Say you've written (or a bandmate as written) a tune that features a sustained Maj7b5 chord. What do you play over it? Probably you don't have standard vocabulary for this type of chord, and since it's unusual it's not likely you'll find many ideas by transcribing. So how could you quickly build coherent vocabulary?

This bit of analysis was prompted by an interesting question asked on the Music Theory forum on Reddit. It ended up as a question about which scales you can transpose and get a completely different set of notes from the set you started with, with no overlap.

I had an interesting question by email today that I thought was worth addressing here. The question was, how do you integrate Slonimsky-style patterns into a "target note" approach to improvising? I should say up-front that I don't do much of this myself, and the solution I've come up with here is just a suggestion for your own experiments: let me know what success you have with it and whether you discover any "hacks" or alternative approaches that make it easier.

Struck by a bout of insomnia, I decided to figure out all the 7-note scales that can be made by combining a pair of common triad or seventh arpeggios, one at the root and one somewhere else. Here are the results.

Here's a great excerpt from a Barry Harris workshop where he introduces an interesting diminished concept, which he (jokingly) calls his "personal scale". It produces a very cool jazz sound by a quite unexpected means. The video is a bit piano-focussed so I thought it might help some guitar players to have a summary from our point of view of the main idea.

There are seven major scale modes, which you can think of as major scales built on 7 different tonics suspended over a single root note. So over a C root we can play the notes from C Major (Ionian), Bb Major (Dorian), Ab Major (Phrygian), G Major (Lydian), F Major (Mixolydian), Eb Major (Aeolian) or Db Major (Locrian). But there are 12 notes in music; what happened to the other five? Step inside...

The Major 7 arpeggio (1 3 5 7) has many uses; it can be superimposed over harmonies in all kinds of ways and I use it a lot. If you flatten the fifth (1 3 b5 7) you get a new sound with different applications. Here I'll talk about some of the possibilities.

I've committed to delivering a free mini-course called "Introduction to Scale Theory with Applications", starting in February 2013. The course will cover a lot of ground and if you're registered during the time it's going on I'll be running Q&A / discussion threads alongside the video lectures. If you come too late you can still watch the videos and drop me a line on Reddit if you need help. Now, I suppose I'd better get down to writing the lectures...

I've been experimenting with drawing graphs of scales for a while now, and have a few ideas on the subject; maybe even enough for an ebook one day. I'm particularly pleased with my latest batch, some selections of which I thought I'd share with you here. Consider them your Christmas present, valued reader.

Just wanted to say that with the launch of Spectral Analysis of Scales, downloads of my three ebooks have whizzed past 20,000 since the first one came out nine months ago. Many thanks to everyone who read one or more of the books and helped spread the word; rest assured there's more in the pipeline for 2013!