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Informative videos about microtonal music on YouTube

I’m always keen to see how other musicians are creating microtonal music and the ideas behind their craft. For a few years now I have been building a YouTube playlist of microtonal music tutorials and explanations. As the playlist now has over 140 videos, it’s a good time to share these hours of content with others.

One thing that makes microtonality fascinating is that the newcomers are exploring new tonal structures that even the old masters haven’t heard of. But new or old, when a musician shares their insight in a video, I include it in the above playlist.

The playlist features videos from: Tolgahan Çoğulu, Adam Neely, Dolores Catherino, minutephysics, This Exists, Elaine Walker, Stephen James Taylor and others.

amsynth 1.8.0 adds support for microtonal tunings

Of all the software synths in the world, very few of them support microtonal scales. If you are a musician using Linux and open source software then your options are even fewer. It’s for that reason that I want to celebrate the news that amsynth 1.8.0 adds support for microtonal tunings!

amsynth is a virtual analog synthesizer that runs as a standalone or VST, LV2 or DSSI plugin. Its sonic characteristic is similar to other popular digital VA instruments – fantastic for leads, basses and stabby chords. It’s light on the DSP and the controls are very easy to understand, so amsynth will rightfully earn a place in my toolkit once I move my music production machine over to Linux.

Installing

The easiest way to get amsynth if you’re on a Debian-based distro is to add the KXStudio repositories and then install via apt. Assuming you already have the KXStudio repos on your system, simply run the following command:

sudo apt install amsynth

If you’re unable to use the above, download the source for amsynth 1.8.0 and build it.

Tuning amsynth

Once you have amsynth up and running, microtunings can be loaded by right clicking the interface and selecting a .scl file. In addition, you can load up a .kbm file for custom key mappings.

If you need some Scala tuning files (.scl) to play with, generate some with my Scale Workshop browser tool, or install Scala itself. Scala is extremely powerful, though you need to install it to your PC along with all its dependencies.

Full-keyboard microtuning

Developers, TAKE NOTE of what amsynth developer Nick Dowell has achieved here – .scl and .kbm formats are BOTH supported. .scl files specify the intervals in the scale, and .kbm specify the base tuning of the scale, whether it is A = 440 Hz or something else entirely.

Without supporting both of these formats, a synth could barely be said to support microtonal scales at all. I’m so pleased that amsynth gets this right.

The future

Judging by this page on amsynth’s GitHub, it looks like amsynth may become cross-platform in the future. Should this ever happen, then Windows and Mac users would also have access to this nifty, free and microtonal instrument too. I look forward to this and will follow amsynth’s progress into the future.

‘Retune for Live’ microtuning with Max 4 Live, by Ursine

Retune for Live is a Max 4 Live MIDI device which accepts MIDI notes as input, then outputs polyphonic microtonal MIDI which you can route to your MIDI instruments. It works on instruments that don’t support microtonal scale input, as long as they respond to pitch bend. You specify the microtuning via csv file or scl tuning file.

It all works simply enough. You have one MIDI track where you can play and record polyphonic MIDI. The Retune for Live transmitter device sits on this track and beams the note & pitch-bend data intelligently to a number of receiver devices, each of which working for one monophonic part. So if you want 8-note polyphony then you must have 8 instances of the instrument/VST each driven by their own receiver device.

When I write microtonal music I usually rely on VSTis which have support for full-keyboard microtuning built in. There should be no compromises in your art – and my art is microtonal so if a synth has no microtuning or dodgy microtuning then I don’t use it at all.

Except that for a long time I have wanted to hear Clotho from the Columns soundtrack rendered in quarter-comma meantone tuning. To faithfully recreate the sound of the original game, I set out to use a YM2616 simulation. I found two YM2616-esque VSTs, GENNY and FMDrive, but GENNY doesn’t even have working pitch bend, so that’s straight out the window.

