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Composition Tools Permutations & Combinations

Orchestrating Possibilities

I’m studying Mozart’s late symphonies and piano concertos these days and thinking about what makes his music extraordinary.

Of course, there are many aspects – taste, harmonic sophistication, lyricism, humor, a sense of inevitability peppered with surprises, and so on.

The incredible variety in his orchestration got me thinking about the possibilities for sub-ensembles within the classical orchestra:

(01 solo)
02 duet
03 trio
04 quartet
05 quintet
06 sextet
07 septet
08 octet
09 nonet
10 dectet
11 undectet
(12 duodectet)

I’ve made a PDF (see below) that lists all of these possibilities within the classical (Mozart, Haydn, Beethoven, etc.) orchestra; it’s helped spark my imagination, and also as a prompt for inner-ear “visualization” exercises.

Take a look at the lists and imagine (hear in your head) what music made from these groups would sound like – its density, timbre, etc.

The Greek composer Vangelis said in a 2008 interview that the classical orchestra was the first synthesizer. Mozart, particularly in the later symphonies (after #25) and piano concertos (starting with #17), uses a great number of the possible instrumental combinations, mixing colors with gradient, chiaroscuro, transparency, and opacity, across the full sound spectrum.

I’ve used parentheses to indicate the possibility of employing solo instruments or divisi within sections; take these into account and the true number of instrumental combinations becomes astronomical.

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Books Chords Composition Tools Inversions Permutations & Combinations Quartal Harmony Tetrachords Uncategorized

Two New Books!

Three & Four-Note Chord Compendiums: Permutation-Based Harmony Workbooks for Guitarists

I’m excited to announce the publication of two new books, both available worldwide on Amazon.com!

Three & Four-Note Chord Compendiums: Permutation-Based Harmony Workbooks for Guitarists

The Four-Note Chord Compendium is the first mathematically-complete book on four-part guitar harmony ever published. 

Nearly 400 pages in length, it contains 5,535 unique chord forms for analysis and exploration: every possible combination of four notes on the instrument.

Also included: suggestions for fingerings, practice approach, and harmonic analysis.

An all-encompassing encyclopedic text, and an essential part of every guitarist’s reference library, this permutation-based workbook will enable you to:

  • Explore all of the possibilities for four-part harmony on the guitar
  • Develop a personal harmonic language through the discovery of unique chord voicings and harmonies
  • Improve analytical skills
  • Expand your harmonic palette exponentially
  • Reinforce your current knowledge base by the comprehensive review of four-note chords and arpeggios

Price: $29.99

Available exclusively from Amazon.com. Please click here to view samples and purchase on Amazon.com


The Three-Note Chord Compendium is the first mathematically-complete book on three-part guitar harmony ever published. 

Over 150 pages in length, it contains 1,820 unique chord forms for analysis and exploration: every possible combination of three notes on the instrument.

Also included: suggestions for fingerings, practice approach, and harmonic analysis.

An all-encompassing encyclopedic text, and an essential part of every guitarist’s reference library, this permutation-based workbook will enable you to:

  • Explore all of the possibilities for three-part harmony on the guitar
  • Develop a personal harmonic language through the discovery of unique chord voicings and harmonies
  • Improve analytical skills
  • Expand your harmonic palette exponentially
  • Reinforce your current knowledge base by the comprehensive review of three-note chords and arpeggios

Price: $19.99

Available exclusively from Amazon.com. Please click here to view samples and purchase on Amazon.com

Categories
Arpeggios Chords Composition Tools Melodic Construction Permutations & Combinations Scales Tetrachords Uncategorized

Complete Tetrachord Combinations: Major, Melodic Minor, Harmonic Minor, & Harmonic Major Scale Harmony

This post explores all of the possible tetrachords (four-note combinations) in Major, Melodic Minor, Harmonic Minor, & Harmonic Major Harmony.

(Download the accompanying PDF at the bottom of the post.)

These exhaustive lists may appear too information-packed to be useful. (There are 840 combinations per scale.)

I suggest dipping into them occasionally to more deeply explore the vertical (chords) and horizontal (melody) aspects of their all-important parent scales.

You’ll find every standard approach to chord voicing contained herein, as well as many uncommon sonorities.

Some structures may be impossible to play as chords unless one or more of the tones are raised an octave.

Experiment with the lists, and you’ll discover many new things about these commonly-used harmonic palettes (scales).

Below are a few examples of how the lists can be used to create chords and arpeggios (taking some liberties with octave placement and contour):