1200-TET: The Ultimate Tone Cluster?
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- เผยแพร่เมื่อ 13 ต.ค. 2024
- An attempt to cram 1,200 notes into a single octave.
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Classical Nerd is a weekly video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
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If any kind soul knows of a way to combine 1,200 notes _without_ peaking, please let me know. What I did for this video wasn’t exactly my computer’s idea of a good time.
Not sure if it's still relevant, but you can make a small part of it and combine it into one audio file then combine multiple small parts into bigger parts and continue like that until you're done. With combined parts like that it should be easier to control volume, so you might be able to avoid peaking too. (Or just use limiter if you're lazy like me :B)
Probably very tedious process, but I think it's doable. At least that's what I would do
you don't get more girth at a certain point due to phase cancellation, even if you trigger whatever waveform you're using incrementially at different points of their phase for each voice. physics n a ll that u know. *shrug*. nice idea though, thanls for sharing.
Only thing I can think of is to go someplace like a Best Buy where they may have a bunch of display speakers set up for demos and see if you can split up the various notes between them and see what happens.
Easily, bounce midi to audio at the level where your CPU is maxed. Then repeat the process with the remaining notes, and play both clips at the same time. In Ableton, you can get this 1200 note cluster quite easily.
Pieter Suurmond did some work on this in 2002, coining 'nanotonality' and creating much open source code. I have not explored closely but have enjoyed the uncompressed compositions. ecomaan.nl/music/nano13/
80 TET = broken piano
120 TET = space cannon firing
1200 TET = whale noise
I have found such a way to produce the 1200-TET tone cluster without your computer frying, as well as the Infinity-TET tone cluster.
So what you are doing here is basically just combining the sound waves of all of the tones. In the examples you used, it appears you are using a pure sine wave, producing them all, and then raw adding them together, which results in the clipping. Let's use some math to just directly calculate what the sound wave should be, then just directly produce that wave.
Suppose for a given starting frequency, we have the sine wave sin(ft). Now we can find the sine waves for any other tone we want. For instance, an octave above would be double the frequency, or sin(2ft). We know that in n-TET, the next tone up would be sin(2^(1/n) ft). (In 12-TET, a half step up would give us sin(2^(1/12) ft).)
Therefore, to create the tone cluster, we simply add all of the sine waves within the octave:
sum of sin(2^(k/n) ft) for k = 0 through n (this includes the starting note and the note an octave above it)
However, directly adding all of these causes the clipping, so multiply everything by 1/(n+1) to normalize (there are n+1 notes because the starting note and its octave are included).
All you have to do is compute this wave mathematically by selecting your n and sampling the function to the resolution you want, then export it to a WAV file.
Mathematically, this also gives a way to produce the octave-wide Infinity-TET tone cluster, which is a close enough approximation to any k-TET tone cluster as k becomes very high, such as with your k=1200. Take the same sum we found earlier but just set the limit as n goes to infinity:
(we remove the note exactly an octave above both to make the math simpler and also because it doesn't matter)
limit as n goes to infinity [ 1/n sum of sin(2^(k/n) ft) for k = 0 through n-1 ]
This looks like a frightening limit/sum to evaluate, but a very simple trick turns it into something very simple: Consider that this limit is merely the Riemann sum of the integral of sin(2^x ft) dt from 0 to 1! Evaluating this integral gives us the final result of:
(Si(2ft) - Si(ft)) / ln 2
where Si is the sine integral function.
www.wolframalpha.com/input?i=%28Si%282x%29+-+Si%28x%29%29%2Fln+2
Applying these methods in a script will allow even a potato PC to produce the Infinity-TET tone cluster in a few milliseconds, faster than producing even the 1200-TET tone cluster.
