Відео

It's a Lumatone (www.lumatone.io) midi controller hooked up to my computer running PianoTeq.

31 EDO

That's right. To name the notes in 31 equal we can use the circle of fifths. Because there are more notes, the circle of fifths takes longer to wrap around, but it happens that 31 equal has a single circle of fifths. So, we can follow the pattern F C G D A E B going up by fifths, and then repeat this with sharps on the right, and flats on the left to get Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B#, and continue this further with double flats on the left and double sharps on the right, and we'll finally end up finding some enharmonics at that point, with Cbb = A## for instance -- the notes 31 steps apart will be the same. The relationship between major/minor thirds and perfect fifths in 31 equal happens to be the same as it is for 12 equal, if you go 4 steps up on the circle of fifths, you find the major third, and if you go three steps down, you find the minor third. So for instance, G# is a major third above E, and Ab is a minor third above F, and Ab is about 38 cents higher than G#. If you use the wrong one, you get something a bit more dissonant, but there's still some harmony hiding there. While the major third is an approximation to a 5/4 frequency ratio (to within less than 1 cent), and the minor third is an approximation to the 6/5 frequency ratio (about 6 cents flat), the interval from F to G# is approximately a septimal minor third, a 7/6 ratio (about 4 cents sharp). This interval shows up in a lot of Middle Eastern music, and can be quite beautiful. The interval from E to Ab on the other hand, is an approximation to a 9/7 septimal major third, though it's about 9 cents out in 31 equal, so I feel it's not quite as convincing, that's not a good enough approximation for 9/7's subtle consonance to shine through. Still, it's possible to make that interval work out nicely in a chord with other notes in context.

lmao

i like this

Hahaha! I've thought about getting Nanoleaf hexagon lights on my wall to fit the theme.

I'm sure if I'd have been any kind of a pianist before I started, it would have felt different, but within a day, I was more capable of musically expressing myself than I'd ever gotten with the usual piano layout. This is despite having a keyboard of some description in the house for the better part of my life and bouncing off of it a few times. You have basically a 12 times advantage (31 times advantage perhaps if you're doing 31edo) just moving to an isomorphic keyboard layout of any kind, because you don't have to learn to play each chord and scale and musical object in each key signature separately, so practising and building muscle memory in one key automatically translates to all keys, you just move your hands and start on a different note. There are some advantages which the more piano-like Bosanquet hex grid layout has -- particularly, it's better at dealing with any tuning where the best major third is not 4 steps up on the circle of fifths (i.e. which doesn't temper the syntonic comma), because it gives you easier access to "strange" intervals that aren't nearby on the circle of fifths. But 31 equal is one of the "meantone" tunings that puts the thirds nearby on the circle of fifths, along with 12, 19, 43, 50, 55, and a bunch of others. All of those play with the same muscle memory (in either Wicki-Hayden or Bosanquet). But Wicki-Hayden is so perfect in a lot of ways -- the octaves being close together makes all sorts of arpeggios and larger voicings way way easier to execute, and the harmonic structure of chords and scales is much more geometrically apparent, whereas the circle of fifths gets really stretched out in Bosanquet and you can't see what's going on as clearly. It's really fun seeing a non-musician's eyes light up when they hit a few keys on my Wicki-Hayden layout and realize that they accidentally played something that sounds good (because the keys were probably close together and so were nearby on the circle of fifths). I feel like if it was a more common layout for keyboards, it would change the way that average non-musicians engage with playing music.

Yep, that's me!

That's interesting! I'm curious if there's any particular thing that attracts you to 50edo. In this example, I chose it mainly to experiment with the small intervals available (while at the same time it's still meantone tempered, so my muscle memory works). I think if I was going as far as fretting a guitar, I'd prioritize having something in 31edo though -- its 5-limit is pretty similar in quality to 50edo (slightly more accurate), but it has substantially more convincing 7-limit intervals. But each temperament does have its own overall tint to it, so maybe the technicalities are less important than the overall character of the sound sometimes. :)

@@cgibbard Yes there is as a matter of fact! 50 has great 5 limit capability as you said. Which I think is very grounding, going back to our roots with early, baroque, renaissance music. Plus it represents mode 8 of the harmonic series well enough in my preference. However what 31 does not have is one of my favorite intervals the 13/12 (or 144 cents in 50) plus the half octave period for symmetrical scales. I used to have a 25edo and 20edo guitar so I am familiar with the flavor of factors of five systems on guitar. Also I like the fact how the intervals values in cents are nice and even. Easy to remember and navigate. To sum it up, it basically has everything that I've come to appreciate within an equal temperament. 50 lines up perfectly in meantone fashion for traditional guitar tuning. 52edo also comes close but the 392 cent major third would not accommodate a traditional guitar tuning of fourths and a third for the b string. Whereas the 369 cent third in 26edo does add up. I also had a 26edo guitar that I wish I still had. I'm hoping to get the 20 out of 50 guitar made by the end of the summer. I have yet to figure out what guitar to use for it. Have a wonderful day and thank you for sharing your music with the world!

