WHAT IS MICROTONALITY?

What is microtonality or microtonal music?

As a default setting, by far the most modern day musical instruments use a so-called 12-EDO tonescale, also called equal temperament. That means that there are 12 Equally spaced Divisions in an Octave, the 12 semitones behind the black and white keys of a piano or a synthesizer. In almost any modern-day music, you only hear this 12-EDO tonescale.

That's not a law, however. It's not carved in stone that all music has to restrain itself to this set of pitches. There's a lot of 'space' in between those 12 divisions of an octave. Any music that uses tones that are not equal to a 12-EDO is generally called microtonal music.

The term covers a very broad range of possibilities of course. Many instruments through different cultures, historical epochs and instrument manufacturers use different tuning systems. From small subtle deviations of 12-EDO to plainly different tuning systems.

 

JUST INTONATION

Let's listen first to an example where small corrections to the 12-EDO scale result in a very different sound: Just intonation. In the following examples a major C chord is played 2 times. First in standard 12-tone equal temperament tuning (most synthesizers' basic tuning), and then using Just Intonation.

Quite a difference, isn't it? Does the first one have some kind of chorus effect on it?

No, not at all... On a just intonated chord like the one above, the three notes C-E-G have their frequencies in proportion 4/4 - 5/4 - 6/4, or 1 - 1,25 - 1,5. On an equal tempered chord that's 1 - 1,25992105 - 1,498307077. So that's only an approximation, the three notes are sounding close, but keep slightly beating. In a just intonated chord, the three notes grab each other close and sound together as an integer unity. Both versions do sound well, but you can't say they're equal! The tuning difference between the two is only very minimal, though.

In a Just Intonation scale, frequency ratios between notes are expressed using rather small integer numbers. An octave has of course a 2/1 freq ratio, and the dominant or 7th semitone above the root mostly has a 3/2 ratio. Other notes can differ a bit depending on the exact implementation.

What is the exact Just Intonation scale Modor uses? We used the most 'strict' version of it, ie. the scale with the smallest numbers in the fractures. Example with root note C:

•	C	1/1
•	C#	16/15
•	D	9/8
•	D#	6/5
•	E	5/4
•	F	4/3
•	F#	7/5
•	G	3/2
•	G#	8/5
•	A	5/3
•	A#	9/5
•	B	15/8
•	C	2/1

 

MIDDLE EASTERN MAQAMS, OR 'ORIENTAL' TUNING

A quite well-known example of microtonality is Middle Eastern, Turkish and Arabic music. Why does it sound so different from western music?

Well, because it uses a different tuning system. It is simply impossible to play Arabic music on a 12-EDO equal temperament instrument. You need an instrument supporting a form of Maqam tuning.

As a first, good approximation to this, many instruments and so-called 'oriental' keyboard and synths use quarter-tone tuning. Certain tones in the tonescale can be tuned up or down by ¼ tone to be right in the middle between the classic 12-EDO tones.

The next example uses a Bayati Maqam. The E (mi) in a 12-EDO scale has been tuned down by a ¼ tone to be right in the middle between E and E♭ (mi and mi♭). The root note of the scale is on D (re).

 

HARMONIC SERIES

The next example is made using the so-called Harmonic Row. That's a row of notes with frequencies f, 2f, 3f, 4f, 5f, 6f, 7f, ... Or indeed, a row of harmonic frequencies of base frequency f. Here, f=33Hz or C-0, so 8f is 264Hz (C-3) and 16f is 528Hz (C-4). In the octave between C-3 and C-4 we have 8 notes in the harmonic row: C-3, D-3, E-3, F-3, G-3, A-3, Bb-3, B-3 and C-4. The F-3, A-3, and Bb-3 notes sound quite severely out of tune compared to the regular 12-EDO tonescale. But they still are in a harmonic relation to the rest, so they still do sound harmonic in a way... It's very easy to play beautiful melodies in that octave. Fascinating, isn't it?

OTHER EDO SCALES

In certain ethnical music styles, people use other equal divisions of the octave (EDO) scales than 12-EDO. Or at least, you can approximate them by using a certain EDO scale, such as Indonesian Gamelan, that uses a subset of 9-EDO, or the 22-EDO indian Shrutis. It would carry us way to far to try to explain it all over here.

 

A MICROTONAL NF-1(m)...

Since firmware upgrade OS13, the Modor NF-1 and NF-1m are hardware polysynths with full microtonal capabilities! But what did we exactly implement on the Modor NF-1(m)?

Modor's approach is a bit different. We collected a set of microtonal scales we encountered and found to be inspiring on our trip down the microtonal jungle. We implemented them in the NF-1(m) for you to roam around, play with them, and get inspired. And once you feel the connection, just store your patch. Your chosen microtonal scale gets saved along.

That's also an answer to another question: where are all the different Just Intonation options? Where are the Ptolemian, Pythagorean, Werkmeister, Meantone, ... etc tunings? Well, we don't want to overwhelm people with dozens of barely different options. We wanted to give a limited but inspiring set of possibilities instead of a plethora of options, as this often kills creativity. Dive into it, you won't drown!

Do you think we overlooked some interesting microtonal scale that should also be implemented? Please, let us know your thoughts for future firmware updates!

 

THE MODOR SCALE: A LITTLE MODOR SECRET...

At the time, when we were implementing the first microtonal options on the NF-1(m) for OS13, we discovered a bug in one of the oldest central core parts of the DSP code. This invoked some imprecise calculations that led to the NF-1(m) always being slightly out of tune. Even up to a few cents on certain notes. Wow! 😮

Of course, we could just simply have fixed this bug, thereby theoretically improving the tuning of our machines. But we didn't! Why not? Because beauty isn't always in perfection. Probably many people would have remarked the NF-1(m) getting 'cleaner' or more 'polished' after installing such bugfix upgrade, and some wouldn't like it without really knowing why. The little tuning imperfections indoubtedly became a part of the Modor Sound through the years.

And so, we didn't fix the imperfections. Of course, for those users who need a *perfectly perfect* equal temperament tuning, just choose 12-EDO from the TONESCALE menu. It's there. But the Modor default tuning still is -and stays- the slightly imperfect Modor Scale.

This means that 12-EDO is not the standard tuning on the NF-1(m). However, you need to use 12-EDO when working together with an application like Infinitone DMT or MTS-ESP (see below) when using the MPE tuning method. Because these apps suppose that your machine is tuned entirely correct, and sends individual pitchbends per note, relative to a theoretical 12-EDO pitch.

• The Midi Tuning Standard messages can be used in cases where a microtuning is relatively static. You load up a project, send a tuning table to the hardware synth, and get playing. The Modor NF-1(m) supports both Bulk Tuning Dumps and Single Note Tunings via the MTS standard.
• However, a few years ago, the Midi Polyphonic Expression standard came up. This allows single notes to be retuned on-the-fly, with pitchbend instructions per-note. So this also allows a more dynamic, constantly retuning form of microtonal music.

The Modor NF-1(m) has now received some MPE improvements under the hood that allow it to cooperate with both MTS-ESP and Infinitone DMT, using both MTS messages or MPE pitchbends.

HOW TO USE THE NF-1(m) WITH MTS-ESP / INFINITONE DMT?

If you want to use the NF-1(m) with one of these applications using MTS, just make sure Sysex Reception (SysexRx) is enabled in the SYSTEM SETTINGS menu. To work with MPE, set up MPE-mode in the SYSTEM SETTINGS menu, and, very important, give your patches a 12-EDO tonescale.