You are browsing the Tutorials category
So, you’re making your own microtonal tunings in Scala. You’ve explored for a while and came up with all kinds of original scales by yourself. There’s just one problem — all those scales are in the key of C! This quick tutorial will show you how to change key in a microtonal scale using Scala.
By default, Scala will assume that the base note of the scale (1/1 or unison) lives on MIDI note 60 (middle C of the keyboard) at a frequency of 261.6 Hz. To change this, we use the Edit Mapping dialog. You can find it at Edit > Edit Mapping.
This page looks confusing, but there are only 3 fields we need to change in order to change the key of your scale.
The first field to change is ‘Key for 1/1’. This field tells Scala which key on a physical MIDI keyboard you want to use for 1/1 (the first note of your scale). You can change this value by 1 for each semitone away from C. For example if you want your scale to start on D then you can enter 62 here. For A above middle C, use 69.
Next, set the ‘Reference key’ field to be the same value as ‘Key for 1/1’. This might seem redundant, but there are situations where they would differ. For an easy time, make these two values the same.
Finally, we can set the ‘Reference frequency’ to any frequency in Hz. So if we want to play in the key of D, we would enter 293.66Hz.
|MIDI note number||60||61||62||63||64||65||66||67||68||69||70||71|
You should save your mapping to use it again later. To do so, you’ll need to open the Edit Mapping dialog again (Edit > Edit mapping). Just click on the Save As button that appears on that dialog.
Scala saves mappings seperately from tunings. The keyboard mapping data is saved into a .kbm file. You can mix and match your .scl tunings with your .kbm files.
Alternative formats such as the AnaMark TUN file (.tun) store the tuning and the mapping all in one file. So if you’re converting a .scl file into a .tun file, make sure that you have loaded your .kbm keyboard mapping beforehand. The same advice applies if you’re using Scala’s relay feature to retune a hardware synth via MIDI.
A little tip for you EDM-loving bass music explorers. The most bootyshakingest bass lives around 45-55Hz. That range approximately covers the keys of F# to A.
You can also use this tutorial to tune scales to 432Hz. Before you follow the tutorial steps, stand outside and absorb sunlight for 10 hours while noticing that the horizon is indeed flat and not a curve. If you see a chemtrail, stand for an extra hour. Finally you can click Save As.
Thanks to Paris for suggesting this tutorial. I recently overhauled sevish.com and it’s now possible to email me directly from my contact page. Most of my tutorials these days were requested by people who discovered my blog. Feel free to send in suggestions.
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.
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:
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.
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:
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.
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.
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.
Just ignore the note names (C4, C#4 etc.) because they don’t have any relation to 22-edo.
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.
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.
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.
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.
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.
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:
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.
A tracker is a type of music sequencer that was popular in earlier days of computer music and the tracker scene is still very much alive today. Some trackers even support microtonal scales, allowing you to compose with xenharmonic, alternative tonal systems, and I wanted to share some of those here.
Post updated on 2021-10-13
Open ModPlug Tracker is a completely free music tracker for Windows. It can also be microtuned, so that you can compose music that explores tonal systems made before and after the reign of 12-tone equal temperament (from here on referred to as ‘The Dark Ages’).
OpenMPT can be microtuned by way of Scala files or TUN file import. (Learn how to produce those .tun files, or download some ready made tuning packs). You an also input notes directly, though they must be in the form of decimals. Once a tuning is imported into OpenMPT, you can edit it within the Tuning Properties screen.
One awesome feature is that OpenMPT will name the notes of your tuning with letters A-Z from the alphabet. This way, if you have more or less than 12 notes per octave then you can easily recognise your pitches. A5 is one octave above A4, X5 is one octave above X4 etc. It’s as easy as that. (DAW engineers take note, this is essential for microtonalists! We don’t need to see 12-TET note names when we’re using microtonal scales).
If you need even more control over your note pitches, it’s possible to fine-tune the frequency of each individual note.
Note that if you’re using VSTs within OpenMPT, the microtuning feature won’t work for those. Stick to the sampled instruments and your OpenMPT tunings will work just fine.
