I like really far-out alien tunings (like the ones I used on The Moses of Stuttgart) but there's also a place for tunings that are grounded in something more familiar. One idea I've used in the past is the melakata tunings, which turned out to be pretty fruitful for me. I recently watched a really good Levi McClain video that gave me a hint about how to expand this idea.

Here's the video -- I'm not going to repeat what's in it but it's not a prerequisite for understanding this post, which will go at a similar idea in a different way:

In particular, Levi's method produces 14-note tunings but I currently only have access to traditional piano-style keyboards so I like to stick to 12 notes, which leads to a slightly different approach.

Because of the black/white dichotomy on the keyboard, it's very easy to think of the 12 notes in an octave as being divided into a group of 7 and a group of 5 that interleave with them. The "double mode" idea as I'm interpreting it is actually very simple: map a 12EDO mode onto the white keys and use each black key as a consistent "alteration" of one of its white neighbours. The alteration is usually going to be small, which creates a very specific aural effect.

I'll refer to this effect as "shimmer" (Levi does the same). This isn't a precise term as far as I know, just an attempt to describe the psychoacoustic effect of the beat frequencies you get between notes that are close together in pitch. Ordinary semitones have shimmer, but you could say smaller intervals have more of it. And it isn't only present in small intervals: because overtones are a thing, almost all intervals have some degree of shimmer.

C Ionian Shimmer 38

Here's a simple example. We leave the white keys alone and map each black key to 38 cents above the white key directly below it (38c is approximately one step in 31EDO). This gives the scale Levi talks uses for most of his video, but with two notes missing (the black notes that would be between E and F and between B and C, if they existed). Here's how it looks in Pianoteq:

Playing all white notes is just C major; all black notes gives F# major pentatonic, but raised by a little over a third of a semitone. The really interesting things happen when we start mixing black and white notes, which of course we can do by playing the fingerings of any of the scales we already know. The closer we get to using an equal mixture of white and black notes, the more "microtonal" the result will sound.

In this tuning you might expect the spiciest major scales to be Ab, A, Eb and E, since they have the largest number of shimmer intervals. But are they? If you play a scale like F major or G major, you'll probably find the single shimmer quite disconcerting. In fact, a lot of experimentation is needed to find the "smoother" and "rougher" scales in this tuning but there's a wide range there.

Note that although we started with C Ionian, there's no reason why you have to play major scales in this tuning. You can play harmonic or melodic minor, whole tone, diminished or any of the fancy exotic scales this blog is full of. Think of a tuning like this as deforming each of those scales in a very specific way. It's like projecting different images on a curved surface instead of a flat screen -- the surface stays the same shape but the effect on each image is a bit different.

Variations

There are two obvious ways to vary the recipe to create new tunings.

One is to change the shimmer interval from something other than 38 cents. Of course there's an infinite number of ways to do this in theory, but in reality we're limited by a couple of things. First, very few people can hear pitch differences smaller than 1 cent, so meaningfully different tunings should have their shimmer intervals at least 1 cent apart. Second, if we go up by more than 99 cents we're doing something a bit different. So there's probably only 99 possibilities, and of those a much smaller number that might be practically useful to have on hand.

The other parameter we can vary is what scale we assign to the white notes. This can be absolutely any heptatonic scale, of which of course there are many. Every choice will yield different effects for all the various scales whose fingerings you play while in that tuning, producing a really staggering number of possibilities.

Scala files for these are easy enough to create by hand with a text editor but I decided to mass-produce some to make them easier to play around with -- you can find 175 example shimmer tunings in the scala folder of my scales project on GitHub -- if you don't know how to use the site there are instructions for getting the files at the bottom of the page.

Practical Approaches

This is another one of my projects that reveals a staggering range of superficially-similar possibilities that can be hard to get oriented in. A place to start is to think about where the (almost-)perfect fifths fall. Those are the pairs of notes in the tuning that differ by exactly 700 cents. These will tend to stabilise each other and be heard as "centres of gravity" for the scale. The number and distribution of fifths depends only on the white-note scale, so this is something we should investigate more fully in a separate post.

As an example, let's look at putting Superaugmented on the white notes and using a shimmer interval of a sixth-tone (33 cents). Here's what the Scala file looks like:

!
!
Superaugmented on white keys with 33 cent shimmers on black keys
 12
!
C# 33
D 100
D# 133
E 200
F 500
F# 533
G 700
G# 733
A 800
A# 833
B 1000
 2/1

This has 12EDO fifths between the following pairs of keys on the keyboard: CF, CG, C#F#, C#G#, DA, D#A#, EG, FB, so 8 pairs instead of the 12 we usually have (in 12EDO every note has a fifth above it!).

Now let's suppose we want to play some major scale fingerings with this tuning in place. For example, if we pick Eb major (Eb-F-G-Ab-Bb-C-D) we have only three fifths: CF, CG and D#A# (respelled as EbBb). That's not many compared to the six we usually have, but note that EbBb is there, so the Eb note does have a fifth to stabilize it. It seems like Eb, F, G, Bb, C will all be important notes and we could think of them as forming a pentatonic subset that's the "core" of this scale.

On the other hand, if we play C# major (C#-D#-E#-F#-G#-A#-B#) our fifths are C#F#, C#G#, D#A# and E#B#. Apart from the last set this covers all and only the black keys, giving us an ordinary pentatonic scale there, with the C and F on the white keys forming their own little fifth a sixth-tone offset from the rest. In this scale every note has a fifth above or below it and that common, 12EDO pentatonic makes the overall vibe much more tonal then the previous example.

I think this is a decent way to get started with one of these tunings -- find the pairs of notes that stabilize each other by being a fifth apart and you have a very immediate way to hear what's going on in the structure of the tuning. Of course it's also worth listening to the shimmering effect of the "imperfect" fifths -- in the example tuning, that those that are a sixth-tone sharp or flat. They have their own character that becomes easier to hear in the context of the tempered fifths they sit alongside.

Finally, as with the Melakata tunings, you can always go back into 12EDO simply by playing in C major, restricting yourself to the white notes. The black notes become subtle alterations to five of your base pitches that can be used expressively. This is the "basic" approach but it can be a comfortable basecamp from which to explore this exotic landscape.

To finish, here's a performance by Gamelan Semara Ratih -- although these microtonal effects are found in musical cultures all over the world, Bali really seems to me to be the epicentre of shimmer:

(The image at the top of this blog is by Roberto Lopez via Unsplash)