Sevish Music

Making microtonal scales with Scale Workshop 1.0

A new web app called Scale Workshop allows you to design and play your own microtonal scales. You can also tune various other synthesizers with it. It has just reached version 1.0 and is now recommended for use by the wider musician community.

Scale Workshop has these aims in mind:

  • Scale creation. Use the tools to generate and modify tunings automatically, or manually input your own.
  • Import Scala and AnaMark tunings. Yes it works with that amazing 4000+ scale library that’s floating around the internet.
  • Export the most popular tuning formats easily. Converting .scl files and .tun files is fast. It also exports tuning files for Kontakt, Max/MSP and PureData.
  • No installation required. Scale Workshop runs in your web browser on Windows, macOS, iOS, Android and Linux.
  • Free and open-source. The software costs nothing and it is MIT licensed. Volunteers have already contributed new features and bug fixes on our GitHub repository. Feature requests and bug reports are welcome from anybody.

What else does Scale Workshop do?

Scale Workshop puts a polyphonic synth right inside your browser. You can audition and perform your scales by playing with a connected MIDI controller, QWERTY keyboard, or by using the touch-screen overlay.

Convert scl files and convert tun files to various tuning formats. Export formats include Scala .scl/.kbm, AnaMark TUN, Native Instruments Kontakt tuning script, Max/MSP coll text format and Pure Data text format.

Share your scales with other people by copy-and-pasting the URL in your address bar while working on your scale. The recipient will instantly see your scale information and can play it using their keyboard. This is invaluable for communicating your tuning ideas with others, or allowing your musical collaborators to export your tuning in whatever format they prefer. Try it out.

Display frequencies, cents and decimal values for your tuning across all 128 MIDI notes.

List of supported synths

Note that this list is incomplete.

Via AnaMark TUN (.tun)

  • Big Tick Angelina
  • Big Tick Rhino
  • Camel Audio Alchemy 1.x
  • Humanoid Sound Systems Enzyme
  • LinPlug Alpha
  • LinPlug CRX4
  • LinPlug MorphoX
  • LinPlug Octopus
  • LinPlug Organ 3
  • LinPlug SaxLab
  • LinPlug Spectral
  • Mark Henning AnaMark
  • PolyGAS
  • Spectrasonics Omnisphere
  • TAL BassLine-101
  • TAL Sampler
  • TAL U-NO-LX
  • u-he ACE
  • u-he Bazille
  • u-he Diva
  • u-he Hive
  • u-he Zebra
  • VAZ Modular
  • VAZ Plus
  • Virtual CZ
  • Xfer Serum

Via Scala .scl/.kbm

  • amsynth
  • Applied Acoustics Chromaphone 2
  • Applied Acoustics Lounge Lizard EP-4
  • Applied Acoustics String Studio VS-2
  • Applied Acoustics Ultra Analog VA-2
  • Cakewalk Dimension Pro
  • Cakewalk Rapture Pro
  • Cakewalk Z3TA+2
  • Garritan Personal Orchestra 4
  • Imageline Harmor
  • kv331audio Synthmaster and Synthmaster One
  • Key Tuner JSFX Script
  • Madrona Labs Aalto
  • Madrona Labs Kaivo
  • Madrona Labs Virta
  • Modartt Pianoteq
  • padthv1
  • Plogue Alter/Ego
  • Plogue Chipsounds
  • Plogue Sforzando
  • PolyGAS
  • Reveal Sound Spire
  • samplv1
  • synthv1
  • UVI Falcon
  • ZynAddSubFX
  • Zyn-Fusion

Others

  • Max/MSP (via text file you can load into the coll object)
  • PureData (via text file you can load into the text object)
  • Native Instruments Kontakt (via text file you can load into the Kontakt script editor)

A personal note

This has been a labour of love for almost 2 years – I hope that many people will find it useful! If you want to share any work you’ve created with Scale Workshop then I’d love to hear about it.

Now that Scale Workshop is in a stable state, I am going to focus my attention back on composing new music and hosting the Now&Xen microtonal podcast.