You will notice that the shape of this waveform will be very similar to the 1200-TET tone cluster waveform you produced. Interestingly, this waveform goes on forever, never repeating, so this cannot be a singular timbre, it can only be played as its own sound. There is an interesting explanation for this. Remember the beating that happens when two sounds are very close in pitch? Well the closer they are in pitch, the slower the beating. The slower the beating, the longer it takes for the beating sound to "cycle" and repeat. Because you have infinitely many pitches that are infinitely close to each other, the repeating cycle will be "infinitely long", or in other words, never repeating.
This explains why such a specifically constructed tone cluster does not produce white noise (which is randomly generated) and why you get the gliss effect some people commented on.
The math behind this can be even more fascinating. Perhaps I'll make a video on it someday on my own channel.
It's such a crime that you have so low amount of subscribers... Keep up with the good work.
The 80-, 120-, and 1200-note may sound equally “thick,” but they sound meaningfully different. There is a gliss effect in the last cluster different from the one before it. We may not be able to identify a 1-cent difference or count the number of notes but 1200-note cluster is still totally cool and worth it.
I need a 1000000-TET cluster.
@Erik Salazar it would be pink noise instead
white noise = same energy per Hz. Pink same energy per octave/halftone/cents
You'll like this album: xenharmonicgod.bandcamp.com/album/-
@@nowandxenpodcast What's that? Is that heaven?
Sort of lol
I definitely heard substantial differences in timbre between the 80-edo, the 120-edo, and the 1200-edo. The 120-edo sounded the most discordant to me.
Eyyyy Stephen Weigel, fancy seeing you here
Bragtime Ayyyyyyyy
Yes. After listening to clusters for a long time, there is a huge difference in those three chords.
1200 tone cluster at 5:01
thanks
t h i c c
I was once in an 81-member choir and I swear I heard some 81-note tone clusters.
Isn't it, that your cluster tends to white noise? As far as I know white noise is a mix of all frequencies in a spectrum (here, one octave), and, while you don't mix "all" frequencies (which isn't practically possible anyways), you mix quite a bunch of them. And the more tones you add, the smaller the distances get between them, and the more the cluster sounds white noisy. I guess.
more of a pink noise, since his octave wasnt really low, right?
im so fuckign high man
Enjoy listening to you but this is soooooo way over my head...surprise? You continue to amaze me.
Funny thing that when he played he played the undecimal comma in sequence, I couldn't tell the difference between , but as soon as he played simultaneously, I could imediately tell they were not the same note.
4:53 omg that was creepy
I'm watching this at night in a dark room alone and I immediately experienced a strong urge TO LOOK BACK at that moment
The "creepy-microtonal-string-cluster" is something that can be found in many a horror film, so I'm not surprised! There's a strong uneasiness about that particular sound.
i'm watching in similar conditions but i didn't have any such reaction to the clusters. the bloody alien at the end though.
If the idea of splitting tones into ever-smaller intervals appeals to you, Mexican composer Juan Carrillo used to make some haunting stuff under the concept of the “Sonido 13”
3:32 That 10 note cluster sounds gorgeous. Like a horn or a pipe organ with a bunch of stops pulled.
Instead of sounding more think it sounds like clusters being ran though a filter of some kind
I'm really not sure how much of that has to do with the phase cancellation between pitches of close proximity and how much has to do with the fact that I was finagling my software for the better part of a day to make it happen.
what software are you using?
For this particular video, I used a combination of MuseScore for the actual detuning of notes, then splicing the resulting waveform in Logic and Final Cut.
@@ClassicalNerd I know this is old but zynaddsubfx.sourceforge.net/ has better microtonal stuff
The 80, 120, and 1200 note clusters definitely sounded different. The 80 note cluster sounded like a great clashing of many notes. The 120 note cluster sounded like thunder. And the 1200 note cluster didn't sound thicker (in fact less), but it sounded like a muted explosion under water.
I want infinitesimal interval cluster
Just a tip on how you could maybe improve this video; after you've done all the work to get these clusters, it would be cool to hear them consecutively at the end. It would have a been a nice conclusion :)
As far as hearing a difference between the clusters go; I feel like I definitely can hear that there is more going on. I think it's possibly that our brain expects to hear a chord so maybe groups the tones we do hear in the clusters. So maybe we perceive all of the notes around every scale degree we're familiar with and that's why when there's a larger cluster, it sounds more wobbly/thicc.
