The purpose of this book is to provide a combinatorial way to contextualize and rationalize all possible harmonies in music. I want to make it easier for musicians more easily make use of any harmony.
All Harmonies is a comprehensive list of all possible chords and scales (together here called harmonies) that can be formed using the twelve pitch classes of twelve-tone equal temperament (12-TET). In particular, it provides a systematic organization of the 12-TET harmonies according to both semitone evenness and evenness on the circle of fifths (called “stretch” in the book). The harmonies are listed in tables, beginning with 2-note harmonies and ending with the 10-note harmonies. Each harmony is presented on the treble staff, along with several of its features to provide the musician with a context for how to use it. Some of these features include: orientation, whether it is ascending or descending (harmonic dualism notion); evenness, how spread apart its pitch classes are within the octave; and stretch, how spread apart its pitch classes are around the circle of fifths. To provide further context for scales (harmonies with more than 4 pitch classes), a series of complementary triads is also included for each scale.
This book encourages organized exploration: each section begins with a summary table containing the harmonic interval patterns found in the section alongside blank space for note taking.
Release Date: August 13, 2021
NOW AVAILABLE in hardcover directly from the publisher at Lulu.com for under $59.99 CAD.
The book is also available in softcover through amazon, barnes and noble, and other large online book retailers shortly, however due to very high distribution costs, this version is more expensive (around $90 CAD) than the hardcover version through lulu.com. So, I highly recommend buying the hardcover version from Lulu. I also get a larger cut of the sale price from Lulu.
Technical Supplemental Document
As mentioned in the book and elsewhere, I am preparing a free downloadable technical supplemental document, which will be available here once finished. I have unfortunately been too busy finishing my doctoral program in mathematics to finish this. Your patience is appreciated.
Error Reporting
All Harmonies was a large project that took me about 3 years to complete, and while I did my best to be diligent in checking the information in the tables multiple times, some errors made it into the final version. I will post known errors here when I get the time.
If you find errors, go ahead and post them below and I will add them to the list.