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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 folks 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!
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.
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:
Seems like there are tonnes of Max OS X users who want to get into microtonal music but don’t know how to jump in. Although I’m a Windows-using peasant, I wanted to gather up some ideas to start you off. Let’s dip in…
Logic Pro supports microtonal scales, and can even load Scala files! This can retune all of its built-in instruments and synthesisers (it doesn’t apply to any AUs or VSTs you’re running).
This online help file from Apple shows you how to find the tuning settings in Logic Pro X.
The big drawback—and I mean huge—it only supports 12-note scales, those scales must repeat at the octave, and each note can only deviate from 12-tet from plus or minus 100 cents (1 semitone).
These limitations restrict you to certain kinds of microtonal scales, and while there’s certainly room to explore within these limits, you’ll miss out on whole genres of microtonal scales that will blow your mind. You’ll miss the unimaginable cloud-like non-octave scales like Bohlen-Pierce and Wendy Carlos’ scales. Stretched-octave scales like Indonesian Slendro and Pelog also can’t be tuned faithfully. And large scales such as the 20-note eikosany, Harry Partch style just intonation, or large equal temperaments, are straight out unavailable.
Nevertheless, Logic makes it easy to microtune its high-quality instruments, even if it is crippled, so if you already own Logic then you should definitely check it out.
If you’re using a DAW that supports AU or VST plugins (such as Logic, Ableton Live, and some others) then you can make microtonal music by using certain plugins that support full microtuning. They can usually import a tuning file and that sets everything up for you.
If you’re willing to spend a little, then have a look through the big list of microtonal software plugins on the Xenharmonic Wiki.
Some people report success running Xen-Arts’ Windows-only VSTs using the free emulator WINE and a free VST host. If you’re of the technical mind to set up WINE, there’s a world of free VST synths for Windows awaiting you!
If you want to design your own tunings and export them for use in other instruments then there’s the Custom Scale Editor (CSE) software from Hπ Instruments. It allows you to tune every MIDI note to whatever pitch you want, exports tunings in a variety of popular formats and can retune the output of sequencers and notation programs. Thanks to Juhani Nuorvala for reminding me to mention it!
I heard that the now discontinued Lil’ Miss Scale Oven was the way to go. Really, I’ve heard wonderful things and wish I could have a little play with it myself.
It’s also possible to install Scala on OS X for free. I’ve never been through this process, but I’ve heard that it’s one of the most challenging things you can attempt to do.
Follow the instructions on the Scala website, and go slowly and carefully. You will be confused. You will have to install other things to get it to work. You will want to cry. But it IS possible…
If you have any other methods of making microtonal music in OS X then get in touch so I can update this post!
Over time I’ve noticed that I get asked this question more and more:
How do I start writing microtonal music?
This always comes from musicians who have enjoyed listening to microtonal music, and are comfortable composing in their own twelveness, but haven’t found the courage or motivation to start experimenting for themselves.
My answer is always the same.
First you gotta get set up with the right tools for the job. In a few hours or less you can set up some free microtonal synths.
The real thing to do, is get ANY microtonal scale up on your instrument, and then play. It’s fine to choose the scale at random. Keep playing until you find something you like about it. Start building up layers over this. This helps you to find how parts of the scale connect with other parts.
After you become a little comfortable with the scale, just try out a different scale and you may find something even better than before. Then over some days or weeks try another and another. Just experiment.
Your composition skills (or lack thereof) shouldn’t hold you back during this time. This is because when you write microtonally you’ll have to discard a lot of the ‘rules’ you already know. Old habits become unable to reinforce themselves. That’s kinda the point of going to all this effort.
Nobody can guide you through microtonal music the same way that they guide you through playing an instrument or learning music theory. There is no established method, instead you get a bazillion competing schools of thought about how to organise and play from the infinite number of scales that are possible. A well-trodden path simply doesn’t exist for you – you make your own path or you don’t enter this forest at all. But if you do make it inside, you’ll find the sweetest fruits. So it’s totally up to you to start trying.
After going through many creative cycles you get to learn about what scales work for you. If you’re the studious type you may be able to read tuning theory concepts and slowly start to grasps small aspects of it.
