A very interested video. Yes, 53-TET sounds differently than 31-TET. I don't know which one I like more. They are just different, but both are great. What you say at 4:45 that human can hear only the difference of 5 to 6 cents is true for the two sounds played sequentially, but when the sounds are played together 1 cent difference is noticable (and maybe even less) and it is heard as a "beat". Here we can listen to an example: en.wikipedia.org/wiki/Cent_(music) In the cords we hear the sounds played together, so when the higher harmonics are mismatched by 1 cent it also can be noticed, though it is more subtle the the mismatch of the base sounds.
53-TET makes 31-TET sound like 12-TET Like 12-TET has this exotic roughness to it when compared to 31-TET; it's not perfect, but it works in its own imperfect way. Hearing the accuracy of 53-TET reveals the "rough spots" in 31-TET, at least for me.
First time I have actually gotten to her 53 EDO -- and it sounds great. You have to be totally awesome to be able to play it, and building an instrument to play it isn't easy(*), but if you can pull it off, here's your almost exact Just Intonation. (*)Especially once you go to non-synthesizer instruments other than those already having continuous pitch.
It would be really cool if there was a "smart" software that could analyze the spectrum of sound being played and "choose" the most harmonic 52-edo option while playing on a simple 12-edo layout without having to memorize the myriad of optimal chords. I could almost imagine it being possible as some sort of post-processing plugin or tool, but maybe too ambitious in real time.
If your goal is to approximate 5-limit JI and still modulate freely, 53 is probably not overkill. (That’s not necessarily the most important goal, but it has meaning.) Given that goal, what I think is most interesting, is what I’ll call _insightful_ JI approximations. That is, excellent approximations because a tuning is _well-chosen_ , rather than just by “shot-gunning” it - just having so many available pitches that you can’t possibly miss! One possible way to get a handle on that, is to require that it approximate that ratio within some percentage of its step size, say 20%. 53TET _absolutely nails_ perfect fourths and fifths - off by less than 1% of its step size. That’s what you call a bullseye! 53TET also has a _pretty-good-but-not-amazing_ approximation of a 7:4 (~5c). That’s off by about 1/5 of its step size. Does a 5c approximation justify the added cumbersomeness and complexity of managing 22 more steps per octave than 31TET, say? That depends in part upon how much more cumbersome those extra 22 pitches are to manage. On a Lumatone, the answer is, “not much” (although 5 octaves of 72TET is impossible even on a Lumatone). On a guitar though, 53TET is a lot more cumbersome than 31TET, and on a woodwind, it could be a deal-breaker!
Which commas are tempered and which are left in is also a very important characteristic of a tuning for example i would like 41edo a lot more if 21/16 and 13/10 weren't equated (13/8 and 18/11 too)
Seeing the pattern on those keys, 53 comes from the four sets of 12-tone "chromatic" scale (counting up to 48 tones), with five more tones to wrap everything up into this configuration. That's one beautiful keyboard with unique sounding. The transition from 12-TET to 53-TET is alike to transition from real to complex numbers, but in terms of music harmony.
You might make a video on 41edo next time. It is a really good tuning, supporting Schismatic (like 53edo and 94edo), Miracle (like 31edo and 72edo), Magic (like 22edo, 19edo, 60edo and 63edo), Octacot (like 27edo and 68edo). It would be excellent for some nice, pretty accurate Lumatone music in the 7-limit, and even 11-limit. Kite Giedraitis has also made a good guitar tuning with frets spaced like every other step in 41edo, so it is a (41/2)edo tuning i suppose, except the tuning in [EDIT: pental (down)major thirds (5/4)] apart strings make it into a full 41edo tuning.
@@KiteGiedraitis Ah thanks Kite. I could have sworn it was fourths (17\41 ~= 4/3), but if you say it is in pental major thirds (13\41 ~= 5/4) then i suppose that's the case.
@@KiteGiedraitis Also yes Dave explained the basics of basics of 41edo in Episode 27 of the Learning Lumatone series, although it seems it is not really 41edo but rather a 41 step spiral of fifths in 94edo (by Cam Taylor). I could be wrong of course, maybe that's just the layout.
@@ValkyRiver There is the Miracle layout i think. Based on the Miracle temperament and Miracle scales. Dividing the perfect fifth into 6 equal steps, then making scales with 10, 11, 21, 31 and 41 steps.
@@axenwald9790 In Miracle temperament, we have a slightly flat perfect fifth 3/2, that is split both in two equal neutral thirds 11/9, and in three equal supermajor seconds 8/7. Half of a supermajor second and simultaneously a third of a neutral third is a kind of semitone lying between 16/15 and 15/14 and representing them both, this semitone is called the Secor. 72edo is almost a perfect tuning for Miracle temperament, extending it uniquely to the 13-limit. So let's tune a Lumatone to 72edo Miracle!