@@zpc9225 Thanks! Some fun stuff to think about with regard to 50 equal. I haven't really explored the 13th harmonic very much yet, but 13/12 is definitely an interesting sort of neutral second. It has a pretty different quality to it harmonically from the approximate 12/11 that 31 equal has. :)

The / diagonals are fifths (so mostly up and a bit to the right) and the \ diagonals are fourths, and so the shallow rising diagonals across are whole tones, and octaves are of course a step up by a P5 and P4, so the same direction that the borders between colours are going. The white keys are the naturals, each row of three white keys being C D E, and then the row of four white keys above that are F G A B. The gold keys are flats and follow the same pattern of letters, so the row of three is Cb Db Eb, etc., and the light blue are sharps, darker orange and purple is double flats, darker blue and purple is double sharps (purple is the overlap between double sharps and double flats). This "Wicki-Hayden" layout is really nice not only to play, but also to analyze harmony. It's like two copies of the tonnetz (which has its three axes as major thirds, minor thirds and perfect fifths) interleaved, and not only does a nicer job of making perfect fourths easy, but also makes most common scales quite ergonomic by making contiguous segments of the circle of fifths a nice contiguous block, and fancy arpeggios are nice and easy because the octave is such a short distance.

​@@cgibbard I'm still learning to recognize these different isomorphc keyboard layouts. I guess this one is especially good if you have some especially large EDO, as long as it only contains a single circle of fifths.

@@Lucius_Chiaraviglio Yeah, it also pretty much implies meantone temperament -- you can use it with non-meantone tunings, but since your thirds will no longer be 4 steps up / 3 steps down on the circle of fifths, it can become a bit more tricky to play then. The more piano-like Bosanquet layout also sort of implies meantone, but it also puts more strange intervals nearby, so the better thirds usually end up being less of a stretch (at the cost of octaves being far and many intervals that you likely want less often being close). Ergonomically, for non-meantone stuff like 22 or 53 equal I think I've so far preferred Sjoerd Visscher's layouts (if you google his name with "keyboard layout" you'll find his online keyboard) -- though the not-quite-isomorphic nature of it can sometimes be a downside. I still have to record a bit of my playing in 22, I think that might be next. :)

@@cgibbard Well, Yes, having thirds be way off to one side would be problematic as well (you would have to 2-hand them for any large non-meantone EDO). I was thinking it might also be hard to adapt Wicki-Hayden to some tuning that has multiple circles of fifths (like 24EDO or 34EDO, unless somebody figured out something I haven't).

​@@Lucius_Chiaraviglio you could split the / and \ axes in half, 7\24 for / and 5\24 for \

you play this very thoughtfully

Dm11 -> Am11 :)

Thanks! I'm a software developer by day and have just been improvising, playing mostly for myself a little bit each night over the past few years. It's not something I ever expect to try to make money at, just something that I do because it's good for my own mental health. I do hope that I can help spread the ideas and music theory that this instrument embodies though. The keyboard is a Lumatone (lumatone.io is their website). Despite the daunting appearance due to having so many keys, I feel like this type of keyboard is actually much, much easier to learn than the usual piano. You don't waste any time re-learning muscle memory for how to play the same scales and chords in each of 12 (or 43...) different key signatures / roots -- you just move your hands and start in a different spot to get a different tonic. So playing something in one key counts as practice for every key, which is a huge multiplier. I think after the first day or two I was already more musically capable with it than I'd ever gotten with the normal piano layout, though that's not really saying all that much -- I'd only gotten a few weeks into practising the piano a few times in my life, and bounced off it precisely because I was frustrated by the asymmetry and having to re-learn to play musical objects I already had muscle memory for on a different root note. It is fairly expensive, and I really hope they manage to produce more affordable models so that this kind of keyboard can really start to take over the world, but in any case, it's well worth the money in time savings, especially if you don't have 8-12 hours a day to practice.

@@cgibbard Awesome in-depth response! Thanks! (Beautiful playing too btw ;)

Sure!

