Josef Matthias Hauer: Compositional Tropes Techniques: Zwölftonspiel

Hi Guys,

Today, a look this great but lesser known Austrian composer:

Many people associate the abandonment of traditional tonality, wether 12 tone/serialism or some other form with the second Viennese school of composers, especially that of Arnold Schoenberg.

But, there was another thinker, composing at the same period of time [some say before] creating in his own unique atonal form…..

His name was Josef Matthias Hauer.

Hauer took a different approach by exploiting atonality and employing “Tropes”.

These consist of an “unordered pair” of complementing “Hexatonic” six note sets/groupings that employ all 12 notes of the chromatic scale. [The key being to play the first 6 notes before moving onto the next 6 notes].

EXAMPLE 1:

image showing Hauer tropes in 2 hexatonic sets

Guitar Version:[Sextuplets]

Image demonstrating an example of Joseph Mattius Hauer tropes for music composition.

EXAMPLE 2: [Exploiting Both Whole Tone Scales]

Although, they are hexachords these tropes can also work well divided into three 4 note groupings of “Tetrachords”

HAUER’S 44 TROPES: [479 million permutations into 44]

Example of Hauer’s personal writing’s:

We, will take this as our “Trope”

image depicting Hauer's trope sets

Now, let’s extend this to two octaves:

Image showing an example of Josef Mattias Hauer tropes for music composition.

From here, we will play the same trope in an intervallic manner: [Strict-each note in order ]

Image showing Josef Mattias Hauer tropes in intervallic form for music composition and improvisation

This time, let’s play each trope with the notes in a different order: [Not strict]

Josef Mattias Hauer's intervallic music tropes fro composition and improvisation

Here, we have “Trope”-in an Arpeggio Form;

Example.1

image of Josef Mattias Hauer arpeggio tropes for music composition

Example. 2

demonstration that shows JJosef Mattias Hauer tropes as arpeggios for music composition technique.

Example. 3

Demonstration image of Josef Mattias Hauer tropes as arpeggios for music composition technique.

Finally, the trope as a lick:

image for Josef Mattias Hauer improvised line
Josef Matthias Hauer Guitar Examples of Trope manipulation

From, our tropes we can create chords.

These can be,

Dyads–2note chords,

Tri-chords–3 note chords,

Quartal–4 note chords,

Penta–5 note chords

Hexatonic–6 note chords.

For this short blog we will exploit 2 note voicing’s.

Here, is an example of our two hexatonic’s as “Dyads”

image demonstrating an example of Josef Mattias Hauer dyad ic2 note chordal tropes for music composition. Music theory lesson guitar tablature and music notation.

We could also superimpose the retrograde of our trope on top of our trope:

image example of Joseph Mattius Hauer superimposing music tropes

From this, we can exploit some more harmony with dyads:

image demonstrating an example of Josef Mattias Hauer superimposition dyads

Here, is an example displaying some harmonic movement and chordal development that I quickly manipulated form our trope. [See-Chords in video chapter above]

image of Josef Mattias Hauer musical tri -chords
Hauer Compositon Tropes Example

This was just a very brief look at Hauer’s tropes. It’s an amazing concept because original harmonic content and original ideas develop naturally as the material reveals itself.

These simple tropes give birth to a wealth of creative content that can lead one into directions that may not have ever been taken or otherwise thought of or even considered.

Frank Zappa:Octave Displacement Composition/Improvisation Techniques

Frank Zappa Octave Displacement Composition/Improvisation Concepts

Hi Guys,

Today, a quick look at the way Frank Zappa exploits octave displacement.

This, is a really useful compositional device especially when writing for a string quartet or stringed instruments.

In this example we can see the use of the displaced octave [or Maj7th interval].

Musical notation showing a Frank Zappa transition between Maj7th chords, octave displacement with notes and annotations indicating 'O/D' and direction arrows.
Musical notation illustrating Frank Zappa’s octave displacement used in string instrument compositions.

With further analysis, we will notice the employment of the minor 3rd interval as a means of connection and predictive avoidance.

Musical notation displaying a Frank Zappa melody with highlighted minor third intervals, with annotations indicating their locations on the staff with octave displacement.
Musical notation illustrating frank Zappa minor 3rd intervals in a compositional example.

Although, this phrase/motif descends a minor 3rd it is actually, [quite cleverly] copied up a semitone:

Music notation displaying two Frank Zappa motifs with labels indicating connections and copy relationships, by employing octave displacement.
Musical notation illustrating Frank Zappa’s octave displacement and minor 3rd connections
Sheet music showing a Frank Zappa guitar piece in 4/4 time signature, including standard notation and tablature for performance with octave displacement.
Musical notation illustrating octave displacement for string instruments, highlighting the use of minor 3rd intervals.

This example is the same as that found in Pat Martino’s 12 chromatic forms:

This amazing shape creates a really nice resonance/blend on the guitar. It’s also useful for various inversions and shifting positions around on the fingerboard.

