Simplifying Large Microtonal Tunings

[00:00:00]Hey everyone, this is sort of an extension to my previous video about morphing diatonic scales. So, if you haven't watched that video first, I highly recommend you do that. The link to that video will be in the description of this video. I talked last time about how we could explore a wide range of tunings using dietonic scales as well as 12 tone unequal tunings that can be played comfortably on piano. But what if you want even more notes? Maybe you want the freedom to play certain kinds of harmony in more keys. Or maybe you want the ability to approximate more intervals from JI, short for just intonation, meaning intervals based on whole number frequency ratios like 7 over 6 or 11 over 9. Many microonalists, including myself, do this with larger EDOS's or equal divisions of the octave like 31, 41, 53, 72 ed, sometimes even larger. But this approach comes with lots of challenges. Perhaps most obviously, large tunings are just clunky, especially if you're thinking about how they'd play on a piano. How many keys apart do you think a major third is in, say, 53 EDO? Even if you do know, you probably can't play it with one hand, and it's even annoying to input digitally for such a simple interval. Because of this, you lose out on a lot of range. Even with a full MIDI channel of 128 notes, you don't even get two octaves in 72 EDO. You can try to get around this with expensive or otherwise limited isomeorphic controllers, but that can only get you so far. Many plugins only work with what you can fit on MIDI channel one, so all those extra keys, ironically, become increasingly irrelevant the larger your tuning is. Some plugins, like Piano Tech, are very well behaved and let you use all those keys across multiple MIDI channels. But then you're left with the choice paralysis. Which third do I use here? Which seventh do I use here? Can I even hear the difference in a musical context? Am I wasting my time if I don't use all the notes? But what if you could isolate a manageable, efficient, nicely structured subset of notes from large EDOS's to gain their benefits while drastically reducing the costs? Well, you can. And you can even do it by applying the same methods we discussed in the previous video. So, this web tool, which I've linked in the description, is how we experimented with different tunings of our dietonic scale last time. Remember that these scales are generated by taking a fifth that's the size that you select here and we stack that fifth over and over to get all of our notes. A dietonic scale has seven notes, but we can stack more fifths to get a 12 note scale that fits nicely on piano while including all of the notes of our dietonic scale that we started with. We can find those 12 note scales down here. If we want to look at scales that are generated by stacking even more fifths, let's drag the slider up to maybe around 30. Now, if we grab and drag the page up, there are even more scales we can select. And by the way, all of these scales are called MOS or moss scales or just mosses. It's not important to know where that term comes from, but now you'll recognize it when people refer to these scales that way.

[00:03:01]Anyway, the mosses I want to focus on here are the 19 tone moss in this range, the 29 tone moss in this range, and the 22 tone moss in this range.

[00:03:13]These particular mosses are important because you can pick any tuning within these ranges, no matter how many notes it has, and consolidate it into one of these three mosses. For example, maybe you're interested in 31 EDO for its really JI accurate major third and harmonic 7th, but 31 notes is too much to deal with. Maybe you've tried the 12 tone moss of 31 EDO, which is basically just quarter comma mean tone by the way, but you were disappointed that you only got a harmonic 7th in two keys. The 19 tone moss of 31 EDO gives you a lot more room to play around with while still being pretty manageable. So, let's try that. We'll click here on 12 L7s, which gives us a 19 tone MOSS. And then we can click here to tune that exactly to 31 EDO. I prefer to set the mode down here so that this says 126 right here. Now you can play your scale in the browser with your computer keyboard or if you want to import the scale into a synth plugin, click here to open scale workshop. And over on the right, you can export your scale to whatever file type your synth needs. At this point, I'm going to move over to my keyboard to give a more practical demonstration of what a bunch of these mosses can do. Let me take a moment to explain the setup we have here. So up top I've got the Lumatone, an isomeorphic keyboard. And then below that you'll see typical piano keys. So I'm tuned to the 19 tone MOSS of 31 EDO that we were just discussing.

[00:04:40]But you'll notice that if I'm playing a C major chord, it doesn't look like C major on the piano keys. That's because it's all mapped out to what it would be if I had 19 tones per octave. So you'll notice if I play a bunch of octave C's, they're exactly 19 piano keys apart.

[00:05:06]This is probably a good time to emphasize just how similar mosses are to the EDO that shares the same amount of notes. In this case, since we're doing a 19 tone MOSS of 31 EDO, it is extremely similar to 19 EDO. Let's look at a harmonic 7th chord in 31 EDO.

