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The Golden Ratio as a musical interval

The golden ratio, also known as φ (phi) or approximately 1.618, is a number with some trippy properties. It’s no wonder that many people treat the golden ratio with a great deal of mysticism, because (here’s the cliche part) it appears repeatedly in nature and also crops up in many fields of mathematics. And we all know that mathematics is the language of the universe. Duuude.

So I want to talk a little about the golden ratio and how it might sound if we used it as a musical interval.

You may have seen or heard some youtube videos which exclaim “this is what the golden ratio sounds like!!” — These are almost always based on the decimal expansion of phi, where each digit is assigned to a note of the major scale. I won’t give an example here because it’s such an unimaginative Western-centric interpretation of nature’s finest ratio. Just imagine the background music for a shitty Google commercial, children and mothers playing, young trendy people smiling while looking into their laptops, and you get the idea.

Let’s have none of this. The truth is that the golden ratio, as a musical interval, is gritty, dirty, dissonant, inharmonic, and not remotely like you’d expect. And it’s explicitly microtonal.

Take for example John Chowning’s Stria, an important electronic work from 1977, using his then-new discovery of FM synthesis. The golden ratio is used as the interval between carrier and modulator, such that the resulting timbre is an inharmonic cloud of golden-ratio-related partials. To get a sense of what the golden ratio may sound like as a musical interval, start from here and let the sounds slowly work their way into your brain.

Which golden ratio is the real golden ratio?

Here is something that causes confusion time and time again. There are two musical intervals which both claim to be the golden ratio! How is this possible?

Consider the octave in terms of cents. Cents are a musical measurement of pitch which divide the octave into 1200 logarithmically equal parts. This means that 200 cents is equivalent to an equal-tempered whole tone, 100 cents is equivalent to a semitone, 50 cents is equivalent to a quartertone, etc. So our first version of phi will simply divide 1200 by phi:

1200 / φ = 741.6407865 cents

~741 cents sounds like a horribly sharp fifth. Well, we already know that the golden ratio sounds dissonant, so this could be the golden ratio that we’re looking for. But first let’s look at the other contender:

1200 * log2(φ) = 833.090296357

While both of these intervals could be used to generate scales that you could play interesting music with, only one of them gives me that one-with-the-universe vibe. To find out why, we need to look at a psychoacoustic effect known as combination tones.

A pine cone showing off its Fibonacci sequence, related to the golden ratio

Combination tones

It is a simple fact of psychoacoustics that any two tones that you play will produce additional combination tones. There are two types of combination tone: difference tone and sum tone. The sum tone is calculated by summing the frequencies of the two tones. The difference tone is calculated by subtracting the frequency of one tone from the other.

Let’s play A (440Hz) and E (660Hz) on the keyboard and work out these combination tones for ourselves.

Difference tone = 660Hz - 440Hz = 220Hz

Sum tone = 660Hz + 440Hz = 1100Hz

The difference tone sits an octave below the root note of A. This is the reason why you hear the missing fundamental being “filled in” by your brain when you play a power chord or a just major triad.

As for the sum tone, it is tuned to the 5th harmonic above that missing fundamental of 220Hz, because 220Hz*5=1100Hz. The 5th harmonic is a just major third plus two octaves. The sum tone is perhaps one of the reasons why the just major triad is such a stable and pleasing sonority.

Just to recap: If I play TWO tones (440Hz and 660Hz), your brain hears FOUR tones, (220Hz, 440Hz, 660Hz, 1100Hz). The effect is subtle, and the combination tones are heard a lot more softly than the real tones, but the effect can be perceived. Bearing that in mind, let’s work out the combination tones that appear when using the golden ratio interval.

We shall play a 1kHz tone and a ~1.618kHz tone. The interval between these two tones is the golden ratio of ~833 cents.

Difference tone = ~1.618kHz - 1kHz = ~0.618kHz

Sum tone = 1kHz + ~1.618kHz = ~2.618kHz

What’s interesting about these combination tones is that they are themselves related to the original tones by the golden ratio. This is easy to demonstrate:

1kHz / ~0.618kHz = φ

~2.618kHz / ~1.618kHz = φ

All four of these tones are related by the golden ratio! If we calculate the 2nd order combination tones, 3rd order, and so on, we’ll find the same thing again and again. Every combination tone is connected to some other tone by the golden ratio. This is exactly the recursion effect that we expect to find when we use the golden ratio properly.

