. Complete lesson for atonal improvisational music techniques. — Jared E Davis Atonal Improvisation and Jazz ii V7 I 1-6 Cadence Example

2 SCHOENBERG EXAMPLES

Lastly, here is a couple of real life examples by the great composer Arnold Schoenberg.

Interval Pair 1-5 [Perfect 4th and minor 2nd]:

Finally, we have interval pairs 3-4

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Schoenberg’s chord of the 15th-Music Examples and Analysis

Posted on August 25, 2025June 1, 2026 by Modern Music Theory and Application

Please watch video above for detailed info:

Hi Guys,

Today, a look at the final chord of Arnold Schoenberg’s “Sechs Kleine Klavierstucke” 2nd movement. In thirds this reads as: C–E–G–B–D♯–F♯–A♯–Cx.

Schoenberg Chord in classic form:

schoenberg_chord_music_analysis_extended_15th_in_music

This extended chord of a 15th, can also be viewed and heard as a bi-tonal construction of C Major 7th with Eb minorMajor 7th superimposed on top

Schoenberg Chord Clarified:

This can also, be thought of [especially in terms of the guitar] as an arpeggio of CMaj7 and an Arpeggio of EbmMaj7.

schoenberg_chord_music_analysis_explained_15th_in_music

Due, to the nature of its sound and collection of notes, it can produce some interesting counterpoint. Especially, as the Eb to E natural resolution creates colour and drama. [view video at top of page].

schoenberg_chord_music_analysis_extended_15th_in_music_guitar

Being, a Bi-Tonal chord it is useful as it gives us triad pairs.

Ascending Line:

schoenberg_chord_music_analysis_chord_pairs_guitar

Now, we will take this a stage further by adding more chords/triads available.

D+ to C to EbmMaj7 to CmMaj7 to Em7 to Bmaj7

schoenberg_chord_music_analysis_chord_pairs

CHORDS:

Let’s now, re voice the chord. Here we will make the chord of C a minMaj7 and add D Augmented [9th] on top.

In the video/audio [a quick demo I created] below, we can hear the dramatic sound of this voicing in the orchestra.

Next, we have two guitar voicing’s. Firstly we have a Bsus/C [or plain B/C] as a typical McLaughlin guitar voicing.

schoenberg_chord_music_analysis_extended_15th_in_music_mclaughlin_guitar

Secondly, we have the same voicing but with a changing bass.

Lastly, another guitar voicing that is useful for chordal picking:

From here, we will add a partial scale descending that is formed from the chord: This chord voicing has a flattened 5th and a sharpened 9th.

Lastly, we can create some interesting and colourful passages by exploiting the intervals inherent within this 15th chord.

EXAMPLE 1 Ascending:

schoenberg_chord_music_analysis_extended_15th_in_music_intervals

EXAMPLE 2 Descending:

PDF DOWNLOAD:

schoenberg_chord Download

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Polytonality:For Concerto/Orchestral Writing

Posted on February 27, 2024March 16, 2024 by Modern Music Theory and Application

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Polytonality: For Concerto/OrchestralWriting lesson

Please watch the video above for detailed analysis:

Hi Guys

Today, a quick look at composing with Polytonality for orchestral and concerto writing.

What is Polytonality?

Polytonality is the use of two or more keys at the same time:

Example 1:

Db Major/C Major [Basic root position]

poly-tonality-orchestral-composing-chords-example

In this first example we have 4 bars of Polytonality with Eminor/DbMajor and EbMajor/CMajor

This then resolves itself with a “Tonal” diatonic cadence of B7/D# to Em:

This method is really useful because we can use the polytonal approach sparingly with it’s thicker and richer harmonic texture whilst then then playing its opposite it with the thinner aspect of diatonicism.

This way the Polytonal nature of the music compliments the diatonic cadences and visa versa.

Example 2:

Polytonality-Orchestral Example

This example explores “Implication”. In this case it is implying the melodic minor but avoiding the cliche by employing the richness of Polytonality:

From here, we will again employ diatonic harmony for a cadence.

To complete this short orchestral example we will go back into Polytonality with another melodic minor implication by employing Dminor/DbMajor:

Here is the chart:

poly-tonality-orchestral-composing-example

Example 3:

Polytonality-Orchestral Example

In this final example we will just “Reverse” the chords. This time it is DbMajor/Cmajor which is then played the other way around with CMajor/DbMajor.