Sega Columns

So I got myself a copy of FMDrive and downloaded a MIDI file of Clotho. MIDI retuning via Scala seemed dodgy and I could hear the results were wrong. After one night of trying different things I gave up. TobyBear’s microtuner is ancient and I couldn’t even get the ruddy thing to work at all. This is all a roundabout way of saying…

I tried Retune for Live and it just worked! So if you have Max 4 Live and want to get microtonal sounds from a synth that can’t be microtuned, give it a try. You can download Retune for Live for free or pay-what-you-like donation from the author Ursine.

As much as this solution was successful in my case, it uses more CPU power since you have to run multiple instances of the same instrument. For that reason I will avoid this solution for larger projects. But if you really need a certain sound (and you already paid big buck$ for Ableton Live and Max 4 Live), then Retune for Live might be the way to go.

Several months after my explorations with Retune for Live, I did convince the developer of FMDrive to implement some microtonal functions, but that’s a story for another day. As for my quarter-comma meantone rendition of Clotho, that was sadly lost in the great didn’t-back-it-up-and-hard-drive-died catastrophe of Spring 2016. It was badass though, I’ll remake it one day.

Microtonal piano roll for Ableton Live

Here’s a tutorial to help you make microtonal music in Ableton Live. We’re going to mod Ableton Live’s piano roll to play 22-tone equal temperament (aka 22-edo). You can apply this technique to other piano roll designs, with some limitations discussed later. Abletonalists unite!

First I should provide some context as to why this tutorial will be so useful. Check out this mindblowing M-Audio Keystation 88 with the keys rearranged to play 22-edo. It was a little project of William Lynch‘s a few months ago.

William Lynch's 22-tone per-octave M-Audio Keystation 88

This keyboard layout is Steve Rezsutek’s design as discussed in Paul Erlich’s paper Tuning, Tonality, and Twenty-Two-Tone Temperament.

There are gaps between some white keys because white keys actually come in different shapes and sizes, making things look a little messy when rearranged. You also need extra black keys to make this work, so you can see a few missing at the upper end of the keyboard. Spare keys can be found on second-hand broken keyboards or bought as replacement from the manufacturer. Soon we’ll be able to 3D print each key for any given piano roll layout (this could be a great project for a music technology student). Obviously this is all very DIY, but at this point in time nobody is mass producing microtonal instruments. Everybody in the microtonal scene right now hacks and invents their own unique stuff.

Truth be told, I’m planning to use some of my Rhythm and Xen album sales to buy a new keyboard and make one of these for myself.

The goal of this tutorial is to recreate Rezsutek’s keyboard layout in the Ableton Live piano roll. Erlich suggests to remove all the E notes, so that you have something that looks like below:

22-tone-temperament-Rezsutek-keyboard-layout

ableton-live-microtonal-piano-roll-22

Not only will this tutorial show you how to make a dope 22-note piano roll like above, but you’ll also be able to actually HEAR and PLAY music in this novel tuning system. It’s a beautiful system that includes such wonderful intervals as the subminor third, the 7th and 11th harmonics, and near-quartertones, plus a variety of rich chords, progressions and comma pumps.

This technique isn’t specific to 22-edo; you can adapt the method for other tunings too.

To make this happen, we will be using the piano roll ‘Fold’ function, as well as taking a few other steps to make everything sound correct.

Making the layout in Live

This is the easiest part, and you might know this trick already if you’re knowledgeable with Ableton Live. We will create a MIDI clip that has one massive chord containing every note except for all the Es. Then we will enable Fold so that the Es disappear from the piano roll. So let’s look at it step by step:

Create yourself a new MIDI clip and make sure that Fold is disabled. Then start building up a chord containing all the notes except for the Es:

ableton-live-22-edo-piano-roll-tutorial-1

It’s easiest to work up from the bottom. Once you have made one octave you can copy and paste to fill in the rest of the notes.

ableton-live-22-edo-piano-roll-tutorial-2

Once you have added all the notes from C-2 to G8 you can move the whole chord to the left, so that it is outside of the range of the clip. This way, you won’t hear an almighty cluster of pain when you play the clip.

ableton-live-22-edo-piano-roll-tutorial-3

Ctrl+A to select all the notes in the chord, then tap 0 to disable all the notes. This will protect you from hearing these notes if you have MIDI Editor Preview enabled.

