So, it’s been a good few years since I wrote this:
About my journey into 24-TET music. When I wrote that, I was only familiar with our standard, “Western” 12-TET system, and the 24-TET system (also know as the 12 EDO system and the 24 EDO system, EDO stands for equal divisions of the octave.) But, boy, have I been on an adventure since then! I’ve listened to music in a very wide variety of tuning systems, Spidermilk by the Mercury Tree is an amazing album, that’s entirely in 17-TET. I’ve spent a lot of time on you tube just listening to a load of different tuning systems, 7-TET, 9-TET, 10-TET, 15-TET, you can’t move for the amount of tunings I’ve listened to!
I also bought a synth a few months ago capable of being set up in any tuning system:
And I figured out a way of dury rigging two of my guitars so that they can sort of kind of perhaps, we’ll get to the sort of kind of perhaps later, play in 14-TET, and in 15-TET.
Coral Sitar copy, that can sort of kind of perhaps play in 15-TET.
A brief note on why I”ll be using the term xenharmonic as opposed to microtonal.
Most people will be used to hearing alternate tunings described as “microtonal tunings”. However, the term microtonal, refers to specifically tunings that have smaller divisions of the octave than 12-EDO, so it refers to anything from 13 EDO up. However, a lot of the really cool tunings actually have bigger divisions of the octave, such as 10 EDO, 7 EDO or 5 EDO. These are called macrotonal tunings. So I usually use the term xenharmonic, to clarify that I’m interested in both microtonal tunings AND macrotonal tunings.
Choice Fatigue
So my Korg Minilogue can, in theory, play in any conceivable type of tuning system. With two caveats. It’s got 37 keys. So you couldn’t, for example, play a song in 38 EDO or higher, where you use all of the keys (this would be highly unusual anyway, even 12-TET songs usually use only 7 notes.) The other thing it can’t do is tune to less than a cent. If you look at the numbers for 14 EDO:
You’ll notice that the numbers are usually less than a cent, as an example your perfect fifth is 685.14. And I have decided to fix this problem, by not fixing it. Few, if any, human ears on Earth are capable of hearing intervals of less than one cent. In my explorations of xenharmonic music, I’ve taken the view that, if the human ear can’t hear something, it’s irrelevant. So when I tune my Korg Minilogue to 14 EDO, or to any other xenharmonic tuning, I tune the intervals to the nearest cent and leave it at that.
So, a synth that can tune to any tuning system! It’s amazing! It’s exhilarating! It’s, hang on, I’ve spent the last two hours just flicking through tuning systems like channels on a tv. It’s, I’ve, got nothing done. I haven’t familiarized myself with the intricacies and nuances of any tuning system. I have just blasted through ten tuning systems, without developing an understanding of any of them!
And that’s where the guitars come in
With my two dury rigged guitars, I can’t go any higher than 15 EDO. And frankly, I couldn’t be bothered changing them to other tunings, because it takes longer to move the pens under the bridge around then it takes to dial in a tuning on the Minilogue. So hopefully I’ll spent the next few months, or possibly years, developing a greater familiarity with both 14 EDO and 15 EDO.
Though it’s important to realize, that these guitars can’t approximate 14-TET and 15-TET perfectly. These guitars were designed to be 12-TET guitars, and, unless I decided to pay a luthier to actually put in new frets, which is something I might well do some day, there is only so close you can get to tunings that they weren’t designed to play. The xenharmonic wiki actually has an article about how “off” dury rigged xenharmonic guitars, such as the ones I have, are from their intended tuning.
https://en.xen.wiki/w/Moving_the_bridge_hack
In a sense, the dury rigged guitars should probably be thought of as interesting tunings in their own right, rather than as good approximations of 14 or 15 EDO. But since I find it easier to write songs on guitar than on synth, they are still very useful. I can always write a 14 EDO song on the guitar, and than actually play it on the synth.
The Simpsons Already Did It
There’s an episode of South Park where the character Butters, in his alter-ego of Professor Chaos, keeps trying to come up with various diabolical schemes, only to realize that “The Simpsons Already Did It”. Am I arguing that you encounter “The Simpsons Already Did It” with xenharmonic tunings? It’s a tortured, tortured analogy, but yes, I am kind of arguing that.
A few days ago, I was doing a bluesy improvisation on my 15 EDO guitar, really getting into it, really having a blast, and then, it hit me, hang on a second, aren’t I just playing a blues scale using the notes from 15-TET that roughly correspond with the notes from 12-TET? If so, what’s the point then?
Or there’s a note that has my really excited in 14-TET, it’s 342 cents. You know what that means? It means it allows you to play a neutral chord. 12-TET is limited to major or minor chords, but many xenharmonic tunings have what are called neutral chords. Where the note isn’t 300, as it would be in minor, or 400, as it would be in major, but roughly half way between, so 342 is only eight cents short of being an ideal neutral chord.
