Excluded by Peers

I have been reading and composing a review of The Mathematics of Music by John O’Sullivan. (Available at Amazon ) This book is a view into one man’s exceptional journey into the intricacies of Just Intonation musical relationships. John explains the history of the development and then the short comings of the current 12 equal system. After defining the problem John then applies a rigorous method that he derived empirically by categorizing a very large number of musical intervals. With this categorization John developed equations that matched his perception of the consonance of melodic notes, dyads, and chords.  John’s goal is a system that produces more consonant  chordal possibilities and relationships than the current Western 12 equal tuning.   John thoroughly describes his new set of chords and a mathematical test to gauge varying shades of major and minor harmonies and melodies.  I plan to do an unusual multi-part review of John’s book facilitated by compositions using the “Blue” tunings and theory presented in The Mathematics of Music. This is in part because the true worth of John’s ideas are what meets the ear and also as a means for me to deal with time constraints and commitments imposed by real life.

To that end, this is my first piece in a O’Sullivan tuning called “Excluded by Peers”. This piece uses John’s Blue JI tuning that I put into scala as a series of JI ratios. Since I am using a keyboard and not a guitar it is natural for my starting note for the tuning be C and this is what I did.  In using the tuning I noticed that it was, in my experience, more flexible then many other JI tunings I had tried.  The only triads that sounded iffy to me were E major, F# major, and F# minor. However, playing the devils advocate I improvised a piece of music in the key of C major that actually featured the F# tritone as a borrowed tone from E minor.

You can hear it here:


The scala file I created from the ratios in John’s book for Blue JI follows:

! C:\Cakewalk\scales\blue-ji.scl
Blue JI

3 Responses to “Excluded by Peers”

  1. Robin Perry says:

    Nice piece, Chris. Thanks for sharing.

  2. […] a large difference between the two tuning systems, that being Just Intonation (see Excluded by Peers) and this tempered (or compromise from Just) system. The scala formatted file is […]

  3. Michael Kasper says:

    Dear Chris,

    I really like the O’Sullivan tuning and the way you weaved it. It carried through in many beautiful directions. I really liked the way this piece sounded and the mysterious of it. Amazing work!



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