Then click on the Fold button to enable it. All of the Es will disappear from the piano roll.

ableton-live-22-edo-piano-roll-tutorial-4

Just ignore the note names (C4, C#4 etc.) because they don’t have any relation to 22-edo.

Making the tuning file

Now we have our custom piano roll layout set up in Ableton Live, but that doesn’t mean that the notes will play a 22-edo scale. You can’t just drop Operator on to the MIDI track and expect everything to be tuned to 22-edo automatically. At this point, you should make sure that you have some kind of MIDI instrument or VST/AU plugin that supports microtonal scales.

I will use Scala to design a tuning file with 24 notes in total. Each note will be tuned to a note from 22-edo, and 2 of the notes will be duplicates that fill in the missing Es.

First we type ‘equal 22’ into scala and hit enter. This generates the scale. Then we click on ‘Edit’ to see all of the notes that were generated. By Scala tuning standards, 1/1 will fall on middle C at ~261 Hz unless a keyboard mapping is specified. So we can assume 1/1 is C, and therefore the notes 218.18182 and 818.18182 should be duplicated to fill in the missing Es.

ableton-live-22-edo-piano-roll-tutorial-5

You can just select 218.18182 and 818.18182, then Ctrl+C and Ctrl+V to duplicate them. Finally, click on the ‘Ascending’ button to make sure that all the pitches are in the correct order. Click OK when done, and save your progress.

Or if you’re too lazy for all of this, save the below text as a .scl file:

! 22-edo-no-Es.scl
!
22-EDO with no Es
 24
!
 54.54545
 109.09091
 163.63636
 218.18182
 218.18182
 272.72727
 327.27273
 381.81818
 436.36364
 490.90909
 545.45455
 600.00000
 654.54545
 709.09091
 763.63636
 818.18182
 818.18182
 872.72727
 927.27273
 981.81818
 1036.36364
 1090.90909
 1145.45455
 2/1

All that’s left is to export this scale for the synth you’re using. You can read your synth’s manual to determine which format of tuning file it needs. Then export the correct format file using Scala. Watch my YouTube video tutorial below to find out how to export various kinds of microtonal tuning files with Scala.

Making it all come together

Head back to Ableton Live as quick as possible, then drop an awesome VST instrument on to the MIDI channel you used earlier. Load the tuning file you created into the VST, then jammmmmm. The setup is finished, so start writing!

Remember that octave transpose works differently now because your scale actually spans (what Live thinks of as) 2 octaves:

Ctrl+↑ to move a note up by a tritone.
Ctrl+↑↑ to move a note up by an octave.
Ctrl+↓ to move a note down by a tritone.
Ctrl+↓↓ to move a note down by an octave.

Make sure to read Paul Erlich’s paper Tuning, Tonality, and Twenty-Two-Tone Temperament for more insight into the musical possibilities of this scale.

Download an example project

Update: I made an example project with one MIDI clip already set up for you. In the project folder you’ll also find tuning files in 3 different formats.

Applying this to other tuning systems

I suspect that the Fold method will work easily for any scale less than 12 notes. It will also work for any even-numbered scale with 12 to 24 notes in total, as long as the pattern of white and black notes repeats every 12 MIDI notes. This is because the “octave transpose” function (Ctrl+↑ or Ctrl+↓) in Ableton Live’s piano roll transposes by 12 notes and ignores folding. So an asymmetric piano roll layout will be broken by octave transposition.

