What is a musical scale? What is a "mode"? How many scales are there and what are they like?
This course presents some notions from pitch class set theory that are useful in thinking about these questions. From the standard ideas in the first session it develops themes related to scale classification that are the subject of current research. As well as presenting theoretical ideas "in the abstract", the course makes practical connections with the real-life musical activities of learning and making music with scales.
The course takes the form of three illustrated video lectures. A thread for questions and discussion pertaining to each lecture will be created in /r/guitarlessons. Additional printed material can be found in the author's books, all of which are available free online.
a. Pitch, notes and pitch classes
b. Definition of a "scale"
c. The numbering system
- The Space of All Scales
a. Binary representations of scales
b. Counting scales
c. Some classification methods and their applications
- Subsets and Supersets
a. Harmonizations of scales
b. "Spectral" analysis and its applications
The course is largely self-contained, since everything is built from the ground up, although if the student knows nothing about music the pace will most likely be too fast. I assume you have some experience of playing a pitched instrument in some Western tradition (classical, pop etc). You need not be a competent player or be able to read music.
A note to music theorists is in order. I've tried to provide a non-rigorous introduction to the subject, not a college-level course. That means I've sometimes allowed myself some hand-waving in the interests of keeping it accessible and moving along at a reasonable pace.
A note is also in order for practical musicians. The course doesn't teach you how to apply specific scales in your chosen style of music. By the end of Session 3, though, I hope it will have given you some useful tools to help you do that.
The difference between a pitch, a note and a pitch class. Octave equivalence. Pitch class numbers. Transposition invariance of scales. Definitions of "scale". Interval maps. Modality and the definition of "mode".
Binary representations of scales. Simple examples of binary operations (inversion and complementation). How many scales are there? Cardinality, interval composition, modality and symmetry as classificatory attributes. Hamming distance and other metrics (mentioned only).
"Harmonization" of a scale at the root position. Some very basic notions from chord-scale theory. Applications of subsets and supersets of scales; generalisation of these ideas.
Although "scale theory" is a somewhat marginal topic in the academic world, almost all of the topics covered on the course are standard and have been in the musicological literature for at least forty years. In one or two places I'll present an idea that I believe to be either original or stated in a non-standard way; I'll give an explicit warning when that happens.
Some representative sources for the course are the following. They're a bit of an odd mixture, and most assume a technical background in music theory that this course doesn't. You do not need to buy or read any of these books to follow the course.
- Forte, Allen, The Structure of Atonal Music
Keith, Michael, From Polychords to Polya
Lewin, David, Generalized Musical Intervals and Transformations
Nettles, Barrie and Graf, Richard, The Chord-Scale Theory and Jazz Harmony
These texts represent very different approaches and this course only presents (at most) a few ideas from each, but they might give some idea of where it's "coming from" to students who already know a bit about the subject.
The instructor is primarily a guitarist and anticipates that a majority of students will be as well. Nothing in the course, however, is guitar-specific and players of other instruments are very welcome.