Friday, 23 March 2012

Ready, get Set, theory: Diminished perspectives 6

The thorny issue of writing diminished 7 chords into a minor 3rds stack has generated some conversation and is opening up a body of work that is being done under our noses: That is: methods to further understand and more deeply relate to the relationships between notes and chords—now we're calling them pitch collections, which has provided through this "Set Theory", a reasonable and more usable description of these relationships. Especially as applied to the diminished chord discussion under way in this blog.

My friend (he is possibly a mentor), Calvin Wong, a well known jazz musician about town who is a scientist by day and a pleasingly creative jazz pianist by night (and day too, no doubt), has some concerns about how the diminished was spelled and how it is used in diatonic tonality.

I quote:

            I liked your new post but aren't we just fitting a square peg in a round hole in forcing a non diatonic scale (and it's subsequently derived chords) into diatonic notation? Consider the asymmetry of the tritone stack that makes up the skeleton of the diminished chord. B-F is a dim5. F-B is an aug4. It's just the diatonic sequencing fails us. If we write a B symmetrical scale without repeating a diatonic note name, we're going to end up on Cb. If we write a B whole tone scale in sequence we have to end up on A## unless we skip a note. Diatonic note names only will work for 8 note scales. Sadly the scales that make up our dim chords (as well as our aug chords) as well as the subsequent chords will have to carry enharmonics or skipped intervals). Just because they aren't 8 note scales. imagine a musical notation where the interval between two note position on the leger actually reflected the actual interval. The problem is our notation has B-C written indistinguishable (for a non musician) from A-B.


I came up with this response from what I had learned from conversations with Dr. Bill Richards @ MacEwan University Music. Dr. Richards basically introduced me to set theory and I was fascinated but also wondered where it might be useful. My response to Cal Wong gave me a small eureka moment when I realized that this theory of pitch collections numbered like the clock was a good way to circumvent the problem. My response:

That's a timely observation Cal. Sometimes I confess I yearn for no chromaticism, but then again I don't like to "force" the square peg into the round hole but try only to persuade it. The articles I've been doing are just to outline the potential for chromaticism through the diminished structure and then perhaps later: augmented structure. In practical terms How something is played has a lot to do with success or failure in the application of this. I'm just trying to share my efforts in this area. It often comes down to context. The way I've been trying to add harmonies/extensions and density is a personal evolution in harmonic application. I've got plenty to learn about the niceties of voice leading and still strive to learn about that. 

The problem with notating diminished 7th chords is mollified by the real symmetrical inversion of these chords. I think historically at one time Cb and B were tuned differently which was truly audible. With the advent of the "Well Tempered Scale" championed by J.S. Bach and now the advent of the equal interval system imposed on the piano gives rise to an actual equality of the notes of the Dim7 chord which when combined with an equally "equal" interval set—(It sounds like you know this already). The practise of "Set theory" dispenses with note names and assigns the numbers of the clock to an ascending set of "pitch classes": pitch class "0" (i.e. 12) is C, pitch class Db (C#) is 1 and so on.... Using this Set Theory system, a "B" diminished chord consists of p.c. 11, p.c. 2, p.c. 5, p.c. 8 thereby eliminating the need to write so diatonically—granted this is often (as in my case studies) married to a diatonic system. It's my hope that this exploitation if you will, can be used in a tasteful way and add to the richness/colors of a musical painting. Sorry to go on but I do agree with you on this—it's just a direction/exploration and it is totally worth talking about and is especially applicable to the improvisation of chord voicings and melody using the diminished stacks etc. 


Like I said this opens up new exploration territory, not that I ever wanted to be a theorist but reading about the great body of work being done in this area by some brilliant people is encouraging. I was reading a Doctoral dissertation on John Coltrane and I can't believe that I don't own the Slonimonsky's Thesarsus Of Chords and Scales. I think I always intended to own a copy but never got around to it. I'm going to correct that asap. There's some high math being done in another dissertation that ties in with the Torus concept with one graphic using the cycle called: Spiral Array: cool. I'm not going to be looking for things to do.

The bottom line for most people when it comes to music is: do I like it? That can be intuitive for a music maker but if the intuition at play is informed, the chances are good for playing music for people to "like" it and that's what it's all about. It's about growth and understanding, and, it is really for our souls.


  1. Here's a couple of links that relate to this particular blog.

    Richard Cohn:


  2. Here's the link from the last blog.