Wow, it’s been a long time since I wrote a post on here.
Over the intervening months and years I have thought several times about writing a book, or several books, and have made some small attempts towards that goal, but thinking more and more about the age we’re living in, the way we communicate and consume media leans heavily in favour of those which are internet friendly, bite-sized, and interactive. So I’m deciding to start a blog, which will hopefully document what I would like to do as a music educator. Some of it will be focused on my piano teaching, and what I do day to day (I teach in a few schools at the primary, intermediate and high school level, but more and more of my work is as a private teacher in students’ homes), and some of it will be focused on my xenharmonic/microtonal pursuits – what I have learned about tuning, how it applies to music, how musicians of any level can use it to make interesting music and to connect the dots between music, art, science, creation and analysis.
I’d like to explore both the fundamental elements of music (for beginner and intermediate musicians) and also the more specialised area of tuning, how it affects melody, harmony, timbre, technique, interpretation, style, notation, instrument design, and general musical thinking. It is interesting going down the road of teaching music from a tuning-agnostic, or tuning-variable point of view. If we are fully agnostic, it’s pretty hard to allow the use of any exact interval, but to appeal to the largest number of people and to make most of the huge corpus of existing music available for us to relate to I will be using some structures that most practicing musicians already know, and simply expanding their meanings to include what might happen outside of 12-tone equal temperament (12TET).
I’m not into telling people who have studied for years to “wipe the slate clean”, and so most of what I do microtonally can be understood through the lens of the everyday musician, or at least, I’d like to think so. I also want to make this intuitive to grasp, and interesting enough to spark creative exploration on the part of the reader (you). Feel free to ask any questions. I’m not much of a writer, so if there’s anything I can clarify, let me know. I have read some fantastic books which deal at least a little with tuning and how it can affect other musical elements. I’d like to try and inspire in a reader a fraction of what Helmholtz’ On the Sensations of Tone or Partch’s Genesis of a Music or Mathieu’s Harmonic Experience inspired in me, and try to stay true to my own direction at the same time. This is probably not a how-to guide on tuning of every kind, but hopefully it will be enough of an introduction to ideas which can be interwoven with common practice music theory.
Before I start my first post proper, maybe I should try to answer the question, why bother with microtonality? Many practicing musicians hear words like microtonal or alternative tunings and think something along the lines of I’m doing pretty well with the tuning I’ve got, why would I want anything different? It already sounds fine, and I wouldn’t know what to do with any extra notes…
Thinking about tuning is just like thinking about any other element of music, it opens up a whole lot of doors into expression, the sorts of sounds and structures one can use, and I think it deserves as much respect as other variables which are taken for granted – style, form, timbre, texture, rhythm, etc. Not many musicians would submit themselves to an entire career playing music of one rhythm, or of one texture, or using one timbral colour, but so many musicians never have the doors opened to tunings outside 12TET, to the universe of other possibilities. It’s like the 12TET system is a planet, supporting all sorts of landscapes and forms of life, but it is still just one equal temperament (among the infinite, let alone the families of linear and higher dimensional regular temperaments, and all their irregular cousins, and of course, just intonation and its countless possibilities for pitch). Who says other planets out there don’t support life?
So many interesting things can be done only in particular tunings, and some of that has been very well explored in 12TET. Most of these features are not taught to musicians as features of the tuning system, but as musical facts. Here are a couple of them:
a chain of 12 perfect fifths is equivalent to 7 perfect octaves, so a “circle” of twelve equally sized perfect fifths can be made, and modulations can be made around the circle. F# and Gb major for example, become the same pitch, and therefore the same key, and the difference between them is lost, except in the notation.
a chain of 3 major thirds lands us at a perfect octave. This means we can have symmetrical augmented harmonies and melodies.
a chain of 4 minor thirds lands us at a perfect octave. This means we can have symmetrical diminished harmonies and melodies.
stacking two identical major seconds lands us on the sweetest major third, close to the simple ratio 4:5.
in a dominant seventh chord, the interval between the third and seventh is equivalent to its inversion, the interval between the seventh and third. This allows progressions where tritones hold and the rest of the chord moves around, and allows tritone substitution without modulation.
Following these four harmonic paths in just intonation leads to four distinct pitches, and none of those are the same as where we started (for those interested, the small resultant intervals have names too – respectively, the Pythagorean comma, the diesis, “major” diesis, Dydimic or syntonic comma, and the jubilisma, though I had to look up that last one!). More importantly, there are tuning systems that share these features, and we can group them in families, e.g. those which make the above intervals into unisons, or “temper out” those intervals. The temperament families referred to above would be pythagorean (12, 24, 36, 48, 60, 72, 84, 96), augmented (3, 6, 9, 12, 15, 18, 21, 24), diminished (4, 8, 12, 16, 20, 24, 28, 32), meantone (12, 19, 26, 31, 33, 43, 45, 50), and pajara (10, 12, 22, 24, 32, 34, 44, 46). I decided to give a few equal temperaments belonging to each family so you get the idea that these features are adopted on some planets, but certainly not all. Laws governing musical life are not the same everywhere in the universe. And in fact any musical universe can be dreamed up, based on any rules, or even a lack of such rules, to give any kind of imaginable structure or chaos.
There is also the (not so small) matter of sound. This is the real point for most microtonalists. Numbers are there for those interested, and I can certainly get carried away with them (as seen above) but music really should be about sounds, and the expressive capabilities gained when tuning is a flexible parameter are not insignificant. One can hear the subtle differences between string quartets playing with near-pure fifths and wide major thirds (often sought after for expressive melodic playing) vs those playing with near-pure thirds (great for music full of rich major and minor harmonies), or how a harpsichord reacts differently in 12TET vs in a good meantone or well-temperament for period repertoire. More often than not one also achieves different kinds of timbres, different kinds of harmonies, different kinds of melodies when playing for extended periods in different tunings.
Sorry, got a bit carried away on this first post. Will try to make the next one a bit more focused on exploring one topic at a time. Might write a bit about the three keyboard layouts I use, the reasons we have them and why they’re important, at least in my musical explorations.
Thanks all for following along. Hopefully back soon.
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