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:

Dolores Catherino, a pioneer in paving the way for future generations to enjoy the beauty that is largely unexplored in the world of microtonal music.  

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?

Before I discovered Just Intonation and Microtonality I thought that I had a pretty strong grasp on what music was.  But boy was I wrong.  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 had sat there behind the wardrobe, powerful, glorious, but unused and ignored… yet patiently waiting.


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 taste and harmony.

12 notes per octave… What I thought before to be the universal truth of music, the foundation… it certainly was not.  There were shortcomings with 12 ET.  It was a relatively recent invention and it was small when compared to the world of Just Intonation.  I had been living inside of a 2-dimensional monochrome world, while the portal to a bright and colorful multi-dimensional new existence was staring me straight in the face.

Now don’t get me wrong. 12ET can produce some beautiful music.  It closely approximates many of the lower partials of the overtone series.  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.  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?  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.

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, and the process to prepare for swimming in them may take a bit more work and time, but the possibilities of experiences that can be had far exceed anything in a closed up and manicured hotel resort swimming pool.

With 12ET or any equal temperament for that matter you’re dealing with something that is like a circle that loops over and over with the same elements that were there before. Which can be constant and stable, but limiting.

Just Intonation scales are like different arrangements of the Harmonic Series, which is more like an open ended spiral that never ends.  There is more “danger” there 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 entered your heart before.

12ET has helped us move forward in music in some amazing ways.  But I truly believe that it would be very unfortunate if we stall there and begin to think of our 12 ET system as the pot of gold at the end of the rainbow.  Or think of it as  more “musical” or more in tune than we would the harmonic series which is part of nature and sewn within the fabric of reality itself.

I truly think it would be more healthy to view music as something more like an organic thing that is lived and breathed, and a bit less like a cookie cutter one size fits all package.  Instead of trying to fit everything into a mass produced 12-ET world with instruments that are conformed to a standard that isn’t based in nature.  I’d love to see us be more creative and open minded about tonality and even the instruments that we use to express it.

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.  If you’d like to dive in deep, then perhaps this is a good place to start.

The Sonic Sky: An Introduction



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!