What an absolutely amazing presentation of a complex topic. Never considered that overtones don't necessarily have to be integer multiples of the base note, or that we can replace the octave with a slightly longer or shorter interval for tuning... Fascinating. The exploration of dissonance curves is also very interesting. I'm now absolutely itching to try removing dissonance from non-12-TETs using this introduction of inharmonicity. Really, huge thanks for making this video.
I had no idea that equal temperament was not harmonically perfect, the way you showed it with the green and yellow lines totally blew my mind. I'm just a casual musician so my understanding of music theory is far from academic. This is incredibly helpful
Easily one of the most informative youtube videos I’ve ever watched (3 times now lol). I hope you keep making videos! Even though the audience is a bit niche for this kind of video, the people who are watching find a great deal of educational value in your content
Thank you! I am very happy that it is helpful. I do not want to abandon the channel and I have many ideas on what to do next. One video is filmed and needs editing and the editing takes a lot of time, but hopefully I will release it in April. I probably need to change the format to have more frequent updates, will think something up.
Thank you for this video! I was searching for some explanations of xen ideas I've found through Sethares, and your video was quite clear and objective for the matter! I hope you can continue making such great and well crafted content 🌳
Thank You! Happy that it was helpful. Was struggling to carve out some time for new videos, but there are topics I want to explore outside of Sethares framework that should accompany it quite well, such as harmonicity, subharmonic modulations and history of tuning. Should be interesting)
Ive been toying with the beating and with the harmonics of the low piano strings and this video answered all of that I was doing. By far the best video to date that I have seen on music. This video is THE foundation on which any serious music explorer should base their understanding on. Also you can attach silly puddy to nodes on the piano strings to achieve deisred harmonics and pair that with the middle (sostenuto pedal) for further control of sympathetic resonance. Thanks for all your work dude!
I must say that I've watched plenty of videos regarding similar topics, searched the reliable information in books and was trying to keep up with the latest studies and I trurly find your work like one of the most precise, legible and substentive trials of synthesising such a complex issue. I admire it much & your studies gave me the whole new perspective on many aspects
Good video! Microtonality is a topic I’ve studied since 1977, and I agree that the relationships between tuning and timbre are indeed all-too-often ignored. In case you’re not familiar with it, I strongly recommend Bill Sethares’ book on exactly this topic, entitled Tuning, Timbre, Spectrum, Scale (Springer Verlag). This book starts out with a similar, stretched-octave illustration. Not super-important, but for the record: 1:25 - A minor 6th above a C is an Ab rather than G#. Similarly, a minor third is Eb rather than D#. G# is an augmented 5th, and D# is an augmented 2nd. In Microtonal tunings, pitches that are enharmonic equivalents in ordinary 12TET typically are _not enharmonic_ , so it’s not just pedantic.
Only thing I have to add to this is that it's free to read on the author's website - otherwise quite expensive. Edit: saw that that book is linked in the sources, too - great!
This is fantastic!!! I have thought and theorized about artificially moving the harmonic series of synths, but have been too dumb to actually make it happen. It's wonderful to see people who know what they are doing. There is so much to learn. Thank you for these very high quality videos, this is important stuff!!
Very great video and production ! i don't usually post comments but this deserves a lot more views ! Also the Gamelan music tuning system make a lot more sens to me now considering all the inharmonicity parameters.
thanks! Nice video, I like what Im learning ironically just got the pdf for "Tuning, Timbre, Spectrum, Scale" by W. Sethares , as this is currently what im trying to go direction was in college! the way we engage with sound and perception generally. thank you again.
this was genuinely a profoundly illuminating video. this has began to actually answer so many of the questions that i have had for such a long time. thank you so much.
