Saturday, June 07, 2014

Myhill's property etc.

I am trying to get my head around this idea in the context of the diatonic scale (diatonic collection).   First, I hope I am beginning to understand the definition, in terms of c- and d-distances (just stating that there are two possible intervals for each "generic" interval does not really explain it for me.)  Next, what is its importance? Coming from a jazz perspective, I feel it somehow exemplifies the importance/interaction of the diatonic collection and "melodic minor collection" in jazz and perhaps other music forms.
If anyone reading this has any idea what I am talking about, please comment and help me out!

2 comments:

admortembibendum said...

Hi Peter, Can you provide some links to the references that you mention in your post? Thanks, David from the Shoefactory course.

Peter Houtman said...

Hi David
My info is from various sources, but the basic stuff on pitch-class intervals is on Wikipedia etc. A good book on the basics is Foundations of Diatonic Theory, by Timothy a Johnson (2008), if you are interested. I also found this old link http://www.mta.ca/faculty/arts-letters/music/pc-set_project/pc-set_new/pages/introduction/toc.html, which I found very helpful. I have just bought Audacious Euphony by Richard Cohn (OUP, 2012), complex but very interesting. I’ve also subscribed to J Music Theory, which gives online access to all the older articles including some original source papers (John Clough and David Lewin are major players). Not much of this is specifically about jazz, and probably of no practical value for “the blowing”, and I’m only scraping the surface at the moment.