For me, it was a lot of listening, and a lot of loading randomly-selected scales into my synth to see what I liked and didn’t. A whole lot of failed experiments, and a few that worked. Reading about microtonal tuning theory is overrated, but it can be a starting point for finding interesting scales. If you have nothing more than a good ear, perhaps it’s you who will excel the most in this unknown territory.
And that’s how to start writing microtonal music. It didn’t take anything more than getting your toes wet with a few randomly-selected microtonal scales.
The mtof object can take a MIDI note number and output the frequency of that note in standard 12-tone equal temperament tuning (aka 12-EDO). But what if you want to get away from this musical dogma? How about we start to explore say 13-EDO, 7-EDO, 24-EDO, or 41-EDO with Max/MSP?
Some years ago I wrote an expression that could quickly be dropped into any Max/MSP synth and then play microtonal equal temperaments. It’s a more generalised version of mtof and I want to share that with you today. It’s an mtof-killer!
First let’s take a quick look inside the mtof object and see how it works. Really, mtof just performs one simple expression.
The mtof object on the left always gives the exact same result as the expr on the right. Got it?
Here is my mtof-killer expression in all its beasthood:
Copy and paste this code into Max/MSP and continue along with this tutorial.
----------begin_max5_patcher---------- 882.3ocyXE0aaBCD94To9evh0GZlxRwfwD1aapaR8gsIsWampHfSp6.Cy3zl 1p0e6yXGRnYg.AkRSdvN9riuu6ymu6bd53i5YLNYNIy.7Qvkfd8dRJomRVtj dEB5YD6OOHxOSsPCF49jw2ZLXwbBxbgRtfSedozjYhHhP7PJQu4FYzoL+HCv uJVwjDlf4Gql23SbpbxhongJgRs7AK7RorYwTlbSUnvtPZpuH3FJa50bRfPq KanyPyA.aSq7NDNu0xbn4JcK2JM.U6ErLjxnOpfDT9iUh+6wGk2K6FzXJZpO kUOWL.XPYhRTRY6FsY61pA1sMJuCpGYgp1vKsYb4Igfvulv7GGovY6sdxig9 AOuwSSq1aUiTmiHmh1pLp1i6IQIxsp5iM479h7Ssw9ro6tmLby1Nrda2xEl2 4XVmm71OP26t4RkOlvqlvx8t+e5RZ6zXIOuNjpmBg0QgRzUr0PK2sPrXOUrA 3H6WShckbdruRynCTmSuc22zAiGZK+3hd04wCTRyc2IMDxbHV9wBujzrcOvH semEQCav05Wl6JkSxHLguflvJYvJOBScZIU.bG6xFZI1zo0oFbvUt+cR9tfj 3XRNmrdEQ+jLgvIr.B3aWb9EfumHHua4phnLRPxLl3EHaBe5XEZFtkXifOmD EtIOR6Z7HyQ1syxDzIz.0IUc9qXWOUbRzn7N8.6sTQw92arAj6W4j+LS9sGd U4Vq8M253fVE.8.jf+x4+vX+PcsnxGjq6tGnrCImN5B8nQsnnQKUfPnKZnir T42.WppdgHYdJGb5ISrAmARStGbpt05pqFHKv8rSlX0W90Snn98Aueqq.1u5 zSaMOdkLMthXmnFTdNTUdts2avKMS8YjUEmLdZPRTBe8TuEMdlPO7FS9Bwsv OyT+NS88RDVwEPSul+zL85TWbV++fPou7IVy3yRlwCJNoKdnLnjFCIxPvrkA fub0COKupanggD1K79CoY4kBDVSs.MFX4NTM.XvNGX6.iA2JvhogoIxp.yJh 6nB3X6piVKeLPwnR5ZeaK3FYKntmjgMBX3NGXvFALkyqcmBLuFiKqNEWtMFW vNEWNMFWls3VLbQNsRiZ1s3Ewz8SSuivyVfFsUHybcqN4DdfdLkoGqSyXvI2 QK9I5+fWCetLsiPlyYFWmEe9HrgbFkBkM+yHSxvn -----------end_max5_patcher-----------
The ‘EDO’ value sets what equal tempered tuning you want. So a setting of 5 gives you 5-EDO, a setting of 34 gives you 34-EDO.
‘Reference Frequency’ is the standard pitch for the scale. Usually in Western music A = 440 Hz. You can also use 432 Hz if you believe in crystal healing and reptilian world leaders.