This answered questions I've had in exactly the ways I suspected, especially regarding bell/metal sounds etc., awesome stuff! I've had some strange frequency shifter experiments sound way more cohesive than I was expecting, as long as I was careful with my timbre and used a narrow stretch of notes. Even with pure sines, you notice how much more consonant an octave is than anything near it, it's so cool how enharmonicity can change that. Simplifying quite a bit, it's like how playing a major scale is more dissonant than a diminished one... over a diminished chord, really simply. It was maybe 2 years ago now that I started to notice something a bit off in TONS of music, it was that 5th harmonic on a fat bass under something like a minor chord that first started to commonly stand out. You notice it a ton when people distort low power chords too, I've also noticed enharmonic overtones on epianos, fm synths and low piano notes etc. etc. etc. just sounding off for the longest time. it's really strange to me how most people just wing this without really knowing what's going on, I felt lost with it for the longest time, especially when trying to get more creative with sound design, which is still tricky and limiting. I really wonder how many others struggle with this and how they deal with it, whether they know what's going on or not. A dream of mine is Harmor 2 btw., taking everything to the next level with several more approaches to programming the overtones according to tunings (And tuning support, obviously), doubling up on the phaser, simulating a sort of pseudo-distortion, flanger and chorus baked into the routing rather than being post-fx, nore versatile and clean resynthesis that let's you clean up the spectral image in the box. Lowering that 5th harmonic to be minor is an amazing sound btw., works SO well for retro planed chord house and jungle etc., working with other tunings amps up how it sounds kinda ''off''. It's nothing crazy like a bell that comes with a bunch more weirdness, so it's very easy to be musical with. It's great cause you may want a deep and warm character, it's really easy to get muddy or even run into the lower interval limit, but this is one way to get more clear harmonic info down there.
That is so true, finally people start to re-realize this fundamental fact about tuning and normal modes…So simple yet modern music theory systems give no attention to for hundreds of years.
Good video. It deserves more play than RUclips has been giving it, so I linked it from the description of my only popular video -- which isn't all that popular, but hopefully anything is better than nothing.
Oh my god you are so cool I love this SO MUCH!!! I'm still a noobie in microtonality, as I haven't figured out how to make digital microtonal instruments yet. I've been bingewatching content about microtonality tho, and if your other videos are like this, your channel is extremely bingeworthy. My jaw literally started cramping because my mouth was agape for so long! OMG I love you and what you make.
Привет! I may be 2 years late to this but this video was super interesting. Just like you said, seen tons videos on temperment and tuning systems but nothing touched anything you covered here. You also confirmed a suspicion I had about the low notes on the piano sounding slightly dissonant... I just assumed it wasn't properly tuned. The spectrogram visualisations were very helpful to understand the concepts you are presenting, all around well crafted video. Also side note, you may know this by now but we don't actually pronounce the b in "subtle" for some reason.
Nice video. I would have loved if you played in equal temperament with equal tempered spectrum, i.e. 2:1 octave, 2^(1/12) semitone and corrected spectrum to fit equal temperament as well. Keep it up!
I picked up on that point you made about the partials of individual notes in polyphonic music lining up on the spectrogram, and wondered, what if instead of creating a stretched timbre and playing with a stretched scale, you simply compose in regular 12-TET and a regular harmonic sound (like piano or synth), and then stretch the whole kaboodle, pitches and timbres, by running the whole thing through something like a frequency shifter or a spectral stretching plugin. I've also tended to find that detuning individual instruments, especially electronic ones, against eachother can bring a whole arrangement to life, such that notes and harmonies beat off of eachother in a manner similar to the chorus effect, but across the whole stereo mix space. EDIT: Also, subbed!
I'm really enjoying your videos, and learning a lot. Thank you! One thing that's still a mystery to me is how my brain is able to receive two separate square waves of different frequencies one after another, each with a completely different (though related) spectrum, and based on the partials from the cochlea, say to itself, "ah yes, those both sound like square waves". Brains are incredible!