(I don't have perfect pitch, but I do listen to a lot of microtonal music so I feel like I pick up on the small changes a lot better than I would have before.)
yeah 120 vs 80 was definitely an increase in dissonance, but 1200 did indeed have a different character
Yeah its also the same in Rock in double tracking guitar music where you have chorused left and right channel guitar tracks. The reason why you double track it and not just copy one track and paste and pan it to the other side is because of these subtle tonal and rhythmic differences that make it sound much much richer and fuller. Good examples would be like say your typical Boston song with left and right channel guitars that are playing the same thing. It’s actually two separate performances where the player plays the exact same thing twice and its recorded twice. And because of the very slight tonal and rhythmic fluctuations between the two it adds a lot of depth and feeling that you don’t get with just copying a single performance and pasting and panning it to the other side. On the subject of the 1200 note cluster there are two prohibitive issues at play here…1st is the limitations of your computer and software, which it’s doubtful that it can actually play all those notes simultaneously without dropping a lot of them. 2nd issue is comb filtering, where wave cancellation between out of phase frequencies will cancel out some pitches while amplifying others. So you will not get an even dissonant chord with every note sounding perfectly. It’s just physically impossible due to the way physics works especially if you are playing all of those notes on a single virtual instrument with the same tonal characteristics. One way around this would be to do this live with a full orchestra and other instruments thrown in. That would help, but you still wouldn’t be able to realize all of the pitches and make them sound equally due to phase cancellation and comb filtering issues.
We did things like this using CSound back in the day. It was rather easy.
The 120 tet is like a flanger. There is a lot of waves cancellation going on! Also if the 1200 notes are sine waves we can listen a filter white noise ? That’s crazy, and we can use the volume of each note to shape and create an instrument timbre like synths can make and create the same note of the piano to start over 🤯
Pink noise is the ultimate tone cluster
3:08 it just sounds like a honky tonk piano preset
Now we need one that spans the entire range of the keyboard
What I find funny about this whole exercise is you’re essentially calculating an integral. As you choose finer and finer divisions between notes, you better and better approximate what the whole octave sounds like. There’s probably some integral equation that allows you to calculate what such a wave would look and sound like in the limiting case, but given our brains can’t tell the difference between super fine tones anyways, it’s more of an academic pursuit to find it. The version you showed off is probably good enough for our ears.
Eric Whitacre is probably foaming at the mouth reading the title: The Ultimate Chord Cluster?
undecimal comma c together with c is like a honky tonk piano note
I could hear the non-unison aspect in the first example and I could hear the difference between all of the different clusters, except, possibly, for the 1200 10 note. One problem with this debate is that the brain can only experience one thing at a time. We process information serially. So, your argument that it's vibrato rather than a simultaneous experience (a chord), is a bit moot. I think it's clearer to say that we can perceive that it's more than one tone being played at the same time, even if we can't truly experience both of them (or more than one) at exactly the same time.
I'm not saying that two very slightly detuned pitches is vibrato. Rather, the physics behind it are somewhat similar, as you're intentionally detuning pitches by a slight amount to provide a general sense of warmth to a given sound.
Can you make a 1200< x tet like 1201 tet?
Just asking 😅
Fascinating. I have a couple of soprano singing bowls and they are so close that it is difficult to rank them as which one is higher and which one is lower!
Awesome video btw. I only wish the audio examples were longer so we could feel the taste of it better.
Also, I'm wondering now: could there be a human being of some alien (to us westerners) culture who experiences the minor second as a kind of wobbly unison?
I would doubt that, only because the way humans perceive tone is universal. This all goes back to the JND. The differences of scales between cultures doesn't have to do with how the people of said cultures perceive dissonances.
