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Just Intonation, Part 6: Synthesizers You Can Tune

In spite of my fond hopes, this page is doomed never to become an exhaustive survey. The original version (retained below) referred entirely to hardware synthesizers. By late 2005, however, the picture had changed considerably due to the ready availability of software-based synths. In particular, a number of synths that don't provide their own microtuning implementation can load tunings in the Scala format. In addition, Native Instruments Absynth has very good tuning tables of its own.

In the early days of synthesizer development -- say, in the 1980-85 era -- manufacturers didn't yet have a clear idea what musicians would want. A number of odd features were trotted out, greeted with a collective yawn, and allowed to vanish from the marketplace. Remember polyphonic key pressure? Ensoniq championed it tirelessly, but nobody else paid much attention. Today Ensoniq no longer exists as a separate company, and poly pressure seems to have vanished right along with it.

Tuning tables haven't suffered quite as drastic a decline, but I wouldn't say there's a burgeoning interest in them. Which is a shame. Most synths today, if they have tuning tables at all, limit them in some unnecessary ways. But since nobody is paying much attention to tuning, manufacturers don't have much incentive to provide better tuning tables.

Broadly speaking, you'll find three types of tuning implementations in the MIDI world (with some overlap and some gray areas):

• Preset tunings, usually historical. Some inexpensive tone modules, from Yamaha and other companies, have a selection of these.
• Octave tuning tables. These allow you to tune each of the 12 notes in the chromatic scale up or down in fine increments. Usually the maximum depth of the retuning is only +/- a half-step for each key.
• Full-range tuning tables. These have a separate entry for each of the 128 notes in the MIDI key range. Usually each note will have both coarse and fine tune parameters, allowing it to be tune up or down across the entire pitch range of the synth. This is ideal for exploring some of the outer reaches of just intonation, as well as other tuning systems.

The preset tunings are mildly interesting, but they don't usually come with good documentation to tell you exactly what the nature of the tuning is. I'll have nothing further to say about them. To explore just intonation, it's really essential to have a tuning table that is user-programmable.

Another resource for microtonal exploration is keyboard scaling. This lets you stretch or shrink the keyboard so as to put more or fewer notes in every octave. Keyboard scaling will only produce equal-tempered scales, however, not just tuned scales, and it often isn't implemented well enough to do a decent job of that, so I'll ignore it in this tutorial as well.

Octave tuning tables have been found, I believe, on most of the professional-model Korg synths since the M1. (Some of their less expensive synths may omit them.) The Kurzweil K2000/2500 series also has an octave tuning table. Roland traditionally ignored tuning tables (let's use the abbreviation "TT"), but in the last couple of years they've added this feature to some new instruments. There is an octave TT in the JV-2080 module, for instance -- but I don't believe the JP-8080 modeled analog synth has one. Nor do any of the new modeled analog synths coming out of Europe, as far as I'm aware.

I've seen one or two synths (can't remember which ones) that let you store a TT with each patch. Most have the TT in their global programming area, which means it's either switched on or switched off for the entire instrument.

The trouble with an octave TT is that it embodies two or three assumptions that may or may not hold true for the music you want to play. First, it gives you only 12 notes per octave. Some just tuning systems need more. (Laying out a 16-note octave on a conventional MIDI keyboard is likely to be a stumbling block for live performance, but if you're using a sequencer, the stumbling block disappears.) Second, an octave TT will always repeat the same tuning in every octave. Third (and here I'm floating off into outer space just a bit) such a TT assumes that you want to use the octave as one of your intervals. The octave is fundamental (pun intended) in every tuning system I'm familiar with, but that doesn't mean it's inevitable. A just intonation system based on a series of minor sevenths stacked on top of one another like a barber pole, for example, can produce some exotic effects. Or you might want to set up a Pythagorean tuning based on an ever-rising series of perfect fifths. Either of these tunings might include some perfect octaves, but without repeating a uniform set of intervals at the octave.

The only current hardware synths I'm aware of that have full-range TTs are the E-mu Proteus 2000 line. The Proteus has 12 of them, in fact, which is a testament to the low price of RAM. (First-generation Proteuses had some preset tunings, including 19-tone equal temperament -- which is a very interesting tuning, by the way -- but no user-programmable tunings.) The Proteus 2000 is a great-sounding synth as well; if you're seriously interested in exploring microtonality, it may be the best deal going.

Yamaha's DX7II line also allowed full-range tuning. My memory is vague, but I'm not even sure the DX7II had an internal TT. You might have had to plug in a memory cartridge to create a user tuning. If you can find a used Yamaha TX802 in good condition, though, grab it. This rack module has a full-range internal TT, and can store up to 63 tunings on a cartridge -- and the clean sound of FM synthesis is ideal for microtonal music. In general, you may find that sounds with less internal animation than the typical "rich," "fat" synth sound work well for just intonation, because they allow you to hear the intervals more clearly.

In principle, any full-featured sampler can be tuned to just intonation, because you can assign a separate sample to each key and then tune each key up or down as needed. (Note the qualifier "full-featured." Some of the newer dance-oriented samplers are not set up to allow this type of thing.) However, there will likely be no way to export your tuning from one preset to another. Each time you want to try another sound, you'll need to set up the tuning again by hand. Because of this limitation, I wouldn't recommend using a sampler to play just intonation music unless you're seriously masochistic or have enormous amounts of free time on your hands. And if you're in that category, there's a much better solution: Csound. This software language for sound synthesis can produce any tuning you can imagine. Not only that, but it's free.

Speaking of software, most first-generation softsynths have been limited to 12-tone equal temperament, but that's starting to change. Native Instruments Absynth has quite a large variety of factory tuning tables, and as of version 2.0 it also has 128-note user-programmable tuning tables. User tunings are not terribly difficult to set up in NI's mammoth Reaktor program. If you're a Reaktor owner, you might want to try either of these Ensembles, which I created myself.

The usual resolution of the fine-tune parameter in a typical TT seems to be from -64 to +63. If the TT allows you to tune the note up or down by a half-step, this works out to a nominal tuning resolution of about 1.56 cents. (A cent is 1/100 of an equal-tempered semitone. Since the equal-tempered semitone is based on an irrational number, so is the cent. Because of that, it doesn't really make much sense to talk about just intonation in terms of cents.)

1.56 cents is not quite fine enough resolution to do a really good job of producing just intonation: You'll still hear slow beating in intervals that shouldn't beat. But it's not too bad. [In a conversation with Robert Rich in March of 2001, he suggested a tuning for which this resolution is very inadequate: an overtone tuning in which the 61 keys of a MIDI keyboard are tuned to a low fundamental and its first 60 overtones. When higher intervals are played in this tuning, the difference tones between the sounds won't resonate well with the fundamental unless the TT has better resolution.]

Bear in mind, also, that I used the word "nominal" in reference to 1.56 cent resolution. The actual resolution of the TT may be less, and it may be irregular. Due to the nature of digital synthesis, the tone-generating algorithm may have to do a little mathematical rounding, either up or down, at some settings. For instance, the D in the tuning table might sound the same with settings of +33 and +34. There's no way to figure out exactly whether or where the rounding takes place, and no way to compensate for it if it is taking place. In fact, I've never read any technical documents on the subject; I'm assuming rounding occurs because when I retune my Korg 01/W, I can hear imperfections that seem to be due to this type of rounding.

By the way, if your synth includes a distortion effect, be sure to try using it after setting up a just tuning. When you play a just major third, the usual grinding sound of a distorted major third will be gone: You'll hear a much smoother sound.