But hang on a second, if you want to not just approximate a neutral chord, but get it bang on, you can get that from 24-TET, where there’s an interval of 350 cents. Simpsons already did it!
What I’m trying to say is, I got into these alternate tunings because I wanted to expand beyond 12-TET and 24-TET and see what else is out there. But the problem is, once you’ve played in both 12-TET and 24-TET, it gets harder to find new, cool interesting sounds after that. So you’ll find a really cool sound. Oh wait, you can do that in 12 EDO, Simpsons already did it! Wait, I’ve found a xenharmonic tuning that does a neutral seventh, this could really change everything. Wait a minute, 24 EDO has a neutral seventh. Simpsons already did it!
But, why does it even matter? If I come up with a really cool idea in 14 EDO, why does it matter if I could play the same notes with a 12 EDO or 24 EDO guitar? Isn’t it possible that playing a “weird” guitar like a 14 EDO guitar is what put my into the head space where I could come up with that idea?
The reason it matters is that, I have two instruments that can play in 14 TET, and two that can play in 15 TET. And as already mentioned, with the guitars it’s debatable. I have, a bunch of instruments that can play in 12-TET, and three that can play in 24-TET, and you can even play 24- TET stuff, to a limited degree if you know how to do it, on 12-TET instruments. So, if I come up with an interesting idea in 14-TET, without realizing it can also be done in 24-TET, then, I don’t have the opportunity to try it out on a wider variety of instruments. Maybe the 14-TET idea I came up with would sound great on my 24-TET saz! So that’s why it’s always important to be constantly, always aware of “The Simpsons Already Did It!”
Can xenharmonic tunings be thought of as song writing tools?
Sometimes I wonder to what extent it’s simply the case that the various tunings outside of 12 EDO and 24 EDO serve as songwriting tools. To what extent is it the case that when you are playing in 14 EDO, or 17 EDO, this simply puts you into a completely different headspace.
I find that, often but not always, I’m better able to write songs when I’ve a guitar in my hands than when I’m in front of a piano. And this has nothing to do with limitations that pianos may have, a piano would be able to play all of the notes in the song I wrote. So for me, guitars, on average, are a better song writing tool than pianos are.
And sometimes, I think xenharmonic tunings can be thought of as song writing tools. And not always because of a greater range of possibilities, but sometimes, because of fewer.
Just a few minutes ago, I was trying out a 5 EDO tuning on my synth. You have to work with 5 notes. So you’ve got your power chords, but if you want anything more complex than that, you’re basically limited to a Sus4 chord, and a “wonky” Sus2. There’s no major or minor in 5 EDO! I’m already wondering about what kind of music I could write if I was trapped in a cave for six months with only an instrument capable of playing 5 EDO. What would I come up with when, outside of your power chord and your Sus4 chord, I’m completely unable to use any of the conventional, bog standard chords at all?
What do I like about 14 edo?
So, let’s talk about why I’ve come to like this tuning so much!
Usable, but wonky, fifths
Fifths, where you play two notes that are seven semitones apart, also known as power chords, are a very important component of rock music. Sometimes when I’m using a new xenharmonic tuning, and I feel completely lost, my first question is, what does the fifth sound like?
If a tuning system has got a note that’s in or around 700 cents, then’s it got a fifth. So 12 EDO and 24 EDO have fifths, and that’s why they’re so “easy” to work with. If you look at something like, for example, 11 EDO:
You’ll notice that the closest notes to 700 are 654.55, way too flat!, or 763.64, way too sharp! So, 11 EDO doesn’t really have fifths to speak of. That’s not to say I won’t find some way of using this tuning in a song some day, but the problem with it is that, with no fifth, you’re “lost at sea” right from the word go!
But with 14 EDO, we have a really usable, and interesting fifth!:
685.714! That’s interesting. But what does that give you? Often times, in a lot of musical contexts, it’ll just sound like a regular fifth like you get in 12 Tet. After all, it’s only about 15 cents flat of a regular 12 EDO fifth. But if you’re playing a few power chords with it, sometimes when you’re switching from one chord to the other, that’s when you’ll hear a wonderful sound, where the brain is quickly trying to process whether what it’s hearing is “in tune” or not, and then the brain just gives up and decides to simply enjoy the sound!
I think that’s often where the magic happens with xenharmonic tunings. If you were to have a fifth of say, 706 cents, it would be fairly redundant, the brain can barely, if at all, perceive six cents, you would just perceive it as a “regular” 12 Tet fifth. But tune your fifth too sharp, to say, 745 cents, and things get so dissonant that the brain automatically just says, “that’s out of tune”. You don’t necessarily perceive it as exotic, or alien, or even novel, just out of tune.
For me, often with xenharmonic tunings a lot of real magic can happen when you get things close, but not too close, to “regular” 12 Tet chords. When the brain isn’t perceiving something as out of tune, but rather, is having an argument with itself over whether something is in tune or not, that’s when things really sound interesting! So that’s why I’m so enthusiastic for those power chords that are just a little wonky!