LSDj (Little Sound Dj) is a music tracker made for the original Game Boy, utilizing the Game Boy’s sound capabilities. It will run on real hardware via a flash cart, or you can run it in an emulator. I run it on an emulator on my smartphone. It’s a great way to kill some time on the bus/train/toilet.
By default, the frequency tables inside the ROM file are tuned to 12-tone equal temperament. But with the aid of a super helpful Perl script by abrasive, the frequency tables in LSDj can be fully microtuned to any tuning system you want. Even non-equal, non-just and non-octave scales are possible – it’s very flexible!
To do this, first of course you’ll need a copy of LSDj, then head to the Microtuning HOWTO page on LSDj’s wiki and download lsdj_tune1.4.
Note, the compiled .exe for lsdj_tune1.4 may give you the following message:
&Config::AUTOLOAD failed on Config::launcher at PERL2EXE_STORAGE/Config.pm line 72.
So it’s best to install Perl on your system and run the Perl script itself. For me, this works just fine. But note that you need to use the command line in order to run the script.
With all that set up, your best bet is to move LSDj and the tuning script into the same directory, then make a .bat file to set up your tuning command. I prefer using a .bat instead of writing directly in the command line, because I can save my command, edit it and repeat it later when I want to change the tuning.
When you run the command, you’ll end up with a patched version of the original ROM, so for each tuning you wish to use, you’ll get a new ROM. My Game Boy folder has several of them for various tunings.
Similarly to OpenMPT, with lsdj_tune you can set the note names of your tuning. This way when you make music in LSDj you won’t be encumbered with 12-TET note names from The Dark Ages. Here’s a really simple example using 5-EDO and the note names U V X Y Z:
perl lsdj_tune1.4.perl --cents 0,240,480,720,960,1200 --base A5 440 --names U,V,X,Y,Z --rom lsdj.gb --out lsdj_5edo.gb
Note: the names parameter doesn’t work in ET mode so here I have specified 5-EDO explicitly using cents.
Then load up your new patched LSDj ROM and enjoy! — 2 pulse channels, 1 PCM channel and 1 noise channel is way more exciting with microtones.
First you’ll need to download some Scala files (or make your own). Then install the tool by downloading it and dragging it on to your Renoise window. Within Renoise, make sure that your instrument is selected, and then run the tool. You’ll be able to load up one of your Scala tuning files and it will be applied to the instrument.
Update (December 2020): Ahornberg mentioned in the comments that GoatTracker 2 supports microtonal tuning via scala files (.scl). It also allows for customizable note names.
Many other trackers have no microtuning function built in, but you can still edit the pitch of each individual note. This can be done by using edit mode and assigning the same sample to different notes of the keyboard, each with some detuning.
Of course this is laborious work, so you might prefer one of the above options. Nevertheless this hasn’t held some people back. Here’s the proof, a tasty jam in just intonation using MilkyTracker:
Deflemask is another tracker that doesn’t have any built in support for microtuning. But my tuning tool Scale Workshop can generate a list of the fine tune parameters for any tuning you want to throw at it. Just load up your scale in Scale Workshop and then Export > Download Deflemask ‘fine tune’ reference (.txt). Then input the values from the text file into Deflemask as needed.
If there are more trackers that support microtonal scales then I would love to hear about them.
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!
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:
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).
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
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.
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.
What is the meaning of ET and EDO, and are they interchangeable?
ET: Equal Temperament
EDO: Equal Divisions of the Octave
In practice, yes they are interchangeable. For example, 12-ET and 12-EDO both refer to the exact same tuning which has 12 equal notes per octave. But there is a slight difference in their meaning.
12-ET suggests that the tuning is a temperament, i.e. it tempers some other interval, usually a just interval. 12-ET tempers 81/80, the syntonic comma, and other intervals.
12-EDO suggests that an octave has been divided into 12 equal parts, but otherwise doesn’t imply that tempering is of importance.
