72 EDO and 6 variations

72 is easily my favorite EDO\ET.  It has beautiful 11 limit intervals that are nearly perfect. There is just something about 11 limit chords that I absolutely adore!  They have a beautiful crunchy, purring resonance to them that I can’t quite explain.

Have a listen to some of the beauty found within this tuning:

Another win for 72 EDO is that it has 12 EDO built within so you can continue playing along with your friends who play in 12.

This is all amazing when working with midi instruments.  But what if you want to play acoustic natural instruments?

When dealing with 72 notes per octave, things can get a bit impractical depending on the type of instrument you want to play or even design.  For example; how could you setup a guitar with 72 notes per octave?  How about a horn or woodwind instrument?

A quick practical solution for bands or ensemble groups of at least six or more could be to look at 72 EDO  as 6 variations of 12 EDO.   Simply because 72/12 = 6.  With at least six musicians\instruments each tuned to a different variation, you’d have 6 variations of 12 EDO right there under your fingers.  You can tune each instrument to a different variation and arrange the music in a way to create beautiful lush 11 limit harmonies and dancing melodies that use the new intervals that 72 EDO brings.

Could this be troublesome for non fretted instruments such as Violin, Cello, etc? I’d imagine that it would take a bit of practice listening to the new harmonies that are unfamiliar.  Then harmonizing with other musicians will come more easily.

Introducing the Harmonic 7th Chord

If you want to experience Just Intonation first hand then please visit the Online Terpstra Keyboard and experiment for yourself.  This was originally created by James Fenn.  I have added a few additions and will continue to build upon his wonderful work.  You can even use this on an iPad or tablet of your choice in order to use multiple fingers for chords and scales.

Online Terpstra Keyboard

Make sure “Enumerate Scale” is not checked, scroll to the bottom and click on  “MAKE ME A MICROTONAL KEYBOARD!”.

Click around to hear how this Just Intonation scale sounds.  If you’re on a laptop or desktop then hold down the space-bar for sustain, or if using a tablet then shake it until you see a message that says “Sustain On” You can turn sustain off by shaking it again (working out the details on that).

To play a Harmonic 7th chord play the following notes:  R, 5/4, 3/2, 7/4.  What you have here is a very stable and consonant chord that is unavailable to you if playing on a piano in 12ET.  This is only a very small beginning of what awaits you in new musical sounds and textures.

Why Just Intonation?

I stumbled into the world of Just Intonation music by mistake…   it was like seeing a brand new world for the very first time.  One that had long existed in beauty, splendor, and majesty. But for me it was unknown and unexplored. Powerful and glorious, but unused and ignored.


I stepped into the wardrobe and experienced  new and exciting possibilities that were previously inconceivable.  Standing there transfixed in this new world, I experienced new flavors of melody and harmony.  All very wonderful and exciting.

12 notes per octave… I never knew music could be built on anything except this.  It was to me the universal truth of what music really was.  The foundation.  But to my dismay, I had been living inside of a 2-dimensional monochrome world, while the portal to a shiny new bright and colorful reality was staring me straight in the face.

Now don’t get me wrong. 12ET can of course produce some beautiful music.  I will always play and listen to music based on it.  But it is just one way of looking at things.  Just Intonation opens the doors to an unexplored world of sound and the relationships between pitches.  These are real and meaningful musical harmonies that most musicians have never heard.  In Just intonation you have a wealth of harmonious treasure, far more so than what 12-ET can offer.  There are so many different ways to combine tones that are just not possible with 12 equally spaced tones per octave.

We are accustomed to hearing 12ET even before birth, so hearing music based on Just Intonation is probably going to seem a bit strange to us at first.  But the reality, believe it or not, is that 12ET is out of tune, and because it’s an equal temperament with only 12 notes, that also limits us in what we are allowed to do creatively. Surprised?  Or unfazed?  Just Intonation is just so much richer and deeper in many different ways.

There are some equal temperaments that are amazing.  72 is probably my favorite and I’d put it up against JI any day.  Our good old 12ET exists within it, but in what I like to call 6 variations. 

I took some time looking these places up, so please allow me to elaborate.  If playing in 12-ET is like swimming in a swimming pool at a hotel resort, then playing in Just Intonation is more like swimming out in the Hanauma Bay in Oahu Hawaii, or in the charming rivers of Bonito, Mato Grosso do Sul in Brazil.

Bonito, Mato Grosso do Sul – Brazil
Bonito, Mato Grosso do Sul – Brazil
Bonito, Mato Grosso do Sul – Brazil


Sure the resort swimming pools are nice, but the latter are more natural,  and far more exciting in my book.  They may be a bit more dangerous and less tame, but the possibilities of experiences that can be had far exceed anything in a closed up and manicured hotel resort swimming pool.  The trade off is that it’s not as easy to compose and play complex music in Just Intonation.  The way I see it, creating and preparing the scale tones and how the intervals will relate to each other will be just as much an art and science as actually composing and playing the music itself.  Also you’ll need to use MIDI instruments and software that allows for micro-tonality. Or have your instruments modified, or new ones designed. This is not for everyone.

With 12ET or most other equal temperaments  for that matter (or at least ones that are octave based and cycle), you’re dealing with intervals that are always the same distance apart. Which can be constant and stable, but limiting in this aspect.

Just Intonation scales are a bit different.  A chromatic scale can have intervals in it that are all different in sizes.  This mean that there’s more “danger” for running into some dissonance that you’ve never encountered before. That can be a bit unsettling and scary at first, but there is also the possibility to find and experience beauty and excitement that would never have been.

12ET has helped us move forward in music in some amazing ways.  But I truly believe that it would be very unfortunate if we stop there.   We can do more.

Much exploration, adventure and discovery await us if only we’d open our minds, our hearts and our ears to something different than what we’re accustomed to.

The Janko Keyboard

Janko Keyboard

What a great idea the Janko Keyboard is.  In 1882 Paul von Jankó designed this marvelous instrument. But sadly it never took off.   There are some brave ingenious people who are endeavoring in bringing this wonderful instrument back to life and to the forefront for others to play and be creative with.

I play a number of different instruments.  Guitar and piano being among them.  When it comes to the piano I recognize something strikingly different in approach than when playing a guitar.  On the piano I have to play scales and chords differently for each of the 12 major scales, but on the guitar the scale shapes and chord shapes remain the same all over the neck (for the most part, depending on your tuning).

The take away is that you get up to speed faster on guitar chops (in all 12 keys) than you can on the piano.  Thus, you can master (I use that term very loosely) the guitar faster than you could the piano.  One of the pluses for the piano is that you always know exactly where you are because of the black key – white key pattern.  If you want to move to a different mode in a different key it might be easier on a piano if you know all 12 scales than on a guitar where you could get disoriented quite a bit easier.

The Janko Keyboard offers you the best of both worlds!  You still get to keep the same 7 white keys and 5 black keys to keep your orientation.  BUT for each scale you play, the fingering will be exactly the same!  Why this has not caught on amongst those in the music world I truly do not know!