14 EDO has two 7 EDO tunings stacked on top of each other
With 14 EDO, you get microtonality, and macrotonality, all in the one. Technically you get macrotonality with 12 EDO, the whole tone scale can also be thought of as a 6 EDO tuning system, but there’s nothing new when you do that, it’s just your whole tone scale.
Macrotonality is any tuning where the octave is divided into fewer than 12 divisions, so anything less than 12 EDO. At first this might not sound useful, why would you want fewer notes? Well, most songs written in 12 EDO use seven notes, or less, think of your bog standard major scale, that’s just seven notes (the eighth note is a repeat of the first note an octave higher). So with a 7 Edo Tuning, you’re working with a number of notes you’re used to working with in 12 Edo, but they’re completely different notes!
With 14 EDO, if you play every second note, you’re into a neat seven EDO tuning. Move up one note, and play every second note from there, and you’ve another seven EDO tuning, so you can change key between two different 7 EDOS. So you effectively get two EDOS for the price of one, your microtonal 14 Edo, and your macrotonal 7 EDO, and you can even do key changes with the 7 EDO!
14 EDO Allows a Good Combination Of Moderate Weirdness and Also Really Weird Weirdness
Remember how I talked earlier about how the fact that the fifth is far, but not too far from regular 12 TET, is a recipe for creating really novel music? Moderating the oddness is often a way of creating weird music, but not always. Sometimes less is more, but other times, more is more!
And 14 EDO really cranks up the weirdness when it comes to minor or major chords, if they can be called major and minor at all. Have a look again at the cent tunings for 14 EDO, and also have a listen, to the nearest equivalents it has to major or minor chords.
A “regular” 12 EDO minor chord is 300 cents. The nearest 14 EDO has to this is 257.143, woah that’s a bit flat!, and in the other direction, 342.857, blimey, a bit sharp that! And the 342.857 is really, really weird, it hovers just below being a neutral chord, like you would get in 24 EDO music, but it’s just, just below, being neutral, so it’s awkward in a good way, refusing to commit to being either neutral or minor.
So, what’s the closest we have to major? 428.571. A regular 12 EDO major is 400, so this is 28 cents sharp of that. And much like the fifth, sometimes if you play the same major chord over and over again, you won’t hear anything, but if you switch from one major chord to another, then you’ll hear it.
But your bog standard major chord gets even weirder in 14 EDO. Because, your fifth is already flat, and your 3rd is sharp, so this makes for a really bizarre sounding major chord, and I love it!
So for me, 14 EDO offers the perfect combination of an ability to reign in the madness, but also, if you’re in the humour for it, you can let things get wild! If you just play power chords, you can compose music that just has a slight touch of weirdness. But bring in those weird major and minor chords from a parallel universe and things can get really strange!
What possessed me to write about 14 EDO?
I think this is the question that people might want to know about. This subject is so niche, that there’s only 3 people who are interested in it, and I’m one of them. I think it’s because the literature on xenharmonic tunings is really, really complicated. I wanted to write something that is, hopefully understandable to, I suppose, people with my level of understanding, however you define that.
After hours, and hours, and hours, of hyperfocusing on xenharmonic tunings, I’ve developed the level of understanding that I have now. And I recognize this is still going to be all Greek to someone who’s never even listened to Flying Microtonal Banana by King Gizzard and the Wizard Lizard. But trust me, it only gets more complicated after this blogpost!
If you look up the literature on xenharmonic music, the first thing talked about is “5 limit tunings” or “7 limit tunings”. I have tried, and tried, and tried, to get my head around what a “limit tuning” is, and I just can’t, not yet anyway. There’s a lot of complex mathematics involved in xenharmonic tunings that I simply can’t get my head around. So, I suppose, this is an attempt, that might well fail, to write about my knowledge of xenharmonic tunings in a simplified way. To try and explain without getting into complex mathematics or difficult to understand concepts, but rather to just say, “This tuning has a cool, wonky fifth” or “This tuning has really weird major and minor chords” or even just, “This tuning is easier to set up on a Minilogue than some of the other EDOS that are out there.”
And now for some listening:
So here’s some 14 EDO music for you to listen to, the first three are some improvisations I did, the rest are from other artists that you should check out.
The first is the pseudo-14 EDO guitar:
This is on the Minilogue:
And this is the Minilogue again, but this time I treated 14 EDO as two 7 EDOs stacked on top of each other, and continuously changed key between them:
And now some 14 EDO music from other artists.
Have a listen to this example of 14 tet, jazz mallet! Isn’t this the coolest?:
This has an eerie atmospheric quality that I love!:
I love this doomy sounding rock track from Feeding Fingers:
A solo piano piece in 14 EDO that sounds absolutely lovely!:
I hope this has been a somewhat useful and informative introduction to this very weird, and very wonderful tuning system!
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