That is a topic for another video that I was making but had to scrap it and do more research)) But my impression from reading literature is that it is evolutionary beneficial to be able to discern harmonic sounds from environment, as human and animal voices are harmonic. So we have a pattern matching neural network just for that purpose. That is why we can also tell harmonic sounds from inharmonic and inharmonic sounds can sound dissonant just by themselves. So how close the sound is to harmonic spectrum is another dimension of consonance / dissonance to play with.
Many thanks for an amazing video with quite interesting content. May I ask a few questions: - what kind of mathematical approximation did you use for the sensory dissonance as a function of ratio between two sinusoidal signals? - when you produce the sensory disonance of two tones with 6 partials each, what metric do you use to you combine their contributions? - given these two tones with their partials how do you select the pairs to consider?
Formula for a dissonance between a pair of partials: d = min(L1, L2) * ( exp(-3.5 * s * (f2 - f1)) - exp(-5.75 * s * (f2 - f1)) ) where d - dissonance, L1 and L2 - loudnesses of partials 1 and 2, f1 and f2 frequencies of partials in Hz, s = 0.24 / (0.021 * f1 + 19). And to convert amplitude to loudness I used a formula 0.25 * 2 ** log10(2*(10**8) * amplitude). To find dissonance of 2 notes with complex spectrum I do the following: 1) I combine partials of 2 notes into single spectrum of 12 partials. 2) iterate over all pairs of partials to find their dissonance using the formula. Note that I didn't include "opposite" pairs, i.e. if I have a pair partial1 - partial2, I do not include pair partial2 - partial1. 3) sum up all those dissonances Iterated this process for every cent in an octave to get dissonance curve that is then normalized so it's maximum value is equal to 1.
Fantastic video, thank you very much, I learned a lot! Quick question: I’d like to plot chords and scales against the sensory dissonance diagrams you show around the 17:41 mark. Is there a place I could find those with numerical values? Also, when compared with the graph at 01:47, why I am not seeing a peak around the tritone area? I would expect one that would reach higher than that of the major second, don’t you think? And again, thank you so much, awesome content!
Hi! I'm very glad that you liked it! I uploaded data as .txt files for dissonance curves for Harmonic spectrum with different number of partials, drive.google.com/drive/u/2/folders/1Pxa73JSmhpFod5Qof8Z7G4PxLeh9In6w There you can see that additional partials create additional dips in dissonance curve. With 7 partials the dip on triton occurs! So according to this theory, tritone it is kind of consonant! I think that happens because classical simple ratio approach to explain dissonance is just not really fully correct. It is just an observation rather than finished theory. Also we are used to think that tritone is very dissonant but actually it isn't, it can sound quite smooth even dreamy and mystical. Lydian mode for example does have sharp fourth and it is the brightest of all modes. Late romantic composers use triton all over the place, it is also very common in blues and it sounds great.
@Objective Harmony Thanks a lot for the files! Yes, I did notice the dip, pretty surprising I must say. I was a little skeptical at first about tritone intervals feeling dreamy, but after experimenting a little, I have to admit that my perspective has changed. Cheers to you for broadening my horizons! On a side note, “Farewell” is a phenomenal track!
( trying to not use all-caps ) this is actually quite mind blowing because i thought that it's strictly simple intervals, This is kinda like non-euclidean music :0 except it's now non-... pythagorean??? lol :3
well thank you _so_ much. I think this is the first “music theory” video I've encountered that seems to actually talk about the theory of music rather than some culture-specific mumbo-jumbo. I'm also thankful for the explanation of why pianos sound so bad to me (and, I think, why Balinese gamelan sounds so good). I _think_ it's also a good sign that this one takes more than a single viewing to take in. ;) Thanks again.