Some people will even say ET for 12-ET, 19-ET and 31-ET, while using EDO for 8-EDO, 13-EDO and others. Perhaps because 8-EDO and 13-EDO are not thought of as temperaments, whereas 12-ET, 19-ET and 31-ET are all useful meantone temperaments.
Personally, I always use EDO in my own thinking and private communication with other microtonalists, but will use TET or ET when I need to be understood by a larger, mixed audience.
To complicate things further, some people use ED2 or ED2/1 synonymously with EDO, because the octave is equal to the ratio 2/1. The good thing about this format is that we can generalise it for other scales that divide some interval into equal parts (e.g. EDphi, ED3/2, ED4). I welcome the move to this kind of generalised terminology that helps us describe more tunings with less words.
The world of xenharmonic jargon is often difficult to navigate. Once you get your head around it, you can forget about the tuning theory politics and remember that the important part is to make inspiring and enjoyable music!
UPDATE August 6th 2020 – this post is now out-of-date because Bitwig have released the Micro-Pitch device. It is excellent so go and check it out. You can still read the rest of this article below to get a sense of life in the before time. :)
If you’re making music with Bitwig Studio, did you know it is also capable of playing microtonal music? It’s not difficult to set up – in fact Bitwig is already a shade above Ableton Live in terms of microtonal scale support. In this article I’ll discuss some possibilities and limitations for microtonal music in Bitwig Studio.
If you’re the kind of musician who wants to compose standard Western tuned music with the occasional microtonal melodic intonation, then the pitch bend method is an easy way to go. Bitwig essentially locks you into standard Western tuning (12-tone equal temperament) as a tonal framework, and you can specify your deviation from that tuning on a per-note basis.
Yes, you heard correctly. Bitwig supports per-note pitch bend for its built-in instruments! This really lowers the barrier of entry for a basic level of microtonality.
But if you want to go deep, using a microtonal scale as your tonal framework, then things start to get fiddly because you’ll be using those pitch bends on almost every single note. Copy and paste will be your friend here.
Remember that per-note pitch bend does not work for VST instruments. The MIDI spec doesn’t support per-note pitch bend, so this technique only works for the Bitwig internal instruments that share Bitwig’s own unique data structure.
You can use the Note MOD device to grab note information from any instrument track. That information can then be used to modulate other parameters within Bitwig’s instruments or effects.
The Note MOD device can be set up to allow you to play in microtonal equal temperaments with the Sampler, FM-4 and Polysynth instruments. That’s because these 3 instruments have a Pitch setting that can be modulated. Use the Note MOD device with the KEY modulator to modulate the Pitch setting of your instrument. A negative value will cause the notes to become smaller than a semitone, while a positive value will cause the notes to become larger than a semitone.
Of course, due to the fact that Bitwig supports VST instruments, you can simply load up tried-and-true VST instruments that support microtonal scales.
If you have a synth that can be tuned via tuning file import, then you’ll need to know how to generate those tuning files or you could simply download a few ready-made tuning packs. And don’t forget to check your synth’s manual to find out how to import your tuning files.
This method doesn’t update the look of your piano roll even if you update the tuning in your VST instrument. So you’ll be stuck in a piano roll scordatura hell, where the notes on the piano roll don’t quite match up with what you’re hearing. But don’t worry, most other DAW microtonalists are in the same ring of hell as you. Get cosy, I’ve been here for years.
In the past, SysEx was how MIDI devices sent and received data for their specific functions. This was a long time ago, before everything was done in the box with a GUI. Some new VST instruments and many old keyboard synths support microtuning via MIDI Tuning Standard (MTS) SysEx messages.
It looks like Bitwig doesn’t support SysEx messages yet (as of Spring 2016), and we’re not sure if it ever will. So MIDI Tuning Standard based microtuning is ruled out for now, sorry. Let’s hope the developers will implement it for all us nerds in the future. Cross your fingers, say prayers, burn incense, and send the developers a feature request…
In the core of Bitwig Studio there is a hidden modular environment that will later be opened up for musicians and tweakers to patch into. Without a doubt, Bitwig’s modular system could be used and abused to bend the notes in any which way you choose. Let’s wait for this one and see what the future holds.
