Ever had that musical crisis where you realise there are only 12 notes in music, and only so many combinations to use them? That crisis that nothing is original anymore and everything you have written has already been written?

Yeah we all get that at some point. It goes away when you learn that there are more than 12 notes in an octave.

These 9 tunings are for experimenters who want to push the boundaries of their own music. These aren’t necessarily the 9 best tunings ever, since there’s no such thing. (By all means, if you disagree then share your favourite tunings in the comments!)

Oh and by the way, the title of this post was a clever ruse; you can use these tunings on the guitar if you’re willing to pull out the frets and rearrange them differently on the fretboard. Check out Steven James Taylor, Jute Gyte, Cryptic Ruse, MonoNeon (on bass), Paul Erlich, ilevens, Dave Fiuczynski, Jon Catler, Microtonal Guitar Duo…

Now that you know we’re talking about real alternative tunings and not DADGAD, let’s begin…

22-edo/22-tet

If I had to stick with one scale for the rest of my life, it would be 22-edo. It has such a variety of sounds from the familiar to the xenharmonic. It also sounds amazing for solo piano music. What’s most interesting is that the familiar sounds (for example major and minor chords) don’t connect to each other in the same way, such that chord progressions necessarily make surprising turns while the individual chords aren’t necessarily xenharmonic.

You could also treat 22-edo as a superpyth temperament, so that it has a diatonic scale just like 12-edo but with one important difference – the major thirds are much sharper and the minor thirds are much flatter. So if you like jangly sounds, this is it right here. Oh and interestingly, the A# turns out to be sharper than the Bb, which betrays the intuition of today’s 12-tone musicians who would think of them as the same note.

Pajara temperament is another lens from which to view 22-edo. Paul Erlich wrote a fascinating paper on the decatonic (10-note) modes of 22-edo which relate to pajara. These decatonic scales are sometimes symmetrical around the tritone, and they use the harmonic 7th (think of a barbershop 7th ringing chord) as an essential part of the harmony. In fact, Paul’s decatonic modes see the tonic chord as a tetrad (4-note chord) instead of the usual triad. So it’s like music++.

Porcupine temperament (yes, these are all real and understood names used by tuning theorists) is yet another new tonality that can be accessed via 22-edo. In porcupine’s case, you can play a 7-note scale scale that contains 2 major triads and 2 minor triads, and these triads can also include the 11th harmonic (a fourth that’s a quarter-tone sharp, sounds amazing).

Bohlen-Pierce

You can’t get much more ‘alternative’ than this: let’s do away with the octave altogether and make a scale that repeats at the perfect twelfth (aka tritave). Then let’s fill the scale with ratios that only contain odd numbers.

Of course I’m talking about the Bohlen-Pierce scale, discovered independently by at least 2 different people.

You can even make a temperament of the Bohlen-Pierce scale by dividing the tritave into 13 equal parts. It sounds really good too, but not in the traditional sense at all. It sounds good in an alien yet harmonious, future-tonality kind of way.

Iceface Tuning

As the legend goes, the pianist Hidekazu Wakabayashi saw a woman in his dream. The piano she played was somehow different; each black key was tuned a quarter-tone sharp. And that’s how he discovered Iceface.

And to be honest, Iceface sounds as dreamy as its origins.

Centaur

Centaur is a 12-note just intonation scale discovered by Kraig Grady. Given that it has 12 notes, it works wonderfully when mapped on to piano keys, though a guitar tuned to this scale would probably require split frets (frets that don’t go all the way across the fretboard).

What makes Centaur interesting is the sheer variety of intervals it features. Despite the fact that the scale has only 12 notes, there are a whopping 50 intervals in the scale. The unevenness of the just notes is what contributes to the many different kinds of interval.

I’m reminded of those people who claim with wonder that the keys of the equal tempered scale all have their own unique identity. They’ll say things like, D minor is tragic and grave, but A minor is calm and tranquil. Of course, this may have been true some centuries in the past but in days of equal temperament it’s utter nonsense. The intervals in an equal-tempered minor scale are exactly the same whether it’s D minor, A minor or any other minor. For me it’s like saying that this chocolate bar is sweeter than the same chocolate bar moved a few inches away.

Well anyway, if you play a ‘D minor’ scale in Centaur tuning and compare it to the ‘A minor,’ you’ll notice a definite change in the intonation and thus a change in the expressive and emotional effect. The reason why is because a fixed set of just intoned pitches don’t allow us to get the same intonation in every key – something has to change. And for that reason, Centaur is a tuning you can study and play for a lifetime, still making new discoveries as you go.

Drone 86, from the music of the island of Anaphoria.

Madagascar

Something I’ve been using a lot in my own work recently. This is a scale that was suggested to me by Gene Ward Smith and I’m so glad he did. There are a host of temperaments related to the “island temperament” and they tend to contain at least two very xen chords.

The island chord contains the following 3 notes: 1/1, 15/13, 4/3. This is like an inframinor 3rd and a perfect fourth placed on top of the root note.

