Gibberish

Music has been described as a universal language. This is a nice way of saying that people all over the world play music. But as a practical matter, every culture develops its own music. When a European or American listener, steeped in pop or classical music, listens to a Balinese gamelan, the nuances of the language are entirely lost. We can tell that it sounds weird and exotic, but we don’t know what’s being said.

Certain aspects of our music perception, such as the ability to perceive and remember a series of pitches, appear to be innate. Other aspects are surely learned. If you’ve been raised on music in the European tradition, you’ll have no trouble following the logic of a I-vi-ii-V7 progression. To an Indian who had never listened to anything but the classical tradition of his culture (music for sitar, tabla, and so forth), this chord progression would have no meaning.

I’m still exploring, in a desultory way, the harmonic resources of 31-note equal temperament. The exotic intervals and bizarre chords are intellectually appealing to me — and yet, I’m not finding it easy to build up any enthusiasm for writing actual music using this scale.

The perception of the new pitch intervals in this tuning is not difficult to master. The problem, I’ve started to think, is that I don’t have

Tune Me Up

For microtonality freaks only — I gathered the information below for an article in Electronic Musician. It’s still available on their website, or was the last time I looked. But just to spread it around a little, I thought I’d include it here.

Scala is a terrific software resource for designing and analyzing any sort of microtonal scale you might dream up. But as a hybrid command line/GUI program, it’s a little twisty to use. Scala’s native file format has the .scl extension, but software synthesizers prefer to see microtonal scale files in .tun format. Scala can save a tuning in .tun format, but you have to know how to do it. Here’s how:

First, create a directory called tun in your Scala directory in which to store the new files. Load an .scl file or create a new tuning of your own using Scala’s features. Then, in the Scala command line, type the following commands:

cd tun
set synth 112
set map_freq 440.0 69
set middle 60
send/file filename.tun

The first line changes Scala’s output directory to the tun folder you’ve created. The 112 in the second line is a Scala code that sets it to output in the .tun file format, and the third line specifies the frequency in Hertz of a MIDI key (in this case, 440.0 Hz for MIDI note number 69, which is key A3); this key will be used as the reference or center of the tuning.

The fourth line sets the starting point for the range of frequencies defined in the .scl file. In this case, we’re telling Scala that we want 1/1 (the reference pitch of the scale) to be MIDI note 60, which is Middle C. In the last line, substitute whatever file name you like.

After the .tun file is saved, you can load it into your soft synth using whatever menu command the synth provides for that purpose.

Footnote: If you’re using Windows 7 and you’ve allowed the Scala installer to install the program in the default location (which is Program Files (x86)), you may not be able to save files to a directory within the Scala directory. For this reason, you may want to install Scala to the root of your C: drive.

The Microtone Zone

Having nothing better to do tonight, I searched YouTube for “microtonal.” I had never heard anything in 26-tone or 7-tone equal temperament, so I learned something. They’re both wildly exotic temperaments, and that seems to be part of the point — to do music that’s entirely free of any sort of grounding in familiar harmonies.

Schoenberg had that impulse too, of course, but he didn’t really understand how to get there.

I can’t help wishing that the music in those videos was better developed, though. The timbres, the recording quality, and the compositional gestures

Notes on 53ET

Had a quick look this afternoon at 53-note-per-octave equal temperament. This is reputed to be a very good-sounding scale, and it is. But its behavior is a little peculiar.

For those who arrived late, the octave-based equal temperaments that have especially good approximations of the intervals 3/2 (a just intonation perfect fifth) and 5/4 (a just major 3rd) are 12, 19, 31, and 53. Equal temperaments are useful because they allow you to transpose the music to any key. The intervals will all sound the same. This is not the case with tunings in just intonation, such as Harry Partch’s 43-note scale.

The fact that we use 12ET rather than 19 or 31 is not because it’s a particularly good scale — it’s rather crude, actually. It triumphed because

The Theory of 31

The theory of harmony in 12-note equal temperament is pretty interesting, and not terribly complicated. (I’ve written a book about it, in fact — Chords & Harmony is available from Hal Leonard Publishing.) Being able to talk about how chords are built out of intervals is useful, because it lets us describe what we’re hearing.

So as I put together little musical sketches in 31-note equal temperament, I’m starting to think about the theory. You can check out a few of these sketches on my channel at SoundCloud, by the way.

In 31ET, there are four “black keys” between each “whole-step” pair of white keys, and two “black keys” each between E and F and between B and C. Constructing a physical keyboard would be difficult, and if we did it we wouldn’t want all of those keys to be black. We could color them purple, aqua, citrus, and salmon, I suppose. But for theoretical purposes, talking about “G purple” would be silly. We need to find a terminology.