However this landscape of recursive inharmonic partials can best be described as a chaotic and complex mess. This is an extreme contrast to the use of the golden ratio in visual proportions, paintings, architecture, flowers and nautilus shells, which most people would agree appear harmonious and pleasing. But that’s just the truth of it. The ear works in weird ways. Not all visual forms have an analogue as sound.

Cross sections of a nautilus shell. Some sections show stronger golden ratio proportions than others.

Generating a scale based on the golden ratio

By now it should be clear that golden ratio music has some interesting properties that the Western equal-tempered scale could scarcely hope to reproduce. If you have some highly accurate micro-tunable instruments and perhaps some scale-designing software such as Scala, alt-tuner or LMSO, then your next step is to design a scale that features the golden ratio.

There are many possibilities when making your own phi-based scale, but today I will only give you one. Developing your own golden ratio scales is left to you as a rainy day exercise.

Almost all scales contain an interval of equivalence, and for most scales that interval is the octave. In octave-based systems, a note such as C appears many times, and each C is separated by one or more octaves.

By the way, an octave is a ratio of 2. If you play an A at 440Hz and then play the A’ one octave higher, the higher pitched note would be 880Hz.

For our scale, we want to pack in as many golden ratios as possible. There’s no room for any boring numbers such as 2. Indeed, our interval of equivalence will be the golden ratio itself. This means the scale will repeat after approximately 833 cents. This scale would fit snugly into the frequency space between 1kHz and ~1.618kHz.

Our next step is to divide this interval into smaller intervals (a & b). Each time we divide an interval into two intervals, those intervals should have the golden proportions.

Golden ratio line

Then take the biggest interval that remains in the scale and break that down into 2 intervals with the golden proportion. Repeat this process until you have enough pitch material to write music with.

I’ve done all the calculations, and the resulting scale (taken to 8 steps) is presented below in Scala format so that you may try it out for yourself:

! sevish_golden.scl
!
Scale based on the golden ratio
 8
!
 121.546236174916
 196.665941335636
 318.212177510552
 439.758413685468
 514.878118846189
 636.424355021105
 711.544060181825
 833.090296356741

Some interesting notes about the above scale… When generating the values, I noticed that the scale was a Moment of Symmetry (MOS) after 3, 5, 8 steps. Those are Fibonacci numbers. I stopped after 8 steps because it will map very nicely to a piano keyboard with linear mapping. With this mapping, you will always hear the golden ratio when you play a minor sixth on the keyboard. Coincidentally, this tuning has some fair approximations to the fifth, fourth, supermajor third, minor third, and major second.

If you want to find more tunings with the golden ratio, you might look at Heinz Bohlen’s 833 cent scale for inspiration.

The golden ratio as a spectral microtuning

When using scales that are based on the golden ratio, you will find that timbre makes a huge difference to the result. If you use an instrument that produces bright and clear harmonic overtones such as the violin or a sawtooth wave, you will hear an unruly clash of a harmonic timbre against an inharmonic scale.

Instead, you could take a similar approach to John Chowning and bake the golden ratio right into the timbre itself by using inharmonic overtones based on the golden ratio. Then suddenly your timbres and your scale will align, resulting in a much smoother sound. It’s just one more demonstration of the fact that tuning and timbre are deeply intertwined.

If you’re a computer musician, download a free copy of the Xen-Arts synth plugins. These instruments can produce inharmonic partials which can be controlled by the user. By default, they include a setting where each partial is tuned to some multiple of the golden ratio. These instruments could be a quick way to explore the topics I’ve been discussing in this post.

Exercises

  • Jam and improvise in the above golden ratio tuning until your ears tune into it.
  • Apply the above tuning method to sequence your own golden ratio rhythms.
  • Write a piece of music that combines both of the above.
  • Make sarcastic YouTube comments saying that John Chowning’s music heals DNA.
  • Change your desktop wallpaper to a picture of a spiral galaxy.
  • Get your head around microtonal tunings by listening to my new album Harmony Hacker.

Mapping microtonal scales to a MIDI keyboard in Scala

I recently wrote a tutorial about how to change the root note of your microtonal scale, where I used Scala’s Edit Mapping dialog. There is so much more I want to say about keyboard mappings. This time I’m explaining how to map various microtonal tunings on to a standard MIDI keyboard in a sensible way.

Needless to say, this topic is important for musicians who want to use microtonal tunings on their standard MIDI keyboard controller. I’ll be using Scala for this tutorial.

First, an explainer on “scale degrees”

This is an incredibly simple but powerful idea. Scale degrees are numbers that describe the order of notes in a scale. The root note of a scale is always scale degree 0, and the degree numbers increase as you go up the scale. For a 7 note scale, the scale starts on degree 0, then passes through 1-6. When we reach 7, we’re an octave up from where we started. In this case, 7 would be called the octave degree.