Would have loved to hear the difference between stretched octave vs harmonic octave on stretched partials, with timbres with more rapidly descending amplitude of partials compared to fundamental
Great. Octavas on piano are not just, there are bigger than the theoretical one, because of the piano's inharmonicity and equal temperament. With violins, cellos etc, it's different. Furthermore, octavas on piano are not equal, they are bigger the higher the pitch, so do all other intervals (major 3rd etc)
Well, the only way the timbre of an instrument can align perfectly to the harmonic series is to generate them digitally. So synthesizers shouldn’t have this problem. That being said having such perfect alignment makes the timbre sound artificial. The inharmonicities of physical instruments are what makes them sound natural :P
@@adiaphoros6842 That's not true, there are many instruments without inharmonicity such as violin, viola, cello, flutes, etc actually most of them are "correct". For the naturalness in piano, it's actually not the inharmonicity but the overlap of several almost tuned chords, eg., A,A+1%,A-1%. The longuer pianos have less inharmonicity, hence are easier to tune and still have this almost tuned chords, a bit like many violins with vibrato playing together; and they sounds better and not less natural.
Check out dynamictonality.com, I stumbled upon them recently but didn’t have time to play with them myself. Seems like Sethares ideas in vst form, so should be super useful
@@new_tonality No problem. I would recommend you checking a bit from that composer, he used similar stuff. Maybe his Gesang der Junglinge is worth checking it.
1:40 I would recommend using something else than red and green for data visualisation, a good portion of the population has color vision problems with this exact pair. Purple and yellow are a pretty safe pair.
18:43 I have a quick question about this part... how did you choose the partials for the 12TET spectrum? It looks like there's a lot of complicated stuff going on with the frequencies and amplitudes here... did you use some kind of optimisation code? Only I'm trying to write exactly that at the moment, but I'm struggling a little to get it right!
I didn't actually reconstruct spectrum from tuning. Sethares has a chapter on how to do that in his book, but I haven't read deeply into it. To get a spectrum for 12TET I use a formula from Sethares book that look like this partial_frequency = fundamental_frequency * 2 ** (Math.round(Math.log2(partial_index) * 12) / 12). Here 12 is number of steps in the octave for 12TET and 2 is the octave ratio (so increase it if you want to stretch the spectrum). From that formula you get a lot of partials that have the same frequency that have to be filtered out. That is because that rounding in the exponent collapses partials to the closest note of 12TET. So all partials are actual notes from 12TET. Amplitudes I think where just 1 / partial_ratio_to_fundamental The spectrum on its own does not sound very good. Some partials are just dissonant (those are just notes from 12TET in the end of the day). But first 6 sounded good. So the way I generated the entire spectrum was: 1. generate 6 partials using the formula 2. copy spectrum and transpose it to the second partial of the original spectrum 3. repeat step 2 for third, fourth, ... partials 4. combine all 6 spectrums into one 5. filter out partials with the same frequency That's it, result sounded good so I went with it.
@@new_tonality Ah, I see - yes, that formula does make sense to me, and I also understand about the partials that end up on the same frequency. I've been working some more on my code and I think I've managed to get the original spectrum you mentioned, which you found was quite dissonant. I really like your idea of using six partials and copying the spectrum to each one, so I'm going to try that. I am writing code that will read random or specific files from the set of Scala files (over 4000) and make "chimes" out of them by generating a good spectrum first. I don't know yet how Sethares does it but the way I construct the spectrum from an arbitrary tuning is very much like the formula above, except I'm careful to round each partial to the nearest scale ratio in the tuning list - and to get the higher ones I have to also keep adding equaves (in case this is a non-octave scale). Pretty fiddly, but I think it's working sort of OK. I think your ideas will really help make it sound more pleasing to the ear, so thank you very much!
I would really like to listen to what 10:12 sounds like with harmonic (12 TET) tuning + stretched spectrum. Like what does it sound like when the dissonance is the note's 'fault'. Also, surely the harmonic spectrum is natural in the sense that a wave with period x also has periodicity of n*x for all integers n. I wonder what would happen with aperiodic (either time-changing frequency or something more subtle) notes.