Music in 22

There’s a long list of 22-tone music on the Xenharmonic Wiki. And here’s a song I created in 22-tone equal temperament back in 2010:

Further exercises

  1. Use the Fold method to create piano roll layouts for other tuning systems.
  2. Find out if absolutely all piano roll layouts are possible with the Fold method. Why/why not?
  3. Recreate this software piano roll in hardware by disassembling a MIDI keyboard and re-arranging the black and white keys by hand. (How to remove keys from an M-Audio Keystation)
  4. If you’re still trying to figure out why the piano roll needs to be modded in the first place, read my article about why DAW developers should design a better piano roll.
  5. Start evangelizing to audio technology developers, asking them to support microtonal piano layouts and microtonal tunings.

Video tutorial – How to export various tuning file formats in Scala

I have covered this topic before on my blog, but I thought I could do better and make a short video tutorial.

When you’re designing musical tunings in Scala, you might eventually want to export your tuning to use it in a synthesizer. Synthesizers support various tuning file formats, so you’ll need to know how to make a few different kinds. This video shows you how to export Scala files (.scl), export AnaMark tuning files (.tun), and export MIDI Tuning Standard dumps (.mid). Right at the end of the video you’ll also find out how to retune other synths like the Yamaha DX7ii.

Free Ableton Drum Racks to customise your piano roll

I’ve written before about how DAWs don’t often allow a custom piano roll designed for microtonal musicians. If you’re using a scale with more or less than 12 notes, then the piano roll doesn’t match up with what you hear from the synth. As an Ableton Live user, I wanted to know what workarounds I could use right NOW in order to make composing microtonal music a little easier.

My goal: display custom note names for every note on the piano roll!

Enter the Drum Rack

Live Drum Rack set up for custom note names

Using a Drum Rack, it’s possible to change the note names displayed in the piano roll. Load up one of my sample Drum Racks (download here) and add it to an empty MIDI track. Create a MIDI clip on that track and make sure that ‘Fold’ is enabled on the piano roll. You should see something like below:

Ableton Live piano roll with a custom 9-note scale mapping

The example above shows a 9-note scale using the letters A B C D E F G H J.

Then, you must load your instrument on a new MIDI track, and connect the MIDI input of that track to the Drum Rack track (pre FX).

Routing for custom piano roll trick in Ableton

Once this routing is set up, you can compose in the piano roll of the Drum Rack track. The note names here can be a useful guide when you’re composing with microtonal scales.

Making these Drum Racks is time consuming because you have to name all 128 notes individually. I have done the hard work for you and made a pack of Drum Rack presets that you can drop into your project. Each one assumes that MIDI note 60 is middle C (this is the default for Scala keyboard mappings).

5 note scale: C, D, E, A, B
6 note scale: C, D, E, F, A, B
7 note scale: C, D, E, F, G, A, B
8 note scale: C, D, E, F, G, H, A, B
9 note scale: C, D, E, F, G, H, J, A, B
10 note scale: C, C#, D, D#, E, E#, A, A#, B, B#
11 note scale: C, C#, D, D#, E, F, G, G#, A, A#, B
12 note scale: lol
13 note scale: C, C#, D, D#, E, F, F#, G, G#, A, A#, B, B#
14 note scale: C, C#, D, D#, E, E#, F, F#, G, G#, A, A#, B, B#
17 note scale: C, Db, C#, D, Eb, D#, E, F, Gb, F#, G, Ab, G#, A, Bb, A#, B
19 note scale: C, C#, Db, D, D#, Eb, E, E#, F, F#, Gb, G, G#, Ab, A, A#, Bb, B, B#
22 note scale: C, C#, D, D#, E, E#, F, F#, G, G#, Hb, H, H#, J, J#, K, K#, A, A#, B, B#, Cb

>> Download the pack of Drum Racks (.zip) <<

About the chosen note names

The note names that I chose for some of the mappings are somewhat arbitrary. But there is some method to the madness.

