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.

 

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Golden Master, February 8th 2010 | Tags: , , , , , , , ,
Posted in Audio And Synthesis, Nord G2 Modular, microtonal, reaktor, software, tracks

The God Chord: Reaching back in Time

An interesting aspect of using special tunings is that it gives you a way to reach back in time and use some of the exact same tunings as older musicians, even ones from almost 3000 years ago!  The greeks wrote down their tuning systems, and they have been translated in numerous publications.  The greeks used a multitude of different scales, all of which would be called microtonal by modern standards.  Harry partch, mentioned in a previous blog, was also interested in these ancient tunings.  Here, for example, is a recording he made with one of his instruments in an ancient greek scale (which is actually explained in one of the following linked websites).

 

Listen to Partch playing an ancient Greek Scale

 

Most famous of these greek tuning magicians is Pythagoras, who is known for his mystical leanings and mathematical discoveries as well as his eponymous tuning system.  The story of pythagoras and his vegetarian followers is a different, but very interesting chapter from what I’m pursuing here–but that sort of thing only adds another layer of interest to an already interesting subject!  

 

pythagoras-1

the dude

 

 

Today I tuned my synthesizers to the ancient scale of pythagoras and pretended I was a polyrhythmically multithreaded robot strumming a lyre at the foot of mount olympus.  Zeus will probably zap me any minute now.

 

 

zeus zapping

zeus zapping

One of the best sites I’ve found with information on tuning and Just Intonation also has a lengthy section on the math and ideas behind ancient Greek Scales.  Make sure your thinking caps are on, because it’s quite technical: 

Music and Mathematics

 

And for you music theory heads, here is a website that goes into many of the details of Pythagorean tuning:

 

More details on Pythagorean tuning

 

Pythagoras’s tuning is the most mathematically simple way to derive a normal major, or diatonic, scale, and requires no ingredients other than the numbers 1, 2, and 3.  Our normal system of tuning is loosely based around a “5-limit” tuning system, which means that the ratios our frequencies are related by use no numbers greater than 5.  Pythagoras’s tuning, by logical extension, would be called “3 limit.”  It may sound conceptually elegant, but in the numbers, it isn’t.  For instance, in a C major scale, the ratio defining the relationship between C and E (a major third) is 5/4.  Because there are no fives allowed in 3-lmit tuning, pythagoras instead stacked 3’s on top of each other until he could get a similar note, defined by the ratio 81/64, which is quite out of tune.

 

That is just one example of the result of blindly sticking to an appealing idea, regardless of the consequences.  Our modern equal temperament tuning system also comes to mind.  Different tunings, have different flavors, however, and I decided to get old school today.  There are quite a few different ancient tunings available, all of which I’m excited to experiment with and try!

 

Here is the track I made in pythagorean tuning:

 

Link to track “Dune Beetle”

 

tech notes:  This track was made with five12 Numerology sequencing my tx81z and a reaktor ensemble I made, all running through various distortion pedals and outboard reverbs and delays.  The main track is in 5/4, but there is some 4/4 and 7/4 layered over the top of it, rhythmically phasing with it.  It was recorded live so there are some little moments of feedback as well.

 

 The pythagorean tuning I used in this particular track doesn’t come across as strong as the other microtunings that i’ve used, because the pythagorean system is somewhat similar in sound to equal temperament, and also because of all the crazy effects and layering that I used :).

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Golden Master, November 4th 2009 | Tags: , , , ,
Posted in Theory, Ideas, microtonal, tracks, tuning

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″

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Golden Master, October 24th 2009 | Tags: , , , , , ,
Posted in Theory, Ideas, tracks