Here, once again we see the exploitation of the minor 3rd interval to move and connect the shape.

A musical notation image displaying Guitarist Frank Zappa's use of octave displacement.
Musical notation demonstrating frank Zappa’s minor 3rd interval and octave displacement

This application employs everything that we have looked at so far in one short example.

Notice, the minor 3rd connection, the open string, the shape, etc. It all becomes familiar.

A segment of sheet music displaying Frank Zappa's musical notes in standard notation and tablature, labeled with annotations including 'M3rd' and 'Shape.' The time signature is 4/4.
Example illustrating the application of minor 3rd intervals and octave displacement shape.

The final example is similar in concept to our first one.

It has a motif/phrase which is connected by the minor 3rd interval, that, then copies it up a half step.

Sheet music showing Frank Zappa's  musical notation with labeled sections indicating a phrase or motif, a minor third connection, and a directive to copy up a step, along with the corresponding tablature for guitar.
Frank Zappa illustrating the connection of phrase/motif using a minor 3rd interval, copied up a half step.

Full Example:

Sheet music featuring musical notes and tablature for guitar octave displacement in 4/4 time signature.
Frank Zappa illustrating a composition example using octave displacement and minor third intervals.

Stravinsky “Rite of Spring” Chord: Analysis/Harmony and Application

Hi Guys,

Today, a look at the amazing orchestral chord from “The Rite of Spring” [“Augurs of Spring ” – Les augures printaniers] by composer Igor Stravinsky.

This is a Bi-Tonal chord consisting of two parts or two different tonalities. In the Bass we have a chord of F flat Major and in the treble we have a chord of Eb7

Musical notation displaying the F flat Major and Eb7 chords, highlighting Stravinsky's "Rite of Spring" chord   [augurs of spring chord]
Musical notation illustrating the bi-tonal chord of F flat Major and Eb7 from Stravinsky’s ‘The Rite of Spring.’

Stravinsky calls this F flat Major as opposed to its enharmonic [E Major] because, he employs an Eb Major key signature making it easier to read and follow, whilst removing any # accidentals that could create messiness. [The extra flats make it legible].

stravinsky_rite_of_spring_chord_augurs_of_spring

In our modern analysis we can think of it this way,

"Les Augures printaniers" sheet music displaying F flat Major and Eb7  Stravinsky chords with annotations.

Here, is how the rite of spring chord sounds in an orchestral context:

From Stravinsky’s score: Here, we can see Stravinsky’s mastery, displayed by his execution of rhythmic brilliance.

stravinsky_rite_of_spring_chord_augurs_of_spring

Below, is how it sounds as a pad on an modern keyboard

Due, to the nature of the guitar we really need an extra finger and an extra string to do this unique chord justice.

But, here are two guitar voicing’s for harmony, strumming and chordal picking:

Musical notation diagram illustrating a bi-tonal "Rite of Spring" chord with tablature for guitar, depicting an F flat Major and Eb7 chord by Stravinsky.
Guitar voicing example for the Bi-Tonal chord from Stravinsky’s ‘Rite of Spring.’
stravinsky_rite_of_spring_chord_guitar-lesson-voicing

In the example below, we can see the amazing way Stravinsky’s “Rite of Spring” chord resolves and how the structure of the harmony moves.

stravinsky_rite_of_spring_chord_augurs_of_spring_analysis
stravinsky_rite_of_spring_chord_augurs_of_spring_harmony
stravinsky_rite_of_spring_chord_augurs_of_spring

Due to the nature of the two chords being a semitone apart we can create some interesting chord pairs lines/licks from this:

stravinsky_rite_of_spring_chord_augurs_of_spring_bi_tonality

Okay, now let’s develop this a bit,

stravinsky_rite_of_spring_chord_augurs_of_spring_bi_tonal_lesson

We, can also build on this concept and create some interesting guitar or solo instrument lines with this approach:

Here is a lick/line example:

A music score highlighting E Major and Eb Major sections improvised Stravinsky "Rite of Spring" chord
Musical notation highlighting the transition between E Major and Eb Major chords in Stravinsky’s ‘Rite of Spring.’
Musical score displaying E Lydian and Eb Major sections, with annotated rhythmic divisions for Stravinsky's "Rite of Spring" chord
Musical notation illustrating the E Lydian and Eb Major scales, highlighting the rhythmic structure and chord pairs from Stravinsky’s ‘Rite of Spring’.

This was just a quick look at the potential of just one chord!

This Bi-tonal and Polytonal approach opens up so much in terms of inspirational ideas, originality and fresh harmonic perspectives.

In this way, cliches can be rung of banality and forged into something interesting and unique and thoroughly challenging.

“Les Augures Printaniers/The Rite of Spring” is such a great example of this, possessing a little world within itself. Add, to this Stravinsky’s brilliant exploitation of rhythm and we have a [Bi-tonal]chord that’s an all time classic!