The note names for the 5 note through to the 9 note mappings just assign a unique letter for each note. The 10 note mapping has 5 naturals and 5 sharps. The 11 note mapping is similar to the standard 12 note mapping, without F#. The 13 note mapping is similar to the standard 12 note mapping, but B# is added. The 14 note mapping uses 7 naturals and 7 sharps.

The 17 note mapping is based on a circle of fifths. C# is actually higher than Db because the fifth is tuned sharp (i.e. it’s a superpythagorean tuning).

The 19 note mapping is also based on a circle of fifths.

The 22 note mapping is designed for 22-EDO, so that the naturals give you a symmetrical decatonic scale such as those described in Paul Erlich’s paper Tuning, Tonality, and 22-Tone Temperament.

The limitations of the Drum Rack method

There seems to be a performance drop if you have too many of these Drum Racks active. I’m using a 4 year old laptop, and editing the Drum Racks become tedious once there were about 4 of them active.

But the main problem is that you can’t change the colour of the notes, so you’re still stuck with the 7-white 5-black Halberstadt layout. Try to look at the note names and ignore the note colours.

It would be a great help if Ableton would implement some kind of key colour mapping feature in the Live’s piano roll. The only way this could happen is for users to actively ask for it. You should go and make the feature request now at Ableton’s forums and beta website.

More words about microtonal computer music

My workflow for making microtonal music in Live
Why DAW developers should design a better piano roll
VSTs for playing and composing microtonal music
Microtonal music in Bitwig Studio

Stereo Panning in Ableton Live

Just wanted to share a super simple Ableton Live effects rack. Despite its simplicity, this is the rack I use the most (in fact it’s my default rack preset). It’s a stereo pan. Download it.

Stereo Pan effect rack for Ableton Live

You see, Ableton Live strangely omits stereo panning while other DAWs such as Logic Pro and Pro Tools sensibly include it.

That thing that looks like a pan pot on the channel strip? Yeah that’s a balance control. It doesn’t actually let you manipulate a stereo signal, it just makes the left or right channel quieter. Stereo panning is different; it allows you to pan the left and right channel independently to any part of the stereo image.

I use this effects rack to tightly control the stereo image of my tracks and busses. And I never use Live’s balance control unless it’s on a mono track.

Installing the Stereo Pan effects rack

  1. Download Stereo Pan.
  2. Unzip the adg file.
  3. Drag the adg file on to an effects chain and Ableton will place the rack for you.

Example usage

  1. Instead of setting the balance control to 10 o’clock, try panning the left channel to 8 o’clock and the right channel to 12 o’clock.
  2. Create a return track with a stereo ping pong delay. Usually these delayed signals are hard left and hard right. Place the Stereo Pan rack after the delay to position the two delayed signals wherever you like in the stereo field.

If you’re interested, check out some of my sounds.

Sleep Deprived Cooked Alive remix stems

Sleep Deprived Cooked Alive is a drum & bass track from my album Rhythm and Xen. It’s written in 14-EDO (a microtonal tuning). It’s definitely one of the more popular tracks, so I’ve decided to release the remix stems for free.

Download the Sleep Deprived Cooked Alive remix stems pack

The pack includes audio stems, MIDI parts and tuning files to help you tune your synthesizers to 14-EDO. Refer to your synth’s manual to see if it supports these files. This should be enough to get a good remix going, or just to study my work if you’re learning microtonal music.

If you make anything with these stems then let me know! I would love to check it out.

Creative Commons Licence
Sleep Deprived Cooked Alive (stems pack) by Sevish is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at https://sevish.bandcamp.com/track/sleep-deprived-cooked-alive.

2 microtonal scales for your standard 12-tet guitar

I was reading some of Ivor Darreg’s writings and a really interesting idea jumped out.

“Try this: Move the bridge down until the 13th (instead of the 12th) fret sounds the octave of the open string. This will give an approximation of the 13-tone equal temperament.”

Here’s how it works. If you have a guitar with a movable bridge, then you can move it down such that the 13th fret gives you a perfect octave. This gives you a 13 tone scale to play on your guitar!