Good luck working with microtonal

@@ikwenmusic it’s not too bad, just chopped bits and added effects to make it a cool ambient sort of thing

i dont think i phrased this correctly but i dont really know how to ask this question so it makes sense, i hope you understood

I'm using PianoTeq, which has a tuning editor that lets you add as many notes per octave as you want, pretty much. Under the "Temperament" dropdown, you can pick "Make equal temperament..." and type in a number to make any equal division of the octave you like. Under "Keyboard Mapping", I have it set to "Extended layout for up to 16*128 notes -> Multi-channel MIDI layout", which puts each octave on its own channel using MIDI note numbers 0 through 42 (or whatever), but where Channel 2 is an octave above Channel 1, etc. I also helped contribute this feature to Surge, which is a freely available synth, as its "Use MIDI channel for octave shift" setting, with a compatible convention for which octave goes on which channel. The Lumatone is then set up to produce those notes on multiple channels in a corresponding way. There are other approaches, but so far, this is the easiest to set up. I have some scripts for the Moony.lv2 plugin that will convert channel-per-octave MIDI into MPE, but they're not perfect about how they do it (I didn't yet bother implementing pitch bend or other global controllers). For these videos I'm mostly not using a DAW, and just capturing output from the standalone PianoTeq, but in cases where I am, it mostly doesn't require special setup. Actually editing the resulting MIDI can be kind of annoying at times though, because my DAW doesn't know that notes in different channels are an octave apart and stacks them on top of each other. :P If you were editing the MIDI by hand, it would probably be good to split channels out onto their own tracks, and maybe to combine some channels together, putting 2 or 3 octaves per channel depending on which EDO (3 octaves just barely doesn't fit on one channel for 43edo, sadly), but so far I've avoided doing much editing. If you'd like any more specifics about getting this stuff set up, feel free to ask further. Also have a look at Sevish's blog, which has lots of good content related to microtonal production.

@@cgibbard oh wow, thats actually super interesting. ive heard good things about pianoteq but i didnt know it was this good, i havent seen basically any other vst have temperament options. maybe im just missing out. ill be sure to check it out, ive only really recently got into microtonal music and even though it still blows my mind and seems incredibly difficult to write i'd certainly like to have a try at it. thank you!

The Xen wiki is great, but it can be kind of bewildering: en.xen.wiki/w/Main_Page Wikipedia is also good once you know the words to look up, but a bit scattered. I like talking about this stuff though, so here's a spiel that hopefully answers your question about why you're hearing what you're hearing. :) A basic thing you probably already know is that when we use our ears to try to tell if a pair of notes are in tune with each other, we usually listen for beating of the harmonics. Most simply-shaped objects like a string, or a column of air, when you cause them to vibrate, won't just vibrate at a single frequency, but instead at usually positive integer multiples of some fundamental frequency. The Wikipedia page for harmonic series (music) has a really good illustration of why this happens for a string. When multiple frequencies occur together, and get close to one another, we hear a wobbling in amplitude called "beating", and when we tune by ear, we're listening for the beating of harmonics in adjacent notes that are approximately lining up with each other. The beating slows as we get closer until it stops (or gets slow enough that the notes aren't long enough to tell it's happening). So, tuning by ear, we'd be listening for the nth harmonic of some note with fundamental frequency f to line up with the mth harmonic of some other note with fundamental F, so we want n f = m F, or n / m = F / f. So the fundamental pitches will be at some integer ratio corresponding to which harmonics we're lining up -- that is, when we use our ears, we're using just intonation, not equal temperament. The most basic intervals are of this form, here are a few that are the ratios between successive harmonics: 2/1 is the octave 3/2 is the perfect fifth 4/3 is the perfect fourth 5/4 is the major third 6/5 is the minor third When we stack intervals on each other, we multiply the ratios, so you can e.g. determine that a major sixth which is a perfect fourth and a major third stacked on each other is (5/4)(4/3) = (5/3). 12-tet just happens to do a reasonably good job of approximating these basic intervals without having too many notes. It's a decent compromise that lets us build instruments that sound equally good/bad in every key without too much expense. So hopefully that answers the basic question, but then, why do we want more notes, and what functions could those additional notes serve? The very next ratio that would have been in my list above, 7/6, the "septimal minor third", and in fact, anything having to do with the 7th harmonic or 11th or 13th harmonic is missing. 12 equal does a poor job of approximating them, and where you'd find them is not a foregone conclusion because 7, 11, and 13 are prime, so multiplying previous ratios won't get you to anything involving those numbers directly. So one reason we might want more notes is to have access to a wider variety of consonances. The seventh harmonic is the secret to barbershop quartets and a lot of Middle-Eastern scales. I've come to feel that the 11th harmonic is a secret behind the wailing sounds of the blues, whether anyone really thinks of it that way or not -- 11/8, an octave equivalent of the 11th harmonic, is a slightly sharp fourth. A perfect fourth above that is 11/6, a neutral seventh, and a perfect fifth below that is 11/9, a neutral third, and those can be thought of as bent-sharp versions of their minor counterparts, which are exactly the notes that blues singers and guitarists tend to bend sharp. Another reason is that with more notes per octave, we can get better approximations to the basic intervals. 31 equal trades a bit of accuracy in the perfect fifth (it becomes about 5 cents flat) to get an almost perfect major third (less than a cent off). 43 equal makes both the perfect fifth and major third about 4 cents out, but makes the diatonic semitone (e.g. the one between E and F or B and C) about 0.1 cent off from 16/15, which makes the major seventh chords shine gloriously, and sometimes feels like it extends the can't-go-wrong magic of the pentatonic scale to the whole major/minor scale. 50 equal that I'm playing in this video is a bit of a weird one, but we're getting to the number of notes where you really are going to find a decent enough approximation to anything. Its perfect fifth is 6 cents flat, and major third is about 2 cents flat. I picked it mainly to have some extra small intervals to play around with alongside being a decent tuning with ergonomics I'm used to. On this keyboard (Lumatone), I can play all of these with essentially the same muscle memory, because the basic intervals are mapped to the same place for my fingers. In every key as well -- chords and scales are the same everywhere, you just start on a different note. One thing that helps is that 12, 19, 31, 43, 50, and 55 among a bunch of others, share the property that the best major third is found 4 steps up on their circle of fifths (and there still is only one circle of fifths). If the octaves, fifths/fourths, and thirds are where your fingers expect them, you can play fine. There are beautiful tunings like 22, 34, and 53 equal divisions of the octave which break that property and have a better major third somewhere else on their circle of fifths, and so the ergonomics are a bit different -- they're playable, but you have to stretch a little more in most layouts. The best-sounding major and minor scales are also no longer contiguous segments of the circle of fifths in those tunings, so all sorts of crazy new ways to modulate between keys open up, at the expense of certain things you might expect, e.g. you no longer really have a ii minor chord in your major scale -- but you can play one and it will take you very smoothly to a new key.