The Barbados chord contains the following 3 notes: 1/1 13/10, 3/2. It’s like an ultramajor 3rd and a perfect 5th placed above the root:

The barbados triad is of particular theoretical interest because, when reduced to lowest terms, it is the 10:13:15 triad. Thus, this triad is only slightly higher in complexity than the 5-limit 10:12:15 minor triad, which means it may be of distinct value as a relatively unexplored musical consonance. It is one of only a few low-complexity triads with a 3/2 on the outer dyad, some others being 4:5:6, 6:7:9, and 10:12:15. It works out to 0-454-702 cents, which means that it is an ultramajor triad, with a third sharper even than the 9/7 supermajor third.
http://xenharmonic.wikispaces.com/The+Archipelago

Madagascar like many of the other tunings from the Archipelago contains these chords. I’ve been using 313-edo as a tuning for Madagascar, and I keep going back to its amazing yet xen consonances.

Machine[6]

Machine[6] is a 6 note scale quite like a warped whole-tone scale with one important property: it contains 4:7:9:11 chords in abundance. This chord has a unique sound of its own; piquant but very solid. Due to the 11th harmonic it will sound dissonant to those who have listened to traditional music their whole lives, but trust me that it becomes very consonant after enough exposure to the sound.

The 11th harmonic is the musical equivalent of durian.

11-edo is an excellent and compact tuning for machine[6]. 17-edo also works.

1Hz-quantized 12-edo

Beating is an acoustical concept where mistuned sounds have a throbbing quality to them. When two frequency components are tuned to a perfect unison there is no beating. But when the two frequencies are out of tune, they will beat at a rate equal to the difference in their frequencies.

Beating can happen not just to the fundamental frequencies of notes, but also within the overtones in the sound. And since the standard Western tuning of 12-edo isn’t perfectly tuned, there is a mess of beating between the upper partials when multiple notes are played.

It seems that if you quantize each frequency to the nearest Hz, then the beating takes on an interesting property…

Listen to this piece by Kalle Aho and read his notes (below):

In this example, a progression of unforgiving sustained octave-doubled sawtooth chords (Csound) is played against a drum track (Native Instruments’ Battery 3). The whole thing is played three times with the following variations:

1. the frequencies are tuned to the conventional equal temperament. The swirling complex beating pattern of harmonics never repeats.

2. the equal tempered frequencies are rounded to the nearest integer number of Hz. The frequencies become harmonics of a 1 Hz fundamental and this results in a repeating beating pattern of 1 second (maximum length).

3. this time the frequencies are harmonics of a 2 Hz fundamental and the length of the beating pattern is .5 seconds.

Any set of steady tones can be tuned to a repeating period, for example detuned oscillators, equal tempered and microtuned pitches. The formula for quantizing the frequencies is simple to implement in a soft synth:

frequency_new=round(period*frequency_old)/period

This is true beat science. The beats are synced with the beats.

14-edo

14-edo is the division of the octave into 14 equal sized tones. 14-edo has the reputation of being the tuning that shouldn’t work, but does. If you look at it on paper, it just falls apart – flat fifth, major and minor thirds are way way out of tune.

But try and compose in it, and it turns out to be a vivid alternate-reality tonality. When I write in 14-edo, I always remember how easy it is to make interesting patterns and chord progressions. You can throw plenty of strange harmonic modulations into the mix, even chromatic melodies, and it just works.

Extended, infinite just-intonation

A veritable rabbit hole of musical exploration, extended or infinite just-intonation uses all the rational numbers as its pitch material. Since there are infinitely many of them, and they connect to each other in dimensionally-infinite ways, this music knows no bounds and thus is the realm of multi-armed gods.

Traditionally just-intonation is viewed as having some prime-limit or p-limit. This means, if the ratios in your scale contain prime factors including 2, 3, 5 and 7 only, then your scale is in the 7-limit because 7 was the highest prime used in the factorisation.

Example of a 7-limit just-intonation scale:

1/1 - no prime factors
9/8 - prime factors 2 and 3
5/4 - prime factors 2 and 5
4/3 - prime factors 2 and 3
7/5 - prime factors 5 and 7
3/2 - prime factors 2 and 3
5/3 - prime factors 3 and 5
7/4 - prime factors 2 and 7
2/1 - prime factor 2
Highest prime used in this scale: 7

A related idea is that just intonation scales can be conceived as a multi-dimensional space where each dimension corresponds to a prime number.

The prime 2 gives us one dimension to move along the scale, which is really boring. Prime 3 gives a 2nd dimension, so now you can move around on the 2- and 3- axis and musically interesting places open up. Prime 5 makes the scale 3-dimensional and offers vastly huger possibilities. Prime 7 makes it a 4-d scale and opens up vastly huger possibilities still…

If you’re still with me at this point, then it’s not a huge leap of the imagination to think of a piece of music starting at one point in pitch hyperspace and navigating itself to another place very far away, perhaps touching upon hundreds or thousands of different ratios along each way. Each ratio being a unique musical note. Movement along the familiar 2-, 3- and 5-prime dimensions offers musically recognisable direction, and the higher dimensions can be used for surprising and dissonant turns.

I can’t offer any musical examples for this music, but I leave it to you as food for thought.

Where to go next

2 microtonal scales for standard guitar
Make your own scales using Scala
VSTs which can be tuned to alternative scales
Download tuning packs to retune those VSTs
The Xenharmonic Wiki – the place to go for learning about xenharmonic/microtonal scales.