While its approximation to 13-edo is far from perfect (you’d need to completely move the frets for that) this should offer plenty of new tonal resources to the experimenting microtonal guitarist. Compared to 13-edo, the error is largest in the middle of the scale.

You can reverse this and push the bridge up such that the octave lies on the 11th fret, giving you a brand new 11-tone scale to experiment with. Again, it poorly approximates 11-edo but don’t worry about that, there are plenty of new sounds available through this method.

The idea can be pushed further:

“I fretted a guitar to 18-tone (Busoni’s proposed third-tones) and can use this guitar as a 17 or a 19 without the theoretical errors from moving the bridge spoiling any performances. So you can have three systems for the price of one.”

This really is “one weird trick that luthiers don’t want you to know!” Bwaha… ok I’ll see myself out the door.

For something a little different, check out 9 Alternative Tunings NOT for Guitar.

How to invent your own musical scales using Scala

When you want to edit photos, there’s Photoshop. When you want to listen to music there’s iTunes (if you’re a pro at life, there’s foobar2000). When you want to create your own musical scales, opening up endless possibility in harmonic and melodic expression, there is Scala.Scala is a multi-purpose toolkit for everything related to tunings, scales and microtonality. You have a hardware synth that you want to retune? Scala will do it. Or a softsynth? Scala can export the tuning files required to make that happen. Want to generate all kinds of crazy scales that you can use to compose new music? Scala has near infinite options for you to play with. Want to experiment with world music and historical scales? There’s a database of thousands on the Scala website.Scala tuning softwareThis is a beginner-level tutorial which deals with scale creation and microtonality in a practical way. I can’t attempt to cover everything Scala can do here. But you’ll learn some fundamentals.First I’ll show you how to create equal scales, then I’ll show you how to create just scales. If you don’t know what the difference is, just follow the tutorial from beginning to end, and read some of the links later to fill in the gaps of your knowledge. By the end of this tutorial you will have invented some of your own musical scales!

Equal Temperament scales

Equal temperaments are scales that divide an octave into some number of equally big pieces. The 12 note scale of Western music is an example, as each semitone is of equal size. So you already have experience with equal temperament scales and didn’t know it.In Scala, equal temperaments are trivially easy to create!A popular thing that beginning microtonalists like to do is to try quarter tones. The quarter tone scale divides the octave into 24 notes. Let’s make the scale in Scala. Load up Scala, type this line into the text field at the bottom, then hit enter:

equal 24

Explanation: When you type the command equal, followed by a number, Scala will produce an equal-tempered scale with that number of notes in an octave.But it looks like nothing happened after we hit enter. We still need to check that the scale was created correctly. So type:

show

This will show you the tuning data for the equal temperament scale you just created. As below:

  0:          1/1               0.000000 unison, perfect prime  1:         50.000 cents      50.000000  2:        100.000 cents     100.000000  3:        150.000 cents     150.000000  4:        200.000 cents     200.000000  5:        250.000 cents     250.000000  6:        300.000 cents     300.000000  7:        350.000 cents     350.000000  8:        400.000 cents     400.000000  9:        450.000 cents     450.000000 10:        500.000 cents     500.000000 11:        550.000 cents     550.000000 12:        600.000 cents     600.000000 13:        650.000 cents     650.000000 14:        700.000 cents     700.000000 15:        750.000 cents     750.000000 16:        800.000 cents     800.000000 17:        850.000 cents     850.000000 18:        900.000 cents     900.000000 19:        950.000 cents     950.000000 20:       1000.000 cents    1000.000000 21:       1050.000 cents    1050.000000 22:       1100.000 cents    1100.000000 23:       1150.000 cents    1150.000000 24:          2/1            1200.000000 octave