Now, there are many cultures in which the minor second as we know it doesn't exist. To those ears, there's still a perception of dissonance, but it's more similar to how we might hear a subminor second.
Hmm it sounds like there is a point where dissonance ends and 'vibrato' begins, where very interesting overtones start happening that actually sound pleasant, and perhaps this level is what constitutes timbre. I would love to know exactly at what interval that starts happening, because a tuning system based on that interval would probably be very good!
I can hear the 16 cent difference
he kinda overhyped the smallness of the interval to be fair. an average person can discern as low as 5 cents a difference.
Călin Guga Indeed. I’ve learned more since then abt pitches and stuff
A good ear can hear nearly all of the impurities of 12-tet compared side by side the pure just tone, certainly below 2 cents.
Could you do Xenakis? I always see his grinning face in your "great composers" intro, and I'd love to learn more about him than what I've gleaned from his Wikipedia article.
I'm looking forward to tackling Xenakis and it has been appended to the request queue [viewable here: lentovivace.com/requestqueue.html ]. The length of the queue equates to a release date in late March.
Teddy Pena yes a video would be interesting. People tend to overemphasize "maths" (in reality are shapes) in his music (which is mainly concerned with his early music) rather than the extremely personal and expressive nature of his work. Some people who hate his music would faint seeing him talk, he's such a lovely human :)
Use 53
Well it is relative with refrance to the formulation of the notes, if one could formulate the distinction of complication and simplicity in an understandable enough way perhaps we would produce a more vivid musical landscape?
Actually, when you played them toghether I was able to tell them more apart. And when you played the 3 note cluster is definitely did NOT sound like a unison. I don't know if it is because I have to tune a lute all day long, and the unison strings are hellishly annoying to get to sound as one.
0:05 could be a new illusion
Maybe thats the sound of the universe. lol.
I could easily hear the difference in the first example
what if in the future humans could augment our brains with technology to be able to perceive these microtonal differences with more precision, & then enjoy crazy micro-micro tonal compositions
1200-edo meta
I wonder how thicker it would sound on different pannings
Like you said in the real world every note is a little bit different causing the unison effect. But in your examples you used the same sample for every note. I think it would sound pretty radically different if the starting phase of every note was random. A lot of synthesizers let you do that you don't get that wet phasey tone but a more stable thicker tone.
But with that comes the trouble of finding a synth with 1200 voices...
Click bait, yes. But 12 tet is not at the threshold of JND for most people, but yes the difference between in tune and out of tune (unison and dissonance) blur around 48-tet give or take a half or double. However, even in 12-tet, we rarely use 12 tones, but rather usually 8. Anyway 19-tet is certainly reasonable and 22- or 24-tet are justifiable. 72- or 80-tet, maybe not.
I kind of object to this being called click bait, which are misrepresentative or otherwise exaggerated titles-one that's designed just to be engaging, in my view, really doesn't count.
@@ClassicalNerd agreed. My clickbait comment was only in reference to your own comment in the video. Sure, you did actually mention and try to reproduce 1200-tet. It's debatable whether it's exaggerated. Any way... That wasn't the thrust of my comment... Which I'll elaborate below:
29-tet and 53-tet more purely reproduce the important pure intervals fifths, thirds, and plenty more. While most ears won't discern a D quarter flat from a C## in 53-tet, that's not really the advantage of more abundant tonal temperaments. We might still only use 8 or a few dozen notes in a key, but we have more colourful options, enormously more progressions, and smoother transpositions. I could f.ex. imagine AI coming up with fugues in 53-tet (or 420- or 1200-tet) using existing music theory that might have brought JS Bach to tears. I also expect we'll come up with new theories, particularly if/when we collectively become more accustomed to deeper tonal spectra.
I recently heard a melodic piece with (if I remember) a scale of 17 notes of 31 equal tempered tones in an octave. That's roughly double 12-tet with a bunch of quater-tones and it sounded quite pleasant. Also a 53-tet "classical" piece littered with melodic augmented and diminished transitions that were purely harmonic, no hint of dissonance whatsoever. The scale is called something like "Eagle 53".