[00:05:27]Sounds like it's practically JI. It's super clean. Now, let's look at the intervals that are shown on the piano keys. This major third that you're hearing here on the piano keys, the difference between that A flat and D.

[00:05:42]Remember, I'm not actually playing A flat and D. That's just what the keyboard looks like. That's a trionee difference on the keys there. Then the difference between my major 3rd and my harmonic 7th that looks like a major 6th, right?

[00:05:59]Because it looks like D there and then B there.

[00:06:04]Now, if I play that same thing and I retune it to 19 edo, my hand hasn't moved at all. And you'll notice it's the exact same keys on the piano. And that's no accident. So now let's check it out in a completely different key. I'll go back to 31 edo.

[00:06:25]Again, really clean sounding. And look at the intervals. They are exactly the same. The difference between these notes, like we determined before, is a trionee, B to F on the piano keys. And then the difference between these keys here, F and D, is a major 6th. So, it's really easy to remember where you are if you're trying to go quickly through these chords.

[00:06:52]It's always the exact same intervals every time. Even though this is a MOSS, it's an unequal temperament, but it's the same intervals every single time.

[00:07:02]Now, since this is an unequal tuning, you don't have a harmonic seventh chord in every single key. This is C sharp, for example.

[00:07:09]It's clearly not right. But if we were back in 19 edo over here, that is the same harmonic seventh chord that you have down here.

[00:07:20]The lesson here is that when you're in a key that does have a certain interval or chord that you're looking for, it's going to have the same shape and the same distance between the keys every time, most of the time. We'll see some counter examples later, but now let's check out this tuning a little bit more.

[00:07:37]We already had a glimpse of just how many harmonic sevenths we have in this moss.

[00:07:47]I mean that's a lot compared to the 12 tone moss of this which is basically quarter comma mean tone. You only get two harmonic 7ths in that. But there we had nine. That's pretty great. And then you get a bunch of like like major 7 chords.

[00:08:11]So you just have immense flexibility and power to explore 31 EDO despite only having 19 notes of it. One of my favorite things to do to kind of test a tuning out is to do a 251 chord progression over and over again and you tritone sub on the five chord and you turn that into a harmonic seventh chord.

[00:08:33]So that would sound like this.

[00:08:52]So, as you can see, I'm playing a lot of minor 7th chords, harmonic seventh chords, major 7 chords in many different keys, and I'm not feeling restricted really. Despite only having 19 notes, despite the fact that it's an unequal tuning, I still feel very free to kind of explore the territory of 31 EDO. And then you even get some keys with your harmonic 11 approximation. So we have a harmonic 11 here, here, here, here, and then here.

[00:09:29]So you get five harmonic 11s total. Now, this harmonic 11 here is actually a counter example to what I said earlier about every interval mostly having the same shape because this neutral third that we have at the top of my chord here is a different neutral third than what we had on this harmonic 11.

[00:09:51]Notice here, this third has, if we look at the keys on the piano, a tritone worth of difference. And then on the other harmonic 11, this is what our neutral third is. It's actually a fourth worth of difference on the piano keys. Only one of those harmonic 11s is different from the others in terms of how many keys are in between the intervals. But what's cool about that harmonic 11 actually is that you can actually play the harmonic 7th along with it, which you can't do with the other harmonic 11 keys.

[00:10:27]And that's a pretty cool sound.

[00:10:29]One of my favorite ways to use that harmonic 7 and 11 sound is to do what's called a backdoor progression. Let's say we're in the key of A flat. That's my one chord. Now I go to my four chord D flat. Now I go to my flat 7 chord with the harmonic 7 and 11 and I resolve to a flat. So a little faster. That would sound like this.

[00:11:01]Let's take a moment to reflect on why this MOSSbased approach has had a lot of value for us in a large tuning like 31 EDO. We clearly have plenty of flexibility to explore many different kinds of new harmony in many different keys. And you can see on screen with the piano keys what this would effectively look like if you had to plug these notes onto your MIDI piano roll. Most of these triads you could play in one hand if you were to play them on a regular piano as well. But you should see that everything is much more concise and close together than it would be if you actually had to play 31 notes to an octave on a piano.

[00:11:44]that would be significantly more spread out and a lot harder to keep track of.