Explanation: The equal command that we just used has produced 24 items for us (24 notes in our scale). The  show command lets us see those 24. Each of these shows some number of “cents.” The cent is a measurement of how wide or narrow an interval is. Notice that each interval in our 24-equal scale goes up by 50 cents. 50 cents is exactly one quarter tone. 100 cents makes up a semitone, and 1200 the whole octave. Cents are a useful measurement to get your head around if you want to compare tunings with each other.That’s enough staring at numbers. Time to hear these quarter tones for the first time. On the Scala interface you’ll see a button which says play. Click that button!Chromatic ClavierHere’s the “chromatic clavier!” You can use this to try out your scale using your PC’s built in MIDI synth. A very handy tool indeed. Play using your mouse, or use the Sound Settings button to set up a MIDI keyboard controller.

Exercises

  1. Find some cool chords in the quarter tone scale which don’t exist in the normal Western scale.
  2. Create other equal tempered scales using the equal command that we used to create the quarter tone scale. Try any number you like, but make sure you play and listen to them using the chromatic clavier. Here are some numbers you can try which are known to give interesting musical results: 5, 13, 17, 22.

 

Equal Temperament scales (no octaves)

In the first part, we divided an octave into some number of equal parts. Amazingly, we are not limited to dividing octaves. We can choose to divide other intervals instead, such as a perfect fifth or whatever you like. But what’s the point?Every note in a non-octave scale has a unique identity. Consider that we know a note A as a note oscillating at 440 Hz, or some octave above (880 Hz, 1760 Hz) or below (220 Hz, 110 Hz, 55 Hz). If our scale doesn’t include octaves, then a note A won’t have any other counterparts higher or lower in the scale. This means that, as we climb up or down into different registers, we keep hitting unique note identities which haven’t been heard elsewhere in the scale!This approach is extremely fruitful for new sounds, sonorities and progressions. However composition technique must change drastically. For starters, there are no more chord inversions, since you can’t raise any notes up or down an octave. Of course, this makes voicing difficult too. But you gain a very wide variety of intervals to play with, and it will challenge and grow you as a composer to exploit non-octave scales. Just try it and see.Here’s how we do it. We’re going to create a scale which divides a perfect twelfth (an octave plus a fifth) into 13 equally spaced parts.

equal 13 3/1

Explanation: The equal command tells Scala that we’ll be making a scale where all notes are the same size. The number 13 shows that we want 13 notes. And that weird fraction on the end? That’s the big interval that will be split into 13 equal parts. Think of it as a pseudo-octave.Why 3/1? For now just take my word for it. 3/1 is a perfect twelfth. So rather than repeating at the 8th (octave), we’re repeating at the twelfth.Notice, if we don’t include the number 3/1, then Scala will assume that this is an octave based scale. (An octave, by the way, can be expressed as 2/1).Let’s see the cents values for the scale we created:

show

And the result:

  0:          1/1               0.000000 unison, perfect prime  1:        146.304 cents     146.304231  2:        292.608 cents     292.608462  3:        438.913 cents     438.912693  4:        585.217 cents     585.216923  5:        731.521 cents     731.521154  6:        877.825 cents     877.825385  7:       1024.130 cents    1024.129616  8:       1170.434 cents    1170.433847  9:       1316.738 cents    1316.738078 10:       1463.042 cents    1463.042308 11:       1609.347 cents    1609.346539 12:       1755.651 cents    1755.650770 13:          3/1            1901.955001 perfect 12th

Can you remember how many cents are in an octave?The answer is 1200 cents. Looking at the above list of intervals, we can see there’s no value too close to 1200 cents at all. But there’s this nasty 1170 cents interval that’s gonna sound noticeably flatter than an octave. On the other hand, that perfect twelfth at 1901.955 cents, is purely in tune. Whatever this scale is, it doesn’t represent anything we’re used to in Western music. There’s no perfect fifth, no octave…The scale we’ve just created is none other than the Bohlen-Pierce scale, a famous non-octave scale with many interesting properties. It sounds very alien until you have taken time to immerse yourself in it. Jam with the chromatic clavier and hear it for yourself (remember, just click the play button on the Scala interface to do this).