The familiar 12-equal scale could also be described with scale degrees. Let’s take C to be our root note, so C = 0. The rest is as follows:

Name C C# D D# E F F# G G# A A# B C’
Scale degree 0 1 2 3 4 5 6 7 8 9 10 11 12

When we’re working with large scales, notating by scale degree becomes an efficient way of describing what notes we want to play. We will also use scale degrees to tell Scala how to map notes to a keyboard.

How to map a 7-note tuning to the white keys

Imagine we have an excellent microtonal 7-note scale, such as 7-EDO, mavila[7], or something else. By default, your synth maps these notes linearly and chromatically across your MIDI keyboard. Press the C key, and at the same time press the key which is 7 steps above it (that’s a G). You will hear an octave! That’s incredibly jarring, because we expect to hear an octave from C to C, not from C to G.

Linear mapping of a 7-note scale on to chromatic keys:

Linear keyboard mapping of a 7 note scale

The scale degrees in red are octaves. NOT fifths!

Custom mappings help to make a regular pattern that is much more familiar and easy to navigate:

Keyboard mapping with a 7-note scale on the white keys

The diagrams above should make it obvious that linear mapping is a problem. With linear mapping, fingering becomes irregular as you go up and down by aural octaves. For a 7 note scale, we can simply skip out the 5 black keys to get a regular, repeating pattern.

Start off by loading a 7 note scale into Scala. I simply typed ‘equal 7’ to get 7-EDO.

Then go to Edit > Edit Mapping (Alt+P).

The mapping should repeat every 12 notes on our keyboard, so set Size to 12. Remember that’s 7 notes from our scale, plus 5 black notes we’ll skip out, totalling 12.

Set a value for Formal octave degree, which is 7 in this case.

Fill out the remaining fields as shown below:

If you don’t see the fields at the bottom, make sure you enter a value for Size. Scala will then create the empty fields for you automatically, and you can type in the scale degrees that you want for your mapping.

Note that we’re skipping the sharps/blacks, so you can leave those fields blank. Or if you’re like me, you will see this as an opportunity to enter duplicate notes and create a sweet sounding pentatonic mode from the main scale.

Once you’re done, click Save As and save the resulting mapping file. Scala mappings are saved in .kbm format. The great thing about this, is that you can mix and match your .kbm mapping files with .scl tuning files that you have collected. So if you have several .scl tuning files with 7 notes, then you can use this same .kbm mapping file on all of them.

While you have a scale and a mapping loaded at the same time, now is a good time to export your tuning for softsynths, or relay it to hardware synths. It feels much easier to play with the new mapping.

How to map a 12-note subset of a larger tuning

Now imagine that we have a tuning much larger than 12 notes, and we want to select just the notes that we want to map on the keyboard. For example, let’s try the calm vibes of 31-EDO. Just for context here is some music written in 31-EDO. 31 is a very nice meantone temperament, very close to quarter-comma meantone.

Here is how 31-EDO would be linearly mapped to a keyboard:

Linear mapping of 31-EDO on to a keyboard

I don’t know about you, but my hands aren’t wide enough to hit that octave.

Seriously this is just ridiculous. 31 notes is too many for most musicians to keep track of, so let’s just pick 12 notes for our mapping:

Keyboard mapping for 31-EDO, quasi-12-equal

The 12 notes that I selected give a quasi-12-equal. But you should feel free to choose your own notes and experiment with what your ear likes.

Go to Edit > Clear Mapping to reset your mapping back to normal, then go to Edit > Edit Mapping to open the keyboard mapping dialog. Fill in the Size (12) and Formal octave degree (31) then enter the scale degree for each note of the mapping.

Scala keyboard mapping dialog for 12-note mode of 31 equal temperament

As before, now is a good time to save your .kbm mapping file, and load it up on a synth of your choice.

How to map a 12-note subset of a larger tuning (alternative method)

Instead of using Scala’s keyboard mapping functions, we could do it with the mode command instead. The mode command lets you choose a subset of notes from your currently loaded scale, and then it deletes the remaining notes.

The end result would be a single .scl file with the extra notes removed, instead of the usual .scl and .kbm pair (containing the full gamut of notes plus tuning information). You might use this method if your synth supports .scl files but not .kbm files.