FWIW "...The 43-tone scale is a just intonation scale with 43 pitches in each octave. It is based on an eleven-limit tonality diamond, similar to the seven-limit diamond previously devised by Max Friedrich Meyer and refined by Harry Partch. ..." Wikipedia It would be nice if keys over 43 could toggle octaves
That would be the Genesis 43-tone JI scale. It is not almost evenly spaced, but can be made so by removing two tones, making it into a JI tuning variant of 41edo. There is a tempered variant of 43-tone Genesis (with no mixup of different JI scale steps) in 58edo.
My mom was an incredible pianist, and wasn’t terribly picky about genre’s either. Definitely not a piano snob, but I know that she would’ve absolutely hated this. She did have some things that bothered her, and she wasn’t a fan of songs with a whole lot of semitones, and semitones is pretty much the whole idea of this thing.
I don't think that makes any sense really. That's like saying because every key on a normal piano is next to two other notes a semitone away, that semitones are "the whole idea of piano". You don't have to play minor seconds if you don't want to on piano, or any of the various small intervals on this keyboard in 53edo. I can only understand "too many semitones" as music that's loaded with chromatic runs, which straight-up sounds like carnival music because that's what that is, and like, sure. It's not pretty, it's disorienting. No one really holds the fact that carnival music exists against the piano (or organ) itself.
The white keys are the fifths-based or Pythagorean diatonic notes. So, for example, from C, you get to E by stacking 4 fifths, C-G-D-A-E. However, doing so gets you a third that is quite sharp. To get the approximation of 5:4, you have to use a different note. Another way to visualize this, say C to D is a major second 9:8. 5/4 divided by 9/8 = 10/9, which is a different whole tone interval (one step lower).
The just major third (5/4) doesn't truly exist in 53-EDO, or extended Pythagorean, which 53 approximates. What sounds like the just major third is actually the Pythagorean diminished fourth, formed by adding one octave (2/1) followed by subtracting two Pythagorean thirds (81/64) to yield the ratio 8192/6561, which is nearly 2 cents (the schisma, 32805/32768) flat of 5/4. Equivalently, we can construct the diminished fourth by adding a Pythagorean third (81/64) and subtracting the Pythagorean comma (531441/524288). Note that either way we end up with a complicated ratio basically constructed from perfect fifths (3/2). To make the jump to true 5/4 we need a different comma, the syntonic comma (81/80). If we subtract the syntonic comma from our Pythagorean third, we end up with (81/64) / (81/80) = 80/64 = 5/4. You'll notice this general pattern with higher limit JIs: intervals with high prime limits, like for example our 5/4, are constructed by adding or subtracting commas from the 3-limit Pythagorean notes. As such, the Pythagorean notes are taken to be the naturals. It's worth noting that all of the twelve chromatic Pythagorean notes are technically naturals, not just the standard "piano white key" diatonic notes, but for convenience it helps if we stick with the "sharps-naturals-flats" system. Any interval that deviates from the Pythagorean naturals, such as 5/4, shouldn't be treated as a natural note. Since 53-EDO tempers out the schisma, it equates the syntonic comma with the Pythagorean comma, and consequently equates the Pythagorean diminished fourth with the just major third. The resulting downmajor third isn't exactly 5/4 or 8192/6561, but takes the place of both intervals. However, the general logic with comma modification still applies. We can think of a 53-EDO step as being similar to a syntonic comma/Pythagorean comma, and so subtracting a 53-EDO step from a 53-EDO natural major third yields a downmajor third. As such, the downmajor third shouldn't be considered as a natural note. FWIW, the "natural coloring" way of thinking also falls apart when you consider that all intervals are equivalent across all keys in 53-EDO. The octave-reduced 11th harmonic (11/8) can be approximated by a doubleup fourth, so relative to the natural C this would be a F near the very top of the keyboard. Yet, you can still play a downmajor third above that doubleup fourth all the same, and despite neither of them being natural notes the interval will sound just as pure as a downmajor third over the natural C.
In my personal opinion, 53-EDO is getting close. There comes a point where the hand gymnastics required to play basic intervals and chords overshadows the better tuning approximation. But that's just me
How velocity sensitive are the keys? Also, how well does it fit into MIDI control? Does it interpret the MIDI mapping for notes, so that it chooses the nearest 12-tone/octave equivalent? Or vice versa if on the receiving end of a controller?
It's spelled "caret", the "carat" is a unit of mass. Also, sometimes ^ is referred to as a circumflex accent, because the reason it came into existence was to be able to add those on a typewriter by moving the print head back (or not moving it forward) and printing it atop another character. There are various formal and informal contexts which call it a hat as well though, so I'd say that's fine too. In HTML for example, you can get one by writing "&hat;"
@@cgibbard and because of that we have these ^ ~ ` symbols that previously meant "circumflex", "tilde", and "grave" but are reinterpreted as "up", "wave", and "slanted quote" because they can no longer be used as their original purposes.
53-EDO is definitely not overkill. Thanks for this demonstration.
I use 53-TET to explore 5-limit just intonation in a schismic way
A very interested video. Yes, 53-TET sounds differently than 31-TET. I don't know which one I like more. They are just different, but both are great. What you say at 4:45 that human can hear only the difference of 5 to 6 cents is true for the two sounds played sequentially, but when the sounds are played together 1 cent difference is noticable (and maybe even less) and it is heard as a "beat". Here we can listen to an example: en.wikipedia.org/wiki/Cent_(music) In the cords we hear the sounds played together, so when the higher harmonics are mismatched by 1 cent it also can be noticed, though it is more subtle the the mismatch of the base sounds.
Agree it’s all about the beating
53-TET makes 31-TET sound like 12-TET
Like 12-TET has this exotic roughness to it when compared to 31-TET; it's not perfect, but it works in its own imperfect way. Hearing the accuracy of 53-TET reveals the "rough spots" in 31-TET, at least for me.
Oh my gosh that piece at the end was beautiful
Really looking forward to your JI video! This 53-EDO might be my favorite tuning you've shown so far.
This is the future of music right here 🎉🎉
Awesome 53 EDO and you know how to use it. Good show!
Always like to see people take times feelings into consideration.
First time I have actually gotten to her 53 EDO -- and it sounds great. You have to be totally awesome to be able to play it, and building an instrument to play it isn't easy(*), but if you can pull it off, here's your almost exact Just Intonation.
(*)Especially once you go to non-synthesizer instruments other than those already having continuous pitch.
Learning it isn't the problem. Affording it is.
It would be really cool if there was a "smart" software that could analyze the spectrum of sound being played and "choose" the most harmonic 52-edo option while playing on a simple 12-edo layout without having to memorize the myriad of optimal chords. I could almost imagine it being possible as some sort of post-processing plugin or tool, but maybe too ambitious in real time.
bro how do you even memorise this stuff.. i cant imagine the hours u put into this. unsung genius
now im imaging a giant touchbed with just pure continuous notes
I think there is an instrument called 'the continuum' or something that is exactly that
There's a video of it on dolores catherino's channel
So you mean any fretless instrument?
So like, a violin?
voice teheh
If your goal is to approximate 5-limit JI and still modulate freely, 53 is probably not overkill. (That’s not necessarily the most important goal, but it has meaning.)
Given that goal, what I think is most interesting, is what I’ll call _insightful_ JI approximations. That is, excellent approximations because a tuning is _well-chosen_ , rather than just by “shot-gunning” it - just having so many available pitches that you can’t possibly miss!
One possible way to get a handle on that, is to require that it approximate that ratio within some percentage of its step size, say 20%.
53TET _absolutely nails_ perfect fourths and fifths - off by less than 1% of its step size. That’s what you call a bullseye! 53TET also has a _pretty-good-but-not-amazing_ approximation of a 7:4 (~5c). That’s off by about 1/5 of its step size. Does a 5c approximation justify the added cumbersomeness and complexity of managing 22 more steps per octave than 31TET, say?
That depends in part upon how much more cumbersome those extra 22 pitches are to manage. On a Lumatone, the answer is, “not much” (although 5 octaves of 72TET is impossible even on a Lumatone). On a guitar though, 53TET is a lot more cumbersome than 31TET, and on a woodwind, it could be a deal-breaker!
Which commas are tempered and which are left in is also a very important characteristic of a tuning for example i would like 41edo a lot more if 21/16 and 13/10 weren't equated (13/8 and 18/11 too)
Who wrote the short piece at the end, the presenter? It's very good.
id love to hear it as a full song
Beautiful video! I love your down to earth approach to these tunings- very refreshing :D lots of love!
That little intro bit he plays was really colorful, and soft, not as dissonant as I am used to hearing in microtonal music.
Amazing. Absolutely stunning
Bro, is the song you played a full song? I loved it and I'd love to listen to it
Seeing the pattern on those keys, 53 comes from the four sets of 12-tone "chromatic" scale (counting up to 48 tones), with five more tones to wrap everything up into this configuration. That's one beautiful keyboard with unique sounding. The transition from 12-TET to 53-TET is alike to transition from real to complex numbers, but in terms of music harmony.
You might make a video on 41edo next time. It is a really good tuning, supporting Schismatic (like 53edo and 94edo), Miracle (like 31edo and 72edo), Magic (like 22edo, 19edo, 60edo and 63edo), Octacot (like 27edo and 68edo).
It would be excellent for some nice, pretty accurate Lumatone music in the 7-limit, and even 11-limit.
Kite Giedraitis has also made a good guitar tuning with frets spaced like every other step in 41edo, so it is a (41/2)edo tuning i suppose, except the tuning in [EDIT: pental (down)major thirds (5/4)] apart strings make it into a full 41edo tuning.
Yeah, 41edo is great. Looks like they did make such a video. BTW the Kite guitar is usually tuned not in 4ths but in downmajor 3rds (13\41).
@@KiteGiedraitis Ah thanks Kite. I could have sworn it was fourths (17\41 ~= 4/3), but if you say it is in pental major thirds (13\41 ~= 5/4) then i suppose that's the case.
@@KiteGiedraitis Also yes Dave explained the basics of basics of 41edo in Episode 27 of the Learning Lumatone series, although it seems it is not really 41edo but rather a 41 step spiral of fifths in 94edo (by Cam Taylor). I could be wrong of course, maybe that's just the layout.
@@KiteGiedraitis Here is the link, if you feel too lazy to find it. 😉 ua-cam.com/video/BfZVnktJZdw/v-deo.html
2:31 Wow, I had a hard time telling one chord from another. The just and supra sound smoother to my ears.
I want to see 72-EDO!
72-TET would require a non-Bosanquet layout, as it has six circles of fifths and has more notes per octave than the Lumatone does with Bosanquet.
I'd love a 72 keys per octave Lumatone too.
@@axenwald9790 That is possible. It’s just that the “Bosanquet” layout doesn’t support 72-TET. A different layout would work, though.
@@ValkyRiver There is the Miracle layout i think. Based on the Miracle temperament and Miracle scales. Dividing the perfect fifth into 6 equal steps, then making scales with 10, 11, 21, 31 and 41 steps.
@@axenwald9790 In Miracle temperament, we have a slightly flat perfect fifth 3/2, that is split both in two equal neutral thirds 11/9, and in three equal supermajor seconds 8/7. Half of a supermajor second and simultaneously a third of a neutral third is a kind of semitone lying between 16/15 and 15/14 and representing them both, this semitone is called the Secor.
72edo is almost a perfect tuning for Miracle temperament, extending it uniquely to the 13-limit.
So let's tune a Lumatone to 72edo Miracle!
Excellent work
This is hurting my brain in a good way
This is what I imagine alien instruments would look/sound like
FWIW
"...The 43-tone scale is a just intonation scale with 43 pitches in each octave. It is based on an eleven-limit tonality diamond, similar to the seven-limit diamond previously devised by Max Friedrich Meyer and refined by Harry Partch. ..." Wikipedia
It would be nice if keys over 43 could toggle octaves
That would be the Genesis 43-tone JI scale. It is not almost evenly spaced, but can be made so by removing two tones, making it into a JI tuning variant of 41edo.
There is a tempered variant of 43-tone Genesis (with no mixup of different JI scale steps) in 58edo.
17-EDO & 15-EDO basics please!❤❤
My mom was an incredible pianist, and wasn’t terribly picky about genre’s either. Definitely not a piano snob, but I know that she would’ve absolutely hated this. She did have some things that bothered her, and she wasn’t a fan of songs with a whole lot of semitones, and semitones is pretty much the whole idea of this thing.
I don't think that makes any sense really. That's like saying because every key on a normal piano is next to two other notes a semitone away, that semitones are "the whole idea of piano". You don't have to play minor seconds if you don't want to on piano, or any of the various small intervals on this keyboard in 53edo.
I can only understand "too many semitones" as music that's loaded with chromatic runs, which straight-up sounds like carnival music because that's what that is, and like, sure. It's not pretty, it's disorienting. No one really holds the fact that carnival music exists against the piano (or organ) itself.
53 edo has the closest approximation of a perfect fifth in the lower edos.
Hey! And why pure major third is not a white key? Is it a standard 53 mapping?
The white keys are the fifths-based or Pythagorean diatonic notes. So, for example, from C, you get to E by stacking 4 fifths, C-G-D-A-E. However, doing so gets you a third that is quite sharp. To get the approximation of 5:4, you have to use a different note. Another way to visualize this, say C to D is a major second 9:8. 5/4 divided by 9/8 = 10/9, which is a different whole tone interval (one step lower).
The just major third (5/4) doesn't truly exist in 53-EDO, or extended Pythagorean, which 53 approximates. What sounds like the just major third is actually the Pythagorean diminished fourth, formed by adding one octave (2/1) followed by subtracting two Pythagorean thirds (81/64) to yield the ratio 8192/6561, which is nearly 2 cents (the schisma, 32805/32768) flat of 5/4. Equivalently, we can construct the diminished fourth by adding a Pythagorean third (81/64) and subtracting the Pythagorean comma (531441/524288). Note that either way we end up with a complicated ratio basically constructed from perfect fifths (3/2).
To make the jump to true 5/4 we need a different comma, the syntonic comma (81/80). If we subtract the syntonic comma from our Pythagorean third, we end up with (81/64) / (81/80) = 80/64 = 5/4.
You'll notice this general pattern with higher limit JIs: intervals with high prime limits, like for example our 5/4, are constructed by adding or subtracting commas from the 3-limit Pythagorean notes. As such, the Pythagorean notes are taken to be the naturals. It's worth noting that all of the twelve chromatic Pythagorean notes are technically naturals, not just the standard "piano white key" diatonic notes, but for convenience it helps if we stick with the "sharps-naturals-flats" system. Any interval that deviates from the Pythagorean naturals, such as 5/4, shouldn't be treated as a natural note.
Since 53-EDO tempers out the schisma, it equates the syntonic comma with the Pythagorean comma, and consequently equates the Pythagorean diminished fourth with the just major third. The resulting downmajor third isn't exactly 5/4 or 8192/6561, but takes the place of both intervals. However, the general logic with comma modification still applies. We can think of a 53-EDO step as being similar to a syntonic comma/Pythagorean comma, and so subtracting a 53-EDO step from a 53-EDO natural major third yields a downmajor third. As such, the downmajor third shouldn't be considered as a natural note.
FWIW, the "natural coloring" way of thinking also falls apart when you consider that all intervals are equivalent across all keys in 53-EDO. The octave-reduced 11th harmonic (11/8) can be approximated by a doubleup fourth, so relative to the natural C this would be a F near the very top of the keyboard. Yet, you can still play a downmajor third above that doubleup fourth all the same, and despite neither of them being natural notes the interval will sound just as pure as a downmajor third over the natural C.
In my personal opinion, 53-EDO is getting close. There comes a point where the hand gymnastics required to play basic intervals and chords overshadows the better tuning approximation.
But that's just me
In 53 edo how many notes does each alphabet have?
How velocity sensitive are the keys?
Also, how well does it fit into MIDI control?
Does it interpret the MIDI mapping for notes, so that it chooses the nearest 12-tone/octave equivalent? Or vice versa if on the receiving end of a controller?
Sorry… I should just go to the website and learn about this. I’ll go look up Lumatone. Thanks for the demo.
We sure wish we could afford one . I’d buy 3 if I could..
I recently compose something that use all 88 keys on the piano - and this obliterate my world of "half notes"
This instrument costs more than my car lmao
Is it just me or are the just chords less wobbly in 53?
Yup your ears are correct the chords are more in tune😊
I don’t sound or timbre of whatever midi piano is being used
If the chromatic scale is 13 edo, why are comparing 53 to 12 edo?
ᴘʀᴏᴍᴏsᴍ 🤘
Ah, yes. "Basics".
now that i've heard the just third rather than the pythagorean third i am disgusted with poorly tuned thirds lol
"Which is represented by this hat symbol here..."
Carat. It's called a "carat".
It's spelled "caret", the "carat" is a unit of mass. Also, sometimes ^ is referred to as a circumflex accent, because the reason it came into existence was to be able to add those on a typewriter by moving the print head back (or not moving it forward) and printing it atop another character. There are various formal and informal contexts which call it a hat as well though, so I'd say that's fine too. In HTML for example, you can get one by writing "&hat;"
@@cgibbard and because of that we have these ^ ~ ` symbols that previously meant "circumflex", "tilde", and "grave" but are reinterpreted as "up", "wave", and "slanted quote" because they can no longer be used as their original purposes.
I tried to play along with this on my guitar. I hate you.
Please don't put the name on the chords, it I'll save time 😝
dude, i love you but what's up with the hair?
Ok that's microtonal, but the sounds are absolutely awful !!!
It sounds really like a 99 $ piano !!!
Do 60 EDO cowards 😂