 

Open Scale Workshop in a new window

 

New albums by ZIA and Jacky Ligon

Hey microtonal gang. Here are two new releases of xenharmonic electronic music that have come out in the last month. I’ll have both of these in rotation as we go into 2019.

ZIA – Four-Momentum

Elaine Walker’s space-pop band ZIA had been mostly quiet since their last album Drum’n’Space in 2011. Seems Elaine was very busy writing and publishing her first book as well as being a mom. I guess that’s a good enough excuse! Four-Momentum is an instrumental album inspired by space-time. The album uses various equal tempered scales (16edo, 17edo, 20edo and Bohlen-Pierce scale).

Jacky Ligon – Transition

Jacky Ligon’s new record Transition is a mix of ambient and dub that could very well be described as ‘drum and scape’. Various just intonation scales are in play here. The rhythmic layers in Jacky’s music are deep and complex – like scapes all of their own. Same for the microtonal pitch structures which could also be imagined as scapes. Everything about this record is deep.

Transition is also the debut release on ScapesCircle Records. Seems they’re off to a very promising start indeed.

Introducing Now&Xen: a podcast about microtonal music

I always wanted to hear a podcast that discusses microtonal music and plays some tunes. Now Stephen Weigel and I have started such a podcast and invite you to listen to the first three episodes of Now&Xen below:

The pilot episode covers some introductory topics and is fairly short. The next episode “1/1” is already recorded and is much longer, going in depth about how to start making microtonal music and what tunings would be good for beginners.

For the third episode we had our first guest, Elaine Walker of ZIA.

Subscribe

DIY Workshop – Build your own Home Swinger – Yuri Landman

March 7th 2019 – Bristol, UK – An event that should interest fans of experimental and microtonal instruments!

The Home Swinger is a simplified version of Landman’s legendary Moodswinger instrument he built for Liars in 2006.

Image of a row of Home Swingers, an instrument invented by Yuri Landman

Yuri Landman presents a 5-hour long Do-It-Yourself workshop whereby participants will leave with a finished Home Swinger instrument as well as a strong understanding of its structure and workings.

Participants require no special skills and the difficulty of the process has been compared to building a piece of IKEA furniture!

In advance of the workshop Yuri will prepare the component parts of the instrument for the participant to use in construction. These include: 4 pieces of ready shaped wood in the required sizes and predrilled with holes, easy to employ machine heads for the strings, one pickup (good quality, equal to Fender), an on/off switch, a jack output, a few screws, bolts and nuts and some metal for the bridges, as well as two sets of strings.

The participants pay 110 Pounds for their own materials. Each workshop is limited to 10 persons.
Duration of the workshop is approximately five hours.

If you would like to attend then you can RSVP on the Facebook event. The event will go ahead if there is enough interest. I intend to join the workshop too so maybe I will see you there!

Microtonal Adventures Festival 2018, May 18-20

Microtonal Adventures Festival

Four concerts, ten lectures, two workshops, and a roundtable discussion exploring music outside the standard western tuning system.

UnTwelve, WWU, and Sound Culture present the Microtonal Adventures Festival, May 18-20 on the campus of Western Washington University in Bellingham (USA).

I’ll be on the microtonal electronica panel discussion, May 20th 2-3pm (UTC-7). The panel includes Bruce Hamilton, Brendan Byrnes, Igliashon Jones and Sevish (via Skype).

There will be other workshop events and concerts so check it out if you’re in the area.

Microtonal Adventures Festival

Informative videos about microtonal music on YouTube

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

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

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

amsynth 1.8.0 adds support for microtonal tunings

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

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

Installing

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

sudo apt install amsynth

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

Tuning amsynth

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

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

Full-keyboard microtuning

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

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

The future

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

Sevish – Harmony Hacker out now

Happy to announce that I finally finished a new collection of microtonal electronic music, Harmony Hacker, and you can hear it now:

9 tracks of microtonal bass music, in much the same style of Rhythm and Xen, Golden Hour, MK-SUPERDUPER, Human Astronomy… The download from bandcamp contains PDF liner notes, where I discuss a little about each track and any processes/tunings used.

Spotify/iTunes/YouTube/Soundcloud release forthcoming – for now grab Harmony Hacker from Bandcamp – enjoy the sounds and thanks the support!

