Sevish Music

Inharmonic Strings and the Hyperpiano

Vibrating strings produce (more or less) harmonic overtones. If two strings are tuned in some simple frequency ratio such as 3/2, 4/3 or 5/3, then those harmonic overtones match up nicely and avoid roughness. But if the two strings are tuned in some haphazard fashion then the overtones of each string won’t match up, causing the overtones to clash with each other.

We can actually plot out a graph which shows the interval between two strings and the corresponding dissonance. This is called a dissonance curve, and for a normal string it looks something like this:

So what.

Well, imagine a weird kind of string that produces inharmonic overtones, such that the dissonance curve looks different to the one above. Because the dissonance curve is different, you couldn’t play Air on the G String and expect it to sound good. You could however write new music that would fit with the novel dissonance curve.

Today, such a string is more than just a mathematical curiosity. It exists in the physical world.

Inharmonic Strings and the Hyperpiano” (by Kevin Hobby and William Sethares) is a paper published in Applied Acoustics. The strings in their hyperpiano have a stretched out dissonance curve where the double-octave sounds most consonant and the octave becomes dissonant. Okay so maybe it’s not going to be used on every new pop record, but this kind of freaky instrument can produce game-changing new tonalities.

Since the dissonance curve is stretched out to the double-octave or “hyperoctave”, Kevin Hobby suggests we might try tuning a hyperpiano instrument to 12 equal divisions of the hyperoctave. Wait, isn’t that just 6-EDO – a whole tone scale? Actually, it isn’t! They may be identical tunings, but the octave is considered a dissonant interval on the hyperpiano, analogous to the tritone on a normal piano. So it makes a lot more sense to describe this tuning as 12 equal divisions of the hyperoctave. Really.

The ringing of the strange hyperpiano sounds like a death bell for the unwavering cult-like belief in pure ratios and true frequencies. Tuning and timbre are deeply linked. If we’re willing to experiment with new timbres then we can uncover new musical vocabulary for the future to come.

The next step is to explore all this for yourself – download the sampled hyperpiano and give it a play.

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.

Xen-Arts VSTi Microtuning Library

Xen-Arts have recently made available a pack of microtonal tunings that you can download and use in your projects. Various formats are included, so all you need is a VST instrument that supports .scl Scala files, AnaMark TUN files or MIDI tuning dumps.

The pack includes equal scales, harmonic scales, subharmonic scales, and three of Wendy Carlos’ non-octave temperaments.

Xen Arts VSTi Microtuning Library

This resource is a good alternative to the whopping 4000+ Scala file database that leaves many beginners paralysed for choice. The Xen-Arts’ pack provides text documentation to help you understand the tunings included. As such, I believe it’s a good resource to get you started.

Some time ago, I also produced some starter packs of microtuning files. Using these in addition to the new Xen-Arts pack will keep you busy for several months at least. By that time, you should be crafting unique microtonal scales of your own.

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.

Wasting & Thirsting by Cryptic Ruse

Increasingly, people in this crazy world are looking for something positive, something uplifting so they can get reprieve from the chaos around them. For some, that comes as an addiction to sharing inspiring quotes on Facebook, while others find peace meditating to mass-produced new-age music.

But we understand that not everybody is in that boat. Some people are actually looking for more DOOM in their lives. This is where Cryptic Ruse’s Wasting & Thirsting comes in.

Wasting & Thirsting is an album of microtonal doom drone metal. It is an atmospheric dark-zone where down-tuned distorted guitar and a ton of processing create the entirety of the music. I could barely tell where one track ends and the next begins as the effect is so hypnotising. Each of the 3 tracks uses a different microtonal tuning system, and yes Cryptic Ruse had a custom guitar made for each tuning.

This music throbs, beats and moans as clusters of sludgy microtones overlap each other. There is no percussion. There are no vocals. Just a droning anti-aum to help you fade away into t h e a b y s s o f d e s p a i r.

Like any good drone, you sorely miss it once it ends. The only solution is to flip over the mp3 and play it again.

Wasting & Thirsting by Cryptic Ruse was released on August 14, 2016. You can download it from their bandcamp.

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.

99% of Western music is beans on toast

Could you survive on a diet of 12-tone equal temperament

Agree, disagree?

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!