Ground's intro to tuning diversity

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NOTE: This article is incomplete. Audio examples and images are coming soon.

If you've been a musician for long, you should be familiar with the 12 notes:

A A#/Bb B C C#/Db D D#/Eb E F F#/Gb G G#/Ab (A)

If you're anything like me, you took them for granted for years. After all, why wouldn't you? No one has told you how these were chosen, that's just how music is. But the truth is, these notes are a centuries-long compromise based on lots of math and stylistic evolution. There are endless other valid ways to do it, some of which may sound a little odd at first, but it's just because you've only been exposed to one tuning system for most of your life. In order to fight this monopoly on music, it's important to step out of your comfort zone.

Let's take a look at the piano keyboard. 12 keys per octave, and the steps between them are all the same size. We call that 12edo, short for 12 equal divisions of the octave. There 7 white keys and 5 black keys. For reasons that aren't important to explain now, 7 and 5 are very important numbers to our diatonic musical practice, with the major and minor scales, and the circle of fifths. So we can add 7 to 12edo and get 19edo. With these extra notes, suddenly sharps and flats aren't the same anymore:

A A# Bb B B#/Cb C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab (A)

The diatonic scale works exactly as you'd expect. Because sharps and flats have been notated separately as a historical vestige, you could play any sheet music in 19edo if you wanted, but it sounds a little different. It's a bit softer and mellower, and the fifth is flat. It may sound jarring, or it may sound even better than 12edo. And because of these extra notes, there's a new scale related to diatonic that you've probably never heard before. This is semiquartal, and instead of being mellower, it's harsher and has two extra small steps. It's full of this interval called the semifourth. As the name implies, it's half of a perfect fourth, and it's also halfway between a whole tone and a minor third. Just this adds so many new possibilities to fit intervals together to achieve new musical moods.

Now instead of adding 7 to 12edo, let's add 5. This gives us 17edo, and it's sort of a mirror image of 19edo:

A Bb A# B C Db C# D Eb D# E F Gb F# G Ab G# (A)

In 19edo, A# is below Bb; in 12edo, they're equal; and in 17edo, they're reversed with A# above Bb. 17edo is sort of a mirror image of 19edo. The diatonic scale is now harsher and more articulate, and the fifth is sharp, but there's a new scale called mosh' that's softer. Mosh is full of xneutral intervals such as the neutral third, halfway between a major and a minor third.

You can keep finding new tunings like this just by adding 7 and 5:

• 19 + 7 = 26edo,
• 19 + 7 + 5 = 31edo,
• 17 + 7 + 5 = 29edo,
• 17 + 5 = 22edo.

But you can also do more interesting things. Let's take a look at a tuning that's just 3 times 5, 15edo:

A ^A vB/vC B/C ^B/^C vD D ^D vE/vF E/F ^E/^F vG G ^G vA (A)

Being only a multiple of 5 does weird things. The fifth is very sharp, to the point that the semitones disappear. It's possible to notate the result in many ways, but I'm using ups and downs notation, which unfortunately means that reading this from sheet music doesn't really work. Despite everything saying this tuning should sound awful, the new chords actually sound pretty good. Instead of being based on a diatonic scale, it has several new ones:

• Blackwood, and
• several scales based on a temperament called Porcupine.