So, while we'll probably never enjoy a scale of more than thirty notes at a time, I do believe there's huge unexplored territory in mega-tet, mega-modes and transposition, perhaps even beyond 1200-tet.
1200-TET is more of a thought experiment than anything else. I really doubt that anything beyond 72-TET has any particular musical use given the average JND-although I would suspect that orchestral musicians would be able to hear smaller intervals due to having to tune to A440. Exploring bigger temperaments gets you some cool effects if you extract certain notes (which in effect gives you a small, unequally-tempered scale, which Sevish uses in some of his music). And, of course, the Bohlen-Pierce scale disregards the octave altogether in a really neat way.
Sounds way different to me
145200 notes in 1200tet is white noise (C0 to C10)
Does the first example really sound like one note in unison to people?
16⅔¢ approaches the average just-noticible-difference threshold, so it will sound like a warbling, out-of-tune unison to some, but two discrete pitches to those with above-average ears (either through birth or training).
get white noise with 144,000 notes from C0 to B9
I'm just spittin' thoughts, but I can't help but feel like these examples aren't being reproduced as faithfully as they would "organically" or "in the wild". If CPU weren't an issue, would these sound different? If they were played on an acoustic piano tuned according to each TET, for instance, would we hear more fullness and volume of what's played?
I'm not sure you would due to the phenomenon of phase cancellation. It would be interesting to have 100 pianos in the same spot to try it out, though ...
You can just play white noise. That's as thick as it gets.
what would the note look like
I could tell every single tone apart. As a violinist I need to know when things are off between two players, so everything sounded weird to me.
That being said, fascinating video.
Does anyone know what software he might have used to do those demonstrations?
If Bill Evans and Rohan cagahu was one person
They all sounded different from one another
do it in multiple octaves white noise
Is it just me or did i notice the difference in them all?
How do you play A 34/64 flat on a trumpet
Anything is possible if you believe in yourself
woah
The video stops working at @2:07
How many cents are there per hert?
So ... not all cents are created equal. Probably a good subject for a video now that you mention it, but I'll take a stab at it here:
If you have a tone of _x_ hertz, then there are _x_ cycles per second. It's a literal measurement of how many waves are moving through the air. This also means that, for a tone of _x_ hertz, one octave up would be _2x._ Every octave, the hertz doubles.
All of this means that the higher the pitch, the greater the distance between two given pitches in hertz.
_Cents_ are more about fine-tuning than absolute pitch. Unlike hertz, the cent distance between two given notes will always be the same.
The cent system treats pitch as we perceive it; i.e. endlessly rising. Hertz treats it scientifically and thus a little less intuitively because we're just flat-out not used to logarithms.
Fascinating stuff man thanks for the answer. I ask because I was writing music earlier this year using sine waves with some similar approaches to what you discuss in this video. Extreme microtonallity and clustered harmony . (not to mention the beatones between 2 frequencies helps give sine music some sense of pulse)
P.s yes it is a good video idea and I'd love to see you make it in the future.
Does the system of cents have a zero-point? It would probably be easier to use for some if it had a value of zero somewhere. This though would fix the scales made with cents to a certain frequency. Infrasound A or the middle A? How would the log fuction cross the middle a? Umm. 3,4375 Hz (infra-A) or maybe use lowest midi freq for this?
cents are a logarithmic scale, hertz are linear, so it doesn't make sense to talk about cents per hertz
sounds like chorus
5:02
5:03
VGOOOOOOM
You speak similarly to how Glenn Gould speaks
Yeah, I use scripts just like he did
@@ClassicalNerd interesting!
duocentitones right?
A tone is just, like a half step, just wearing fancy clothes.
t h I c c
sounds phasey to me. we need better software.. or something
Did I destroy your computer? Go to this comment
Bro, just listen to distorted instruments, some prog metal. The whole point of distortion is to get a thicker sound.
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