[00:11:49]Let's check out a slightly larger tuning. Now, this is a 22 tone MOSS of 39 EDO. And like I said before, the amount of notes that your MOSS has means that it's going to be very similar to the EDO that's of the same size. So, this is going to be actually very similar in sound and in terms of how it plays to 22 EDO. And 22 EDO is a really cool tuning in its own right, just like 19 EDO, which corresponds to the previous scale we checked out. But there are multiple things about 39 EDO that I like that I can't quite get from 22 EDO despite them being very similar. So, for one thing, the fifths are a little bit more accurate to JI in 39 EDO than in 22 EDO, but that's a fairly subtle difference. The more extreme difference that I personally notice is that when you play a C add9 chord like this, I just find that that sits really nicely in 39 EDO. But in 22 EDO, if we listen to that now, the interval between the D and the E, or really it's the down E, this interval is quite narrow. And I really feel like that sticks out like a sore thumb to me.

[00:13:12]And sometimes that sounds cool, but a lot of the time I like the more smooth sound of 39 EDO. So let's hear that one more time. This is 39 EDO.

[00:13:26]This is 22 EDO.

[00:13:33]Another thing that people would probably care about even more is that 39 EDO actually has the ability to approximate the 13th harmonic and 22 EDO really doesn't. And what's cool about 39 EDO is that those approximations of the 13th harmonic are all over the place really.

[00:13:53]You can hit them just everywhere. And what helps with this is that there are actually two 13s in 39 EDO. So if a key lacks one of those, then it'll have the other one. So let's check out this sample progression where I play a 13 on the second chord of the progression. And I'll play it in two different keys. In the first key, I'll use the sharper of the 13s. And on the second key, I'll use the flatter of the 13s.

[00:14:38]Now, you don't get those cool tritone subs with the harmonic 7 that you do in the previous tuning, but because it's a super Pythagorean tuning like 22 EDO, you can do these really cool harmonic 7th pentatonic things in almost every key. It's just absolutely everywhere.

[00:14:54]So, you can do stuff like this.

[00:15:04]And that's just all over the place. You can do that in almost any key. Now you are slightly limited in terms of your major thirds or technically in this case they would be considered down major thirds but you still have nine of them total. Uh you have seven uh one for each white key and then one in the key of E flat and one in the key of B flat. So you have this.

[00:15:29]That's all the white keys. And then you have E flat and B flat.

[00:15:35]And the 11th harmonic is almost everywhere. You can do it in many different keys and it's even more accurate than it is in 22 EDO. So you've got this all over. You can do it with the harmonic 7th in so many different keys.

[00:15:52]It's just everywhere. Finally, let's talk about some 29 tone mosses. They're the biggest of the bunch, but you'll find that they're the most rewarding if what you care about is extreme ji precision. Naturally, since we're talking about 29 tone scales, this bears a really close resemblance to 29 EDO, which is a really interesting tuning. I think it's a Pythagorean tuning, so it has very accurate fifths, even more so than 12 EDO. And its harmonic approximations up to 13 are really in tune with each other, but they're noticeably flat from your root. So, for example, you could play something like this.

[00:16:31]And those top notes I'm playing up here are really tight with each other.

[00:16:38]But then if you just play a major chord, that third is really noticeably flat.

[00:16:44]It's actually flat almost the same amount that the 12 EDO major third is sharp. So we can try to correct that by making a 29 tone moss of one of my personal favorite JI approximating tunings which is 46 EDO. So now in 46 EDO if we try to play the same thing much cleaner even on those major thirds and you can hit those really accurate harmonic approximations in multiple different keys as you can see here.

[00:17:24]all those different keys and more. But some keys will lose out on an occasional harmonic here or there. Now, suppose that's still not close enough to Ji for you. Maybe you're wondering about 41 EDO or 53 EDO. You can make 29 tone mosses of those, too. But let's go even bigger.

[00:17:42]Let's go to 94 EDO, which is even better at approximating JI overall than any of the other tunings we've discussed so far. And it only needs a 29 tone MOSS to do it. Now that I'm in 94 EDO, I've got my harmonic 7 trione subs back. So, I can do stuff like this.

[00:18:18]You've also got a few keys with 11 and 13, although unfortunately they're not the same keys that have your nice major third and a harmonic 7th.

[00:18:33]And that's why I made this 29 tone nested double MOSS sort of thing of 94 EDO that lets me hit all of those harmonic approximations within the same few keys. So I can do stuff like this.

[00:18:53]The links to all the scales I've shown off are in the description below. Thank you so much for watching. Please like and subscribe and hopefully this helps to simplify larger tunings and make them more accessible.