intervals – 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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Pat Martino Intervallic Studies: Un-Published Book Lesson

Posted on May 21, 2024May 25, 2024 by Modern Music Theory and Application

Pat Martino Intervallic Studies: Un-Published Book Lesson

PLEASE WATCH VIDEO ABOVE FOR DETAILED INFO:

Hi Guys!

Guitarist Mark Koch one of Pat’s students kindly sent me a copy of Pat’s un-published book on “Intervallic studies“.

pat-martino-intervallic-studies-umpinlished-book

It’s a fascinating look at the imaginative thought process and creative concepts that Pat was investigating for the development of the improvising guitarist.

Also, it’s a real eye opener for the development of scale applications and creating fresh lines form nearly every scale imaginable. This book has around 294 examples.

pat-martino-intervallic-studies-unpublished-book

INTERVALLIC STUDY #1 “Whole Tone Scale”

In this first example we will look at the “Whole Tone Scale” Study:

From a music theory perspective if we take away the intervallic approach and place the notes in order we will get a whole tone scale ascending followed by a whole tone scale descending:

Now, we will put them back into the “Disguised” form with the clever approach of the intervallic design:

The key to playing these studies on the guitar is to decide on a methodical fingering and stick to it. [Below=Pat’s Fingering]

pat-martino's-unpublished-book-intervallic-guitar-studies

Also, it’s a really good idea to play in a staccato manner because there is a tendency for the open strings to resonate sympathetically with the string that has just been plucked.

I am employing strict alternate picking for this study starting on an upstroke:

FULL INTERVALLIC STUDY:

Same Study: From Pat’s book with fingering examples:

pat-martino-intervallic-studies-unpublished-book-whole-tone-scale

INTERVALLIC STUDY #2 “Pentatonic Scale”

Now we will look at how Pat breathes life into the pentatonic scale:

As before we will take this from a music theory perspective and remove the intervallic approach:

pat-martino-pentatonic-scale-guitar-lesson

Here, we again find the same principle as the previous example. But, this time we have the Pentatonic scales ascending and descending:

Now, let’s disguise this with the use of intervallic exploitation and alternate picking starting on a “Downstroke”:

Same Study from Pat’s unpublished book:

INTERVALLIC STUDY APPLICATION with the “Chromatic Scale”

Finally, we will employ these intervallic concepts through a iim7b5 V7 i cadence.

Once again, we see the intervallic set up:

pat-martino-intervallic-improvisation-example

Now, let’s employ our music theory and place the intervallic notes in order. Here we find that we have the exploitation of the chromatic scale.

pat-martinochromatic-scale-guitar-lesson

This clever approach is really effective because in the second bar beats 2 and 3 we have a literal chromatic scale that then anticipates the coming minor tonic chord of Em with an Em arpeggio.

Full Example:

In Conclusion:

This was just a quick look at the creative thought process and unique approach of Pat Martino, resulting in the application of this material into a minor iim7b5 V7 i improvised line to hear how they work and sound.

This approach to scales and improvising [and composing] with them is highly original and extremely useful when there is a need to bust out of cliches and seek colour and creativity in our playing.

FREE PDF DOWNLOAD:

pat-martino-jazz-book Download

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String Skipping/Intervallic Guitar Part 3-HARMONY

Posted on April 4, 2023April 6, 2023 by Modern Music Theory and Application

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String Skipping/Intervallic Guitar Part 2-HARMONY

PLEASE WATCH VIDEO ABOVE FOR DETAILED ANALYSIS:

Hi Guys,

Today, one last look at “Intervallic string skipping” for a contrapuntal-esque picking style.

The first thing to do is take one position on the guitar fingerboard and find the “Harmony” embedded within that position.

I have taken the A Major position [F#m Relative]

Now, let’s make an A Major basic arpeggio from the 1st string and the 6th string.

Straight away, you will notice that the notes on the 1st string and the notes on 6th string are the same but in different octaves. This gives us an easy and excellent way to exploit the High to Low or Low to High counterpoint effect.

Now let’s do the same with a piece of scale: [Starting on an “Upstroke”]

Again, the octave makes this flow and connect easily from the low to high.

The next point is to take a chord sequence and use this “String skipping/intervallic” effect: Here we have Vi ii V7 I

HARMONY

Th next essential point is to acknowledge the harmony in this position:

We will do this by exploiting the Cycle of 4ths in this simple 5 fret position.

Here you can see that we have a huge amount of harmony available to us right under our fingertips. These chords don’t have to be Major, they can be minor, diminished, augmented etc. This gives us even more material to work with.

If we move down a fret [Semitone] then we have another set of harmony in 4ths awaiting us.

Along, with this we have chord inversions and all of the inversions of A Major:

So, as you can see there is a huge amount of harmony right in front of us even in this one position that we can exploit and create lots of music from.

Lastly, let’s create another “String skipping intervallic” example:

I’m going to create a phrase outlining a D Maj#11 chord.