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.

Cycling ’74: New retune~ object for Max 7 offers pitch correction with incomplete support for microtonal tunings

Cycling ’74 have released a new object for Max 7 for real-time pitch correction of incoming audio. That highly promising object is called retune~. It looks like Cycling ’74 have also spent time thinking about the struggle of microtonal musicians, because this object supports microtonal scales! You can specify your tuning in cents or ratios, and you can pick a reference pitch in Hz. This is just fantastic to see, and I hope more Max/MSP artists will now be exposed to the world of microtonal scales.

retune~

Here’s the catch

The problem is that intervals of an octave or larger are somehow not supported by retune~. retune~ assumes that your scale will repeat at the perfect octave of 1200 cents (2/1). If you try to add an interval of 2/1 or larger, then you will receive an error message:

Note must be between 1 and 1199 or a relation (1/2, 5/4), value '2/1' ignored.

This will cause difficulty for many because it rules out the use of non-octave tunings. The Bohlen-Pierce scale, the slendro and pelog scales of Indonesia, and Wendy Carlos’ Alpha, Beta & Gamma are amongst the most interesting collections of pitches that you should ever hope to hear.

The documentation for retune~ says that Scala format tuning files (.scl) can be loaded, but I fail to see how this is possible as Scala has support for non-octave scales while retune~ doesn’t. That means that many of the Scala files from my library will cause errors when I load them into the retune~ object. This is patently not Scala support, this is a dodgy hack.

To their credit, Cycling ’74 have gone to great effort to include microtonal tunings in their new retune~ object, and I am truly grateful for that. But it looks they didn’t consult any of the microtonal musicians who would want to make sure that all kinds of microtuning were permitted.

If you are a Max user who would like Cycling ’74 to take some action on this issue, write in to their support team now and also post on their forum. The retune~ object may improve if people make their voices heard.

This is my appeal to all audio technology developers

New instruments are appearing on a regular basis with incomplete support for microtonal scales. Whether it is down to inexperience with microtonal scales, or lack of time/materials/money to do the job properly, it’s sad to see some developers getting it wrong while others get it 100% right.

Please consult with microtonal musicians who work with these ideas on a daily basis! The limitations in your approach will soon become clear as day.

Thankfully some developers are implementing microtonal scale support in the right ways, whether by supporting scl/kbm pairs, MIDI Tuning Standard, or scripts.

If any developers want to reach out to me personally, you can do so via sevish.com/contact and I will do my best to reply by email. You can also join the world’s busiest online microtonal music community at Xenharmonic Alliance II, where hundreds of microtonalists will be willing to provide you with insight into our dark art.

Other ways to make microtonal music in Max/MSP

It is possible to make microtonal music in Max/MSP by synthesis using two methods that I find really easy to work with. You can use a coll object to store a frequency for each MIDI note number, or you can use the expr object to convert MIDI note numbers directly into frequencies of any n-tone equal temperament.

The coll method is more appropriate for just intonation, unequal or empirical scales, whereas the expr method is nice if you want to play equal temperaments or harmonic series based scales and you want to allow the user to adjust the tuning on-the-fly.

To see this in action, download my Max 4 Live instruments where I use both tuning methods.

Oh and you can already use retune~ in Ableton Live

If you want to use retune~ in Ableton Live, Cycling ’74 have released a pack of Max 4 Live devices to do just that. The pack is called Pitch and Time Machines and the two devices to pay attention to are Autotuna and Microtuner:

Autotuna – A scale-based microtonal auto-tuner that can use Scala files [lol]. This device uses the retune~ object to tune the audio to a given scale. Scales can be either entered by hand, or loaded from Scala files [lol] – a file format for musical tunings that is a standard for exchange of scales. Learn more about Scala.

Microtuner – A table-based microtonal auto-tuner that can use Scala files [lol]. This device is similar to the Autotuna example device, except that scales are entered using a graphic function whose shape can be curved, thus providing some unexpected pitch scales.

Thanks to Todd Harrop for his research and Joakim Bang Larsen for bringing retune~ to my attention.