‘Reference MIDI Note#’ is the MIDI note to be tuned to the reference frequency (above). This could be MIDI note 69 if you want to tune to middle A, or MIDI note 60 if you want to tune to middle C.
For starters, try 5 for the EDO value, 440 Hz for the reference frequency and 69 for the reference MIDI note number. Have a play on the keyboard. It’s a cool sounding pentatonic scale, right?
If you played with my example patch and got it working, then you don’t need to read this section. Just start using it in your projects and have fun exploring equal temperaments.
But if you absolutely must know how this magic is done, then keep reading! (Warning: I will assume that you already understand how to make expressions with the expr object).
Let’s look back at the original mtof expression, try to understand it, and then try to generalise it.
Output frequency = 8.175797 * pow(1.0594633,$f1)
Note that pow(a,b) is just the expr object’s way of saying a^b.
8.175797 is the frequency (in Hz) for MIDI note 0.
$f1 is the MIDI note number being played.
1.0594633 is the size of the smallest step size in 12-EDO. It is the value of a semitone.
Therefore an mtof object has this general structure:
Output frequency = Frequency of MIDI note 0 * pow(step size,MIDI note number)
Let’s start by swapping the step size of 1.0594633 with the step size from any n-EDO we want. But how do we calculate the step size? For n-EDO, it’s calculated like this:
step size of n-EDO = pow(2,1.0/n)
So let’s bring that into our in-progress generalised mtof:
Output frequency = Frequency of MIDI note 0 * pow( pow(2,1.0/n),MIDI note number )
That’s great, but unless you want MIDI note 0 to always be equal to 8.175797 Hz, how will we go about tuning our scale up to some standard pitch? Well first we need to know what our standard pitch is (aka reference frequency) and we also need to know what MIDI note number to assign that reference frequency to. Once we know these, we work backwards to find the frequency at MIDI note 0.
If our reference MIDI note number is higher than 0, then the frequency at MIDI note 0 will always be lower than the frequency at the reference MIDI note number. In fact:
Frequency at MIDI note 0 = reference frequency / pow(step size,reference MIDI note number)
We can re-use the step size calculation from before and insert it into the above calculation for MIDI note 0 frequency:
Frequency at MIDI note 0 = reference frequency / pow( pow(2,1.0/n),reference MIDI note number )
Above, we’ve just found a way to calculate the frequency at MIDI note 0 for any reference frequency assigned to any MIDI note number for any EDO of size n. That’s the entire left side of the mtof-killer worked out. So let’s bring alllll of this together:
Output frequency = Frequency of MIDI note 0 * pow(step size,MIDI note number) = (reference frequency / pow( pow(2,1.0/n),reference MIDI note number )) * pow( pow(2,1.0/n),MIDI note number )
And finally we replace these English-language variables with integers and floats in expr format, such that:
$i1 = MIDI note number from the keyboard
$f2 = n-EDO
$f3 = reference frequency
$f4 = reference MIDI number
($f3 / pow ( pow (2,1.0/$f2),$i4)) * pow ( pow (2,1.0/$f2),$i1)
Well done if you kept up! I hope that explains how this expression alone can allow you to play microtonal equal tempered tunings in your Max/MSP projects.
UPDATE: Homebrewed methods like my one above are often inefficient. A commenter Toby noted:
This does the same thing in a simpler way:expr $f3 * pow(2,($f1-$f4)/$f2)
If you need more power than this, for example you wish to create scales with arbitrary and variable step sizes, or you wish to play just intonation scales, then you should read How to play microtonal scales on a Max/MSP synth.
My recent album Rhythm and Xen uses many microtonal tunings. Give it a spin and see how all of this theory can be used to make accessible music with new moods.
Thanks for listening.
Here’s a helpful Scala tutorial for intermediate tunesmiths. Jacky Ligon (xen-arts.net) has explained batch processing and keyboard mapping in Scala. Batch processing is great if you have 4000 Scala tuning files (.scl) and you wish to export them as, say, MIDI tuning dumps or Anamark TUN files, without saving each file manually! You’ll also get a taste for using text commands in Scala, and creating script files from those commands.
To be fair I learned a thing or two from this article myself, and I’ll be using these tricks next time I get the chance.