I’m calling the smallest intervals chroma-steps. The distance from C to D or from D to E is five chroma-steps. The distance from E to F or B to C is three chroma-steps.

We might want to call the first note above C “C high.” This would be followed, in order, by “C sharp,” “D flat,” “D low,” and finally D. The note immediately above a white key is “high,” while the key immediately below a white key is “low.” The note two steps above a white key is that key plus “sharp,” while the note two steps below a white key is that key plus “flat.”

We could conveniently abbreviate these: C, C/, C#, Db, D\, D.

One oddity of this system of nomenclature is worth pointing out. C# is below Db — but E# is above Fb. E# is the same note as F\ (F low), while Fb is the same note as E/ (E high). This may seem obtuse, but it preserves the correct enharmonic spellings: If we’re in the key of C#, the major 3rd of a C# major chord will be E#, just as we’d expect. And the 3rd of a Db major triad (one chroma-step higher than C#) will be F natural, again just as we would expect.

I haven’t yet started thinking about the nomenclature for the many varieties of triads and seventh-chords, let alone suspensions and stacked voicings. Maybe the triad C-E\-G is a low major triad. But what about C-E\-G\? That’s even lower.

The names of the intervals are a thorny enough problem. We can preserve the old terminology of modes and say that there is no such thing as a major fourth or minor fourth, only perfect, augmented, and diminished fourths — but we have to add high fourths and low fourths to the list. But that’s potentially confusing. If the interval C-F/ is a high fourth, then so is the interval C\-F. Maybe we should say they’re big and small rather than high and low.

The reason to toy with these ideas is simple: I’m making the sounds already. If I have some terminology, it will be easier to think about what I’m doing. Translating the physical layout of a 12-note MIDI keyboard onto a 31-note scale is challenging enough. If I’m going to play a chord made of stacked intervals 12 chroma-steps wide (octaves, on the MIDI keyboard), it will be useful to say “these are narrow fourths.”

More About Tunings

Thanks to the improved workflow in QuteCsound, it’s getting easier to experiment with alternate tuning systems. Also, I’ve learned a couple of tricks for organizing Csound scores.

While enjoying the pure sounds of just intonation, I’ve been realizing that I don’t actually mind 12-tone equal temperament (12ET, for short). It has a beautifully developed harmonic language, which is not the case with any alternate tuning.

Also — and this is a subtle point — with equal temperament, you always know where you are. If you’re composing in just intonation, arbitrarily tiny micro-intervals can flit around like gnats, and every chord root will tend to grow a different forest of harmonic possibilities.

Csound has a very nice opcode (cpsxpch) for experimenting with equal temperaments. So last night I thought I’d play around  little with 31-tone ET. 19ET and 31ET are notable

Fun with Microtuning

The latest version of u-he Zebra2 (2.3) adds an on/off switch for “voice drift.” This is great news for anyone who cares about alternate tunings. In earlier versions of Zebra, there was a small hard-wired random pitch variation from note to note, which made predictable microtuned intervals impossible.

Zebra2 can also load .tun files (which you can create using the Scala software), so the on/off switch had me salivating for about ten minutes. But then I started thinking (again, as I have often in the past) about composing for microtunable instruments.

The bottleneck of the Zebra/.tun implementation, which is inherent in the underlying MIDI specification, is the concept of a “scale.” A scale is an ordered series of frequency ratios. Typically, a scale repeats every octave (that is, at a 2:1 ratio). Scala allows you to define “octave” in other ways, and there can be an arbitrary number of steps in the scale, but whatever scale you define, it will contain the same ordered sequence of ratios, which will be used by Zebra or any other microtunable MIDI synth until you load a different scale.

If your scale has more than 12 notes, good luck playing it on a MIDI keyboard. This can be a real brain-twister.

Right now I’m leaning back in the direction of using Csound for composing with microtunings. Compared to Zebra and a MIDI sequencer, Csound is very slow and balky to use (though Steven Yi’s wonderful front end, which is called blue, speeds it up a bit). But with Csound, there’s no need to define a “scale” ahead of time. The precise frequency of each note can be separately defined.

This gives the composer enormous freedom. You can start a piece with one group of related frequency ratios and then, after writing a phrase or two, add notes with new ratios that weren’t in your original group. In Csound, you can easily define a scale if you want to, but you don’t have to. The composition can move through the infinite space of frequency ratios rather than being tethered to a scale that was chosen ahead of time.

This kind of freedom is what the creative artist needs. “I’m out of red paint” is not a good thing for the painter. In the same way, ”I need 45/32 for this chord, so I’ll have to load a different piece of software, create a new scale, copy it to the right directory, then delete Zebra from my project and add it again so it will load the new scale, after which I’ll have to edit the MIDI track because now my scale has more notes in it than before, so most of the MIDI note numbers will be wrong” is not a good thing for the composer.