i like 26edo

Wicki-Hayden is a brilliant layout. I feel like more people would, if not become musicians, at least engage with music on some level in their daily lives if this sort of keyboard were more commonplace. It's fun watching a non-musician's eyes light up when they touch my keyboard in Wicki-Hayden layout and realize that the random keys they hit sounded good together because they probably weren't too far apart. :)

43edo makes a really brilliant compromise between the accuracy of its major third and perfect fifth -- both are only about 4 cents out, and its 16/15 diatonic semitone is only about 0.1 cents off, making it more harmonically consonant than the usual semitone in 12 that is overworked trying to be both the 16/15 diatonic semitone and the 25/24 chromatic semitone at the same time. Because of that, it kind of feels like some of the usual can't-go-wrong pentatonic magic that the black keys have on a normal piano gets extended to the white keys also. :) The major seventh chords also benefit greatly.

bro i play the piano but never learned musical theory, its 3am, i found your video and other, you all seems to speak japanese to me. should i study music theory more to understand what yo'ure talking about ? looks fascinating@@cgibbard

@@yetresaMaybe! Specifically a lot of the stuff we talk about is tuning theory specifically, or stuff about microtonality, rather than general music theory. Most of the music theory you'll see out there tends to assume that the octave is divided into 12 equal parts which is a decent compromise that enables the construction of instruments that all play reasonably nicely together without needing very many keys or frets. But there are lots of other possible notes in between those and systems for naming and thinking about more pitches than that, and it can be fun to explore how things from normal music theory can still find homes in these larger tuning systems, and also what new concepts become possible. Looking up information about just intonation can be helpful because even if you're using a tempered system, understanding how it approximates justly tuned intervals can be a helpful guide to figuring out harmony. In this video, I'm subdividing the octave into 43 equal parts. If you've ever heard of the circle of fifths in ordinary music theory, it turns out that 43 equal has a single circle of fifths as well, and that the best approximations to the major/minor scales are still contiguous segments of seven notes on that circle of fifths. So the music theory of 43 equal behaves a lot like that for 12 equal, only with many more keys (as in key signatures) you could reach out into, as well as to a reasonable approximation some new types of consonant harmony and dissonance that aren't on the usual piano keyboard.