Imagine that we want to recreate the above quasi-12-equal mode from 31-EDO. Just type these commands into Scala:

equal 31
mode 3 3 2 3 2 3 3 2 3 2 3 2
show

You’ll get the following output from Scala:

  0:          1/1               0.000000 unison, perfect prime
  1:        116.129 cents     116.129032
  2:        232.258 cents     232.258065
  3:        309.677 cents     309.677419
  4:        425.806 cents     425.806452
  5:        503.226 cents     503.225806
  6:        619.355 cents     619.354839
  7:        735.484 cents     735.483871
  8:        812.903 cents     812.903226
  9:        929.032 cents     929.032258
 10:       1006.452 cents    1006.451613
 11:       1122.581 cents    1122.580645
 12:          2/1            1200.000000 octave

Note that, when you use the mode command, you enter the difference (in scale degrees) between successive notes of the scale. The table below shows you how the difference between scale degrees relates to the scale degrees themselves.

Scale degrees 0 3 6 8 11 13 16 19 21 24 26 29 31
Difference 3 3 2 3 2 3 3 2 3 2 3 2

You should also notice that 3 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 2 = 31. The sum of these digits must be equal to the octave degree, which is 31 in this case. Otherwise, the mode command will give you an error: Scale and mode size are unequal.

Further exercises

  • Load up a random large EDO, such as 23-EDO or 50-EDO, then pick a really fruity sounding pentatonic scale to map to the black keys.
  • Combine this tutorial with the previous tutorial: Create a custom keyboard mapping that also sets a base frequency and base key.
  • Experiment with Moment of Symmetry scales (e.g. mode 2 2 2 1 2 2 in 11-EDO, or mode 1 2 1 2 1 2 1 2 1 2 in 15-EDO).

 

Scala tutorial – how to change the key of your scale

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.

Changing key in 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.

Note name C C#/Db D D#/Eb E F F#/Gb G G#/Ab A A#/Bb B
MIDI note number 60 61 62 63 64 65 66 67 68 69 70 71
Frequency 261.63 277.18 293.66 311.13 329.63 349.23 369.99 392.00 415.30 440.00 466.16 493.88

Saving your keyboard mapping for re-use

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.

scl/kbm format

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.

Some frequencies are better than others

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.

That’s it

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.

Further reading

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.

Making microtonal music with tracker software

A tracker is a type of music sequencer that was popular back in the day. The tracker scene is still alive, and you can thank it for all the catchy tunes you hear while using keygens. A handful of trackers also support microtonal scales, and I wanted to share some of those today.

OpenMPT (Open ModPluG Tracker)

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

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.

OpenMPT microtonal tuning

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.

Little Sound Dj

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.

LSDJ

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.

LSDJ-5edo

Renoise

Renoise instruments can be retuned by using a neat scl to xrni tool.

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.

MikyTracker

MilkyTracker doesn’t have any microtuning function built in, but you can 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.

Obviously this takes a while to set up, so you might find OpenMPT to be more user friendly. Nevertheless this hasn’t held some people back. Here’s the proof, a tasty jam in just intonation using MilkyTracker:

Other trackers

If there are more trackers that support microtonal scales then I would love to hear about them.

Important links

Further reading

FM synthesis with Xen-Arts FMTS 2 video tutorial

This is my first video tutorial, showing how to design a distorted bass sound using FM synthesis in Xen-Arts’ FMTS 2 VSTi.

FMTS 2 is a freeware VST instrument for Windows which allows you to play microtonal scales. It’s developed by Xen-Arts. The FM operators can themselves be tuned to microtuning-related frequency relationships, so that the timbre has a sort of spectral microtuning within it. Quite mindblowing stuff and seriously underrated.

Download Xen-Arts FMTS 2– http://xen-arts.net/xen-fmts-2/

The tutorial just demonstrates a basic workflow, and it’s possible to go way deeper with this synth. If there is any interest in further videos like this, best to leave a comment below or on the YouTube video itself.

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

What’s the difference between ET and EDO?

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!

Microtonal music in Bitwig Studio

Bitwig Studio Microtonality

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.

Pitch bend method

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.

Bitwig Pitch Bend

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.

Equal temperaments with Bitwig Note MOD

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.

Bitwig Note MOD

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.

This gives you a world of microtonal and macrotonal equal tunings to explore. But note that this method won’t allow you to play just intonation scales or other unequal scales.

VST instruments

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.

SysEx / MIDI Tuning Standard support?!

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…

If you’re using the Xen Arts plugins in Bitwig Studio under Windows or WINE then you’d better just load the .mid tuning-dumps via the UI directly on the synth itself.

Bitwig modular microtuning

Bitwig Modular

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.

Further reading