If Bitwig Studio’s modular system inspires the same kind of sharing culture that Max for Live does, then it’s only a matter of time before some bright spark patches a microtuner plugin or microtonal synth in Bitwig modular.
If you know any other ways to squeeze a microtonal scale out of Bitwig Studio then drop a line in the comments.
This is my answer to the question “Sevish, how do you make your music?”
I won’t discuss my creative process but I’ll explain my workflow and the tools used to get music made. What I like about my workflow is that it works superbly for me.
I use Ableton Live to write, record, and mix my music. Within Live, I load VST instruments that have built-in microtonal scale support. I use Scala to produce the tuning files necessary to retune those VSTis. I play the VSTis using my MIDI keyboard, C-Thru AXiS-49, QWERTY keyboard and through mouse input. I also sample recordings that I have made using my Zoom H4n portable recorder.
Ableton Live is a DAW (digital audio workstation) that has an effective workflow for electronic music. For my drum’n’bass, breakbeat electronic, it works just fine. Live has no built-in microtonal scale support, and the piano roll is always locked to a 12-note Halberstadt layout, which can be tricky.
It’s possible to make microtonal music in Ableton Live by using VST instruments or Max 4 Live instruments with microtuning support built in. As far as Ableton knows, MIDI data goes into these instruments and audio comes out. It’s up to the instruments themselves to provide the new tunings and scales that I use in my music.
I use a couple of Max 4 Live instruments that I made myself, plus several VSTi: Xen-Arts FMTS2, IVOR, XenFont, TAL-Sampler, u-he ACE and Garritan Personal Orchestra 4. All of these plugins have full keyboard tuning support, which is why I choose to use them. To tune up, they each require you to import a tuning file. I’ll elaborate on that later.
Before writing a piece, it works well to have an idea already of the tuning you want to use. Scala can be used to invent musical tunings or specify an old one. I have written about how to invent your own scales with Scala, described other superbly expressive tunings that already exist, and hand-selected some interesting scales to download.
Once I have a scale in Scala that bends my ear in just the right way, it must be exported as a tuning file for it to be usable in those VST instruments. The common formats are:
I wrote a guide to exporting .tun files, and the process is much the same for producing MIDI tuning dumps and .txt tuning files.
After I have some tuning files to work with I’ll load them up in one of my synths, and jam away until I play something I really like. I don’t go too deep in to the theory of it all; I leave that up to others. Using your ear and finding sounds you like is a good way to go.
I like to record sounds on location with my H4n portable recorder. After recording I keep the audio in my personal sound library until I’m ready to use them in a project.
I almost never use the preset sounds on my synths. It’s best to patch in your own sound designs because that becomes a recognisable part of your craft. It’s well worth practicing this skill for yourself. Some days I do nothing but come up with new sound designs with my fave synths. That way I can save them in my personal library and use them only when inspiration strikes.
The AXiS-49 is a hexagonal keyboard controller, and it’s best suited to exploring microtonal scales because it makes fingering really easy. Imagine trying to play a 15-note scale on a standard keyboard where the pattern repeats after every 12 notes… The fingering gets totally perplexing and that gets in the way of creativity. With the AXiS that’s no problem at all. The AXiS also greatly increases my reach, so I can play large chords easily.
The difficulty I find with the AXiS is that I use so many different tunings that it’s difficult to build up a muscle memory for any of them. And the buttons are so close together that I make mistakes quite easily.
It comes in handy to have a standard keyboard at times. I was given a 2 octave MIDI controller with some knobs on it which I can map to various functions in my DAW. Using this to recording automation in real-time is one way to breathe some life into a static synthesised part.
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.
[Update Jan 2023: This article is quite old now. If you’re looking for something more user-friendly than Scala, try Scale Workshop. If you want to learn more about Scala, read on!]
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.This 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 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:
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:
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!Here’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.
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:
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).
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).
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.
Below are a few examples that follow the above guidelines.
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:
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.
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: