Making Sense of Microtones by Stacking Fifths
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- Опубліковано 16 вер 2024
- This video covers generators of 12edo, historical tunings like quarter-comma meantone and the pythagorean tuning, and gives fifth-based construction for edos of 17, 22, 5, 31, 19, 7, 23, 16, 9, 11, 13 and 8 in that order with short musical examples.
As the president of the Society For Putting Fifths On Top Of One Another, I thoroughly approve of this video. I would encourage every viewer to become proficient at putting fifths on top of one another.
Python reference?
@@samsoa19 Of course!
One must become proficient in generation of Pythonic, super-Pythonic, and sub-Pythonic scales.
As the Duchess of Louest Input commanding the Ministry of Funny Walks as they Pertain to Bass Guitar and Bass Fiddle Playing, I commend you.
@@AlexandraMcCloud 🤣🤣🤣
im so confused but they all sound so cool
Honestly, I've been learning about this stuff for a while and I still can't completely keep up with a video like this.
It's not your fault, I've studied meantone, superpyth and other tunings very closely for years and this guy just kinda glossed over without explaining anything well. Not a good intro for people who actually wanna learn what he's talking about but it's okay if you just wanna hear microtonal stuff
this is a really good explanation/visualization of MOS scales! one small nitpick i have is that the fifth could be made a little bit more obvious (e.g. making it yellow), but context allows the viewer to get it anyways. the low-fidelity visuals remind me of the videos by The Geometry Center such as Outside In (more commonly known as 'how to turn a sphere inside out'), so it's actually kind of a good thing. i'd absolutely love to see more videos like this!
This was such a cool video. I never realized how all these effects and properties can arise just by flattening or sharpening the fifth. The diagram with lines and colored regions at the end really sums it all up so neatly.
This is an excellent vid! I certainly didn't understand everything but it is worth watching several more times. Thanks!
These visualizations are so cool! Great job! I wonder, have you ever thought of animating the transition between a line and a circle with that piano visual? That’s a really neat idea for showing pitch class! I also wonder if there’s someway you can indicate that the pitches actually fall in the center of the key so that it’s a little bit easier to see… for layouts with double black keys, I would also make those touch each other so that it’s clear that there’s not an additional white key in between… (such as with 17edo and 19edo).
Something else that I didn’t expect you to mention, but hoped that might be mentioned, is that those tunings that have flatward fifths (flatter than 7edo) really shouldn’t be notated as described in the xenharmonic wiki, letting “sharp” mean “down” - this is too much of a tweak in logic for the average musician to get used to, and usually such EDO’s have another viable notation strategy. I plan to talk about this in an upcoming video actually :)
Looking forward to more videos from you in the future!
Thank you for your feedback! I appreciate it.
I did think about animating the transition between the line and the circle with the piano visual, but my Blender skills just aren't there yet. In the rig I'm using the pitches actually do not fall in the middle of the white keys while they do fall in the middle of the black keys. I chose this visualization for aesthetic reasons. If I were to redo the video for clarity I would use a sector based visual to fan out all of the pitches equally.
Notation for flatward fifths depends on the application. I'm mainly working in a digital environment where I find it important that muscle memory from 12edo piano translates to meaningful structures in the tuning of my choice. In my day-to-day composing I treat the symbols # and b as abstract indicators of distance along the chain of fifths and use midi channel data to distinguish between them in my DAW.
I think there's a plugin for fifth based tuning for Musescore which is handy if you use the program to render the sound as well, but would be confusing as a performance instruction as you mention.
I'm looking forward to your video! I haven't yet collaborated with other musicians in a xen context so it would be instructive to know what to look out for. I hear Juhani Nuorvala has had success using notehead shapes and easy note names like ”square B flat”, ”triangle F”, etc..
See you in my next video!
When is this upcoming video coming or have i just missed it?
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@@romeolz I don't think he ever published it, after a quick scan.
Mavila has different notation, Johnston notation is sharp-up while pythagorean is sharp-down.
11edo and 13edo is notated edostep notation of 22 and 26, 8edo and 9edo to 24 and 27.
Edostep is valid between 686c and 720c, 5edo and 7edo uses natural fifths while 4edo and 6edo uses 12-notation.
You are correct. It's just fun to keep using the same notation to see what happens.
That's the best visualisation of this subject, I have seen so far! Great job! Thank you for your effort! ♪♫
Really nice Lumi! Thanks for your effort and on having these visualizations and a concise script.
this made my musician brain, over being in denial, finally realise music is all about applied maths, and I now can say I love maths
Not the video I was expecting, but a perspective haven't seen! I'm surprised that this video wasn't about 53 edo...
Just use 12 tet and modify notes to be different if you're going to be so extreme
I watch this video recurrently, great effort and educational.
Very informative. Thank you for sharing 🎶
Glad it was helpful!
This video is totally kick ass. Thanks. It really helped demystify the relationship, I had settled on 22edo as a personal fav, and now I know why! Thanks.
This is a good video to watch while reading The Harmonic Experience.
insane content
Great illustrations! Thanks. Your tuning optimizing 5:4 and 5:3 strikes me as intriguing.
I first got into Microtonality back in 1977, and at the time, we could only illustrate such distinctions on the pages of a Xenharmonikôn - on the printed page. Animation like this makes the trends more understandable!
Nevertheless, I have a nitpick: Your underlying white-key circle in these illustrations is a little hard to understand. I personally think that picture would be easier to understand if the white-key backdrop weren’t there, and instead, color the blue lines white to describe the white-key positions.
In other words, for me at least, it wasn’t clear that what the blue lines show, is where the underlying white patch is … focused … relative to the black and red chromatics.
Again though, that’s just a nitpick. Otherwise, excellent illustrations!
I agree with your nitpick. If I were to redo the video I would make it more clear, but at the time of making it I decided to get flashy instead of informative.
@@lumi-musictheory3476 😂! Again though, great illustrations of the interrelationships between such a great diversity of tunings!
I really wanna hear 29 tone equal temperament. You've got very pure fifths that are slightly sharp, so all other notes become extremely dissonant. It's kinda like an extended pythagorean tuning.
29 is a fun tuning. Instead of focusing on fifth you get more mileage from the fact that the nearly pure fourth is 12 steps of 29-tone. For instance, using 4\29 as the generator (the fourth divided into 3 equal steps) you get a nice alternative to the porcupine temperament.
@@lumi-musictheory3476 That's a cool way of looking at it. I'm interested in it from more of a drone guitar type of perspective. Having those microtones droning against an open low B of a baritone is intriguing to me. I'd love to use them as sorta blue notes that don't fit the scale.
@@somepunkinthecomments471That's just B minor?
@@user-ze7sj4qy6q You are absolutely correct. That was a massive blunder on my part. Sometimes the simple things slide right past me. I fixed my comment. Thank you.
@@somepunkinthecomments471 hahaha i do the same thing. i fw the content of ur comment tho i am also into drop tunings, drones, microtones, blue notes etc lol
Subtitles are a must for this
Mielenkiintoista settiä
thanks! though, weird choice of timbres (like, why do you change them from one example to another)
Based on the tuning of the intervals some harmonics can clash in quite dissonant ways. 12edo works reasonable well with almost all timbres, but some of the featured tunings do not agree with my ears if the timbre features the fifth or the tenth harmonic for example. I tried to design instruments that sound best in the context they are featured in. By the way, it is possible to design a harmonic timbre that sounds as dissonant as possible when played as a 12edo major chord. The effect is somewhat hilarious. I might make a video about it one day.
@@lumi-musictheory3476 oh how do you create these different timbres? i assumed it’s by altering which harmonics show up in the acoustic overtones and to what intensity, but what software do you use for this?
@@alexr3912 I use Bitwig and design the instruments myself in the Poly Grid. When I want more control over the timbre I start by stacking Sine wave oscillators with the frequency multiplier set to 1,2,3,4,5,6,7, etc. and mixing them together. Then I either phase modulate the oscillators or replace them with other waveforms until I get the sound I like. The important point is to doodle withing the tuning of your choice. Designing a something that sounds good in 12edo may not be ideal for 17edo or whatever your working with.
@@lumi-musictheory3476 Time to make a 12-EDO Prank. :]
@@lumi-musictheory3476 It would be nice to experiment with a timbre especially highlighting many prime harmonics, like e.g. the 2nd, 3rd, 5th, 7th, 11th and 13th harmonics. And try it out in some really accurate temperament, like 87edo.
[ from the wishlist ]
How abt "back to the roots" - take gregorian into after Guido and try to show electronically the influence of the vowel-patterns.
The central problem of singing is the influence of pitch and vowel on eachother.
If you would choose the 7 italian vowels for a model you could start with fixed vowel-characteristics. Those are with the italian set of vowels clearly differentiated ... in fixed qualities which is not the case in other languages.
( at the moment : reading good old HELMHOLTZ again ;-)
-
Thank you for your efforts + excuse my poor english ...
I tried to follow what you're doing from 9:40, but I ended up confused. I figured you're asking for a scale in which seven fifths minus 3 octaves is equal to (5/4)*(5/3) = 25/12. This means that a fifth is 1200*(log2(25/12)-3)/7 = 695.81 cents. If a fifth is three big steps and one small one then we must have that a big step is 191.62 cents and a small step is 120.95 cents. This gives a scale that has a pure 25/12, and it happens to be very close to 50 edo. But the confusing thing is that while the major thirds and major sixths are pretty good, they are very slightly worse than 31 edo, and also the perfect fifths are worse than 31 edo. So if you have time to reply, my questions are (i) did I correctly interpret what you meant in the video?, and (ii) you say in the video that this gives a minimax compromise. I guess I interpreted that as something like "this is the scale with the best 5/4 and 5/3 among scales of this kind", but now I'm wondering if you meant something else - would you mind explaining the minimax point a bit more? I'm not sure if my scale is the same as yours but I really like the way yours sounds in the video, so I'm curious to know more about how it's derived.
You somehow got the cents correct, but it's +3 octaves in the formula you had written out.
@@lumi-musictheory3476 Ah yeah, it's +3 in my code, I must have just mistyped it when I wrote that comment
siisti video, mukava nähä että täälläki päin on mikrotonaalisia muusikkoja!
It's so ironic that music, something considered to project a "feeling, or feelings" becomes so mathematical when employing microtonal elements. It's very ironic.
I disagree with any irony. I play drums and maths geometric patterns and even plain whole numbers, (not only fractions) are what describes some of the most beautiful structures in the known world and in and of the cosmos. So why do some people cling to the idea that numbers are some how separate from emotional connection? I think this type of thinking derives in origin from a Pop culture trope that seems to suggest that science and math or logic are somehow inferior to poetry or art but that's just silly and any artist of basic technical ability would laugh because without math painters could not accurately show depth or vanishing point or even represent light and shadow interplay on any imagined curved surface...so why again is it strange that numbers are involved in provoking emotional engagement?
Not only music but sound itself is completely full of mathematically described parameters. And not only temporal frequency vibration cycles and amplitudes but timbre and rhythms are made of numbers. Light shines just as sound vibrates. So if light shines on something that triggers emotions, is not that light integral to the experience of the perception? And is not light simply a unit of energy packed into an occillation of magnetism taking place where math is needed to figure out relativistic time units related to mass/acceleration and involves both gravity energy mass time and space and aren't these things inherently of an emotional nature when perceived by human consciousness?
@@subfragment I don't disagree with what you are saying. But there is feeling and then there is "feeling." Meaning, the sound AND feel of say the song "Holy Wars" by Megadeth is VERY, VERY different primal feeling... it conjures things inside of the listener... assuming the listener understands the message of metal. Take a band like Muse and Radiohead. Muse, IMHO, is for those who cannot comprehend what is happening in Radiohead. Muse, to me sounds forced, mathematical, boring. The IRONY is, Radiohead is probably MORE methodical and MUCH more, for lack of a better word 'educated' in music theory. That's due to Jonny Greenwood's understanding of the feelings certain musical notes/structures/combinations conjure up. This is a very interesting and timeless conversation. At the end of the day... it’s alright, it’s music, and music only.
who told you that music is considered to project feelings?
I don't think you know what "ironic" means
205-edo gives exact quarter-comma mean tone temperament. 236-edo gives exact adaptive limit-5 just intonation.
Another good approximation to quarter-comma meantone is 143EDO, which is very slightly flat (while 205EDO is very slightly sharp). The Xenharmonic Wiki has this information but doesn't make it easy to find (you have to know the EDO number to go to or find it in a table of approximations of a key interval). I haven't found any EDO between 31EDO and 143EDO that provides a better approximation of quarter-comma meantone than 31EDO. (I am almost tempted to make an interval approximation EDO finder spreadsheet.)
The Xen-Calc web app that the Xenharmonic Wiki links to from pages for intervals actually revealed that before you get all the way to 143EDO, 112EDO very closely approximates quarter-comma meantone. Unfortunately, Xen-Calc quits showing closely approximating EDO values after 120, so I can't absolutely swear that another one doesn't occur in between. Unfortunately, although Xen-Calc will show statistics for higher EDO values (like 143EDO and even 205EDO), it doesn't seem to let you systematically search those beyond 120EDO for approximations to specified intervals (I even tried manually typing the values into the "hiEDO field in the URL, but entering anything >120 actually results in setting the high limit to 6). Both 112EDO and 143EDO are fractional cents flat of quarter-comma meantone, and 205EDO is almost spot-on, just very slightly sharp of it, compared to 31EDO, which is still in the fractional cent range but enough sharp to count more like 20/83-comma meantone.
EDO approximations of 1/4 comma meantone with decreasing absolute error: 0, 1, 2, 5, 7, 12, 19, 31, 112, 143, 174, 205, 584, 789
EDO approximations of 1/4 comma meantone with decreasing relative error: 1, 2, 5, 7, 12, 19, 31, 174, 205, 789, 2572, 3361, 9294, 12655
no they don't
5:01and then he Whips Out 17-tone!
>:3
What software/plugin can I use to generate these precise intervals? I’d like to be able to run it with Logic Pro X.
Scales were generated using Scale Workshop and imported to Bitwig as .scl files.
@@lumi-musictheory3476 that sounds complicated. But I bet I can figure it out.
@@johnnyroman3888 Tha last time I checked Logic Pro X could only do detunings of 12edo, but that was years ago.
oddsounds mts
@@lumi-musictheory3476 I was able to do it using softsynths from Garritan as a 3rd party instrument. Garritan supports scl. files.
Clearly a lot of work has gone into this video, but the round diagram is not clear. What do the black marks mean? I really wish I could understand but it's just too fast and I'm not embarrassed to say I'm lost.
I watched it again and I see that the black ticks are supposed to be the black notes (sharps/flats) but why so small compared to the white notes? It brings an unhelpful distortion to the graph.
@@julianpinn5018 its a piano
It’s a piano keyboard wrapped into a circle
5:20 brooo magnolia part 2 🔥
I'm not sure the white and black notes thing is the best visualisation... its a bit unclear what I'm meant to understand when I see black keys flying over a bunch of white keys to form a new scale.
After all, the black keys on the piano are only an artefact of 12TET, in particular an artefact of the 12TET major scale - considering notes of other xenharmonic scales to be "black keys" seems totally redundant
Awesome :)
why did that c and f# sound harmonious to me
2:12 DORAEMON ALERT
FDTG';L
DHFJTY';L
FKU'
;KJ'
GJYH
Did you reference The IT Crowd when you said "sweet consonants"?
Anyone wanna recommend me some fun interactive games or tools to play with microtones? (I do not have a keyboard)
Not Making Sense of Microtones by Stacking Fifths
Are there theories on composition using non 12tet tunings?
At 3:00: no it doesn't. Generating with fifths at 3/2 12 times does not return to the original but to 1.0136432647705078125 times the original.
You only had to watch the video for 51 more seconds
gonna be honest I understood none of this
mannfishh anyone?
Are you synesthetic? You mentioned an ‘orange’ note.
I am not. Which timestamp was this?
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Whaaaaaaaaaaa
7:59
💘💘❤❤💕💕
Hi! How do I contact you in a way that isn't ridden with fucking cancer these days? I ran into you while listening to a *cough* streamer *cough* and I absolutely have to talk to you about these things, thinking of music in circles and algorithms I think I discovered what you did but I'm way earlier in my journey please can we talk
Just let me know your contact details and I'll get in touch. You can drop them in a SoundCloud private message if you like: soundcloud.com/frostburn
i am not a music lover
Super video man I wanna connect with you personally can we connect on any social media platform?
I'm on Facebook as "Lumi Pakkanen" or in Discord as frostburn#8033. You can also send me message in SoundCloud: soundcloud.com/frostburn