Exercises

  1. Try some other scales which divide the perfect twelfth. Use the same method as above, but replace the number 13 with any number you feel like.
  2. The perfect fifth is a ratio of 3/2. With this knowledge, try out some scales which divide the perfect fifth.
  3. Search for Bohlen-Pierce music on YouTube, and hear other people’s approaches to the scale. But only after you have tried to explore this unusual tonal territory for yourself.

Just Intonation scales

The topic of just intonation (JI) is deserving of several books in its own right. It is an old mathemusical theory in which many cultures have their own take.What could a name like “just intonation” mean… If you think of “just” as meaning fair, right, exact, and perfect – and intonation of course having to do with the accuracy and flavour of the pitch – then you should get the general idea. Just intonation is a tuning system that uses exact, perfect intervals.In fact, the pitches of just intonation are made up of ratios. Think of numbers such as 2/1, 3/2, or 15/8. (These intervals are an octave, perfect fifth and major seventh, respectively).

Just one quick way of making just intonation scales

Time to get creative! There are many ways to go about making your own just scale, but here’s one way that can get you exploring quickly.On the main Scala window, click on the Input button to open up the Input Current Scale window. Here you can enter the pitches you want to use. In this case we’ll enter some fractions at random, following some simple guidelines.

  1. Put one fraction per line.
  2. The last line should be 2/1. This makes sure that your scale repeats at the octave.
  3. To ensure that every pitch fits within a single octave, make sure that the numerator of each fraction is greater than the denominator, but less than double the value of the denominator.(For example 3/2 is okay. 1/2 isn’t okay because the numerator is less than the denominator. 5/2 isn’t okay because the numerator is greater than double the denominator.)
  4. The pure “JI effect” is generally stronger with simpler ratios, so avoid complicated fractions such as 51227/29096 and keep things simple.

Below are a few examples that follow the above guidelines.

ji-example-1 ji-example-2 ji-example-3

You can also use Kyle Gann’s anatomy of an octave to find some interesting numbers to plug in.Once you’re done, hit OK and you’ll be taken back to the main Scala window. At this point you will find 9 times out of 10 that Scala says “Scale is not monotonic ascending.” If you saw this message then it means that the pitches of your scale are in a weird order. To fix this issue, tap the Edit button on the main Scala window, tap the Ascending button, and finally click OK.Let’s take a quick look at what you made:

show

Take a quick look at the interesting names that Scala gives to the ratios you randomly chose.Now it’s time to hear your scale! Hit the Play button to show the Chromatic Clavier. You can hold shift when you click to hold multiple notes down and hear that solid JI sound.Alternatively you can play your scale using a connected MIDI controller or MIDI keyboard. To do this just click the Relay button on Scala’s main window and then click the Start Relaying button.Repeat this process of JI scale creation a few times, each time playing your scale using a keyboard to get a feel for the unique musicality of each one.Once you become comfortable with this process and you get to know certain ratios that you love the sound of then you can start to ignore the guidelines I gave before.

Further reading about just intonation

Now you know how to come up with a just intonation scale of your own. But you still might not know why you would want to use just intonation. There are many differing opinions out there and it’s easy to find them using Google. And I recommend you spend a lazy afternoon doing just that. Here are a few suggestions:

Further exercises

  1. Load up various scales from the Scala scale database. Use the command show to display the tuning data (boring numbers) for a scale. Is it meaningful to you?
  2. Jam with each scale. Is it meaningful now?
  3. Pick the weirdest scale you can find from the Scala scale database and jam until it sounds normal.
  4. This tutorial has only shown you how to create and play scales within Scala. Now learn to use your creations in other synths by reading my tutorial on exporting scales in Scala.
  5. Explore other tuning software. There is CSE and LMSO (for Mac OS X) and alt-tuner (for Reaper). Find what works best for you.