Harmonic Ratio Arpeggiator

I’ve gone on another microtonal trip lately, and have been working with ratios again.  The thing about composing music with frequency ratios is that it places you in a brave new world where each interval is made up of TWO numbers instead of one (as in the traditional system, a fourth, third, fifth, etc).  There are also all kinds of undiscovered tones and frequencies and relationships.  There has to be a way to explore all this!

 

picture of the GUI for the reaktor arpeggiator

picture of the GUI for the reaktor arpeggiator

 

For those of you that aren’t hopeless music nerds like myself, a frequency ratio is just a relationship between frequencies.  It is also the language of a tuning system called “just intonation.”  A basic example:  In the key of A, with the root frequency being 440 hertz, the A in the next higher octave is related to the original note a440 by a frequency ratio of 2/1, and is 880 hz.  A major third is the ratio 5/4, or 550 hertz.  Instead of the normal 12 steps per octave of Equal temperament, there is an infinite gradation of frequencies that you can manipulate to your heart’s content.  

 

With all that freedom comes massive confusion.  I have been trying to come up with some systems for composing with these numbers.  The first most obvious idea would be to just make a fixed scale, choose a few notes, and play with that.  That is fun!  But, it doesn’t take advantage of all the flexibility that working with just intonation truly gives you.  Instead of just choosing 7 or 12 or 10 notes, you can start with a set of 5 notes, and make them mutate and evolve into an infinity of other frequencies, but all logically related by numerical relationships!

 

This is my first system for making melodies and chords in just intonation: a harmonic arpeggiator.  There are two different tables containing numbers for the numerator and denominator, and these tables can be moved through independently, at different speeds.  Midi input triggers notes, but only the time and octave of the input notes is taken, and the rest is controlled by the ratio sequencers.

 

I have implemented this system in both my Nord g2 modular and in Reaktor, so I can make them work together.  

 

Here is a simple melodic sort of track I did with the g2 patch:

Mp3 Audio of “Hydrogen”

 

Here is the Reaktor patch:

Reaktor Harmonic Arpeggiator

 

Here are a couple g2 patches:

G2 Harmonic Arpeggiator with Karpluss Synthesis

 

I will be coming up with more stuff soon!  I want to make some programs that allow you to dynamically change the scale as you play.  Not sure how easy that will be to do in the g2, but I’ll definitely be able to do it in reaktor.

 

Micro Tune your MIDI synths with Reaktor

More microtuning stuff: I’ve been using my TX81z and reaktor lately for synthesizing microtonal music.  I didn’t realize I had another way to get microtonal sitting right under my nose: I could just use reaktor to microtune my synths using pitchbend data!  The limitation of this method is that you can only have one note per midi channel.   However, with a multi-timbral synth, you can still make harmonies!  It’s a very simple patch, as you can see:

microtuneInstrument

It’s very basic:  the pitch goes into a microtuning macro, the midi pitch is quantized by a modulus operation, the difference between the microtuned note and the equal tempered note is sent to the pitchbend output.  piece of cake!

Link to the reaktor file

Here’s a demo of what this sounds like, with a gamelan scale, using my MKS-70

Microtonal Gamelan Melody on MKS-70 synthesizer

Golden Master and my Golden Numbers

On the header of this site, it mentions “tunings,” in addition to the musings and so on.  I thought it was about time to explain these golden numbers to my humble followers.  

 

Recently, I’ve been interested in other things, but last year I especially dove into researching the overtone series, where musical harmony comes from, and how to make music that relates directly to natural harmony.  Among musicians it’s commonly known that the “equal temperament” scale that we’ve been using since roughly the time of Bach compromises the purity of the tuning of a scale in order to allow musicians to explore more harmonic relations and progressions without having to worry about howlingly out-of-tune notes.  The practical value and elegance of this compromise have been proven by the fact that it’s been the standard for tuning of western instruments for about 300 years now, and even modernity with all its breakings-down of traditions and upheavals has hardly managed to make a dent in the ubiquity of this tuning system.

 

In fact, in my experience, I’ve found it very difficult to use anything besides this ingrained-by-centuries system.  Any instrument that has a fixed tuning–nearly all of them, except for fretless instruments like violins–is always tuned to equal temperament.  People interested in composing with other pitches have usually had to resort to using difficult software or building or modifying their own instruments, like Harry Partch. Electronic music instruments, despite offering new frontiers of sound, generally offer no way to circumvent equal temperament, though there are options out there.  The only hardware synthesizer I own that is capable of micro-tunings is my Yamaha TX81z.

 

 

Harry Partch, one of my inspirations, built many beautiful instruments so he could perform his own microtonal music.

Harry Partch, one of my inspirations, built many beautiful instruments so he could perform his own microtonal music.

 

I’ll get into the details and theory behind this at some point, but for now, I’ll just share what I was working on today.  I decided that I should go ahead and take advantage of the tuning capabilities of the TX81z, naively assuming that it would be fairly easy to operate.  I was wrong, of course.

 

The TX’s microtuning system is based around a weird system of 1/64th semitones, instead of the usual 1/100th “cents” that are used almost everywhere else.  Besides this, ‘cents’ are quite different from the ratios that Harry Partch, others, and myself prefer.  So, I’ve slapped together a little spreadsheet to make all the necessary calculations.  

 

 

excerpt from the excel spreadsheet I use to determine microtunings

excerpt from the excel spreadsheet I use to determine microtunings. If anyone is interested in these, feel free to email me.

 

Yes, it seems like it’s a lot of work to make microtonal music.  But I think, to break free of old traditions and make something new, that kind of work is always required.

 

here is the track that I made today. Somewhat of a test just to see if everything was working, but I liked how it turned out.  Panned to the left is the tx81z, and the other synth, with the granular effects, is a reaktor patch i’ve made.  

 

In this track, I linger a lot on the “harmonic minor seventh,” which is a minor seventh that is based on the seventh overtone in the overtone series, as opposed to a more typical one, which normally is composed of a fifth with a minor third stacked on it, or two fourths stacked on each other.  The harmonic minor seventh is much flatter than the one we’re used to, but also has a completely new sound.

 

Link to MP3 audio of “ratio etude #1″