Great video! I'm wondering how much of the math about the harmonics of the low piano strings is off because of the fact that the frequencies are calculated as integers instead of decimal numbers. There's much less integers between lower octaves than higher ones so therefore much less accuracy.
for example if that low frequency was 32.3, it would round down to 32, but doubled (64.6) would round up to 65. This would lead to the same deviation you show, without any actual octave stretching. Every octave higher would have half as much deviation as the last since there are twice as many integers and thus a finer grain.
Good point. The number for inharmonicity seemed a bit high, but the practice of octave stretching in piano is mainstream, ear can detect beating if octaves are perfect 2:1. So the inharmonicity is definitely there but more accurate FFT in the video would be better for sure.
This video is fantastic! Just one question, if we use this measure of dissonance, wouldn't it imply that, for example, f played against 7f would be perfectly consonant (since all overtones coincide) just as a unison or octave? Wouldn't this be a bit problematic with our understanding of consonance?
Not sure what you mean by 7f, but yes generally speaking it can be at odds with conventional understanding. One thing that I am not mentioning in this video is that we could say that inharmonic timbre by itself is more dissonant than harmonic. But than we can say that unison or octave can be dissonant)) which also has problem with conventional understanding. I think that because dissonance is such a complex phenomena I should in future use the word roughness instead, as it is much more specific and is only one of many parts comprising dissonance. You can use app that I develop to experiment with that yourself at newtonality.net/lab. Its in early stage, but I’ll post updates.
@@new_tonality so glad to hear! I’ve subscribed and enjoy your thoughtfully explained music theory videos. I hope you keep exploring more subjects in depth!
So if I have produced an FM sound in Serum that sounds very good but has dissonant harmonics, what can I do to fix them? I tried lowering/raising the octaves, semitones of the oscillator but it distorts the sound. Cutting annoying frequencies using the equalizer doesn't solve much and still denaturalizes the sound...
at 6:26, that interference frequency is 5 hz, not 10, cause it's half the difference between the frequencies, not the difference itself. have you also done any research on the effects of the higher interference frequency (which is halfway between the original frequencies), or do you think that's probably irrelevant to how we perceive harmony?
Yes you are right, thank you for correction! The research and results are done for the correct beating frequency so they should be valid. I just screwed up when making the video))
There is one more facet here: bass. A lot of intervals in bass cannot be played simultaneously as frequencies are very close to each other. With that in mind bass has its own rules (especially sub bass). Maybe a topic for another video?
Anyone knows synths and synth sound libraries that can be or are finetuned to work with each other? To point at the gamelan video, it seems you _do_ need a master tuner who can tune different instruments to work with these inharmonic, metallic sounds. It ain't no simple task, you can't just grab a couple of different gamelan samples and push some subbass under it, it seems.
Around the @16:30 mark you mention that the bandwidth of critical bands is larger in the low frequencies, and smaller in the high frequencies. I believe this is incorrect, the effect of which being that humans have increased* pitch perception in the low frequencies rather than in the high frequencies.
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What an absolutely amazing presentation of a complex topic. Never considered that overtones don't necessarily have to be integer multiples of the base note, or that we can replace the octave with a slightly longer or shorter interval for tuning... Fascinating. The exploration of dissonance curves is also very interesting. I'm now absolutely itching to try removing dissonance from non-12-TETs using this introduction of inharmonicity.
Really, huge thanks for making this video.
I had no idea that equal temperament was not harmonically perfect, the way you showed it with the green and yellow lines totally blew my mind. I'm just a casual musician so my understanding of music theory is far from academic. This is incredibly helpful
Easily one of the most informative youtube videos I’ve ever watched (3 times now lol). I hope you keep making videos! Even though the audience is a bit niche for this kind of video, the people who are watching find a great deal of educational value in your content
Thank you! I am very happy that it is helpful. I do not want to abandon the channel and I have many ideas on what to do next. One video is filmed and needs editing and the editing takes a lot of time, but hopefully I will release it in April. I probably need to change the format to have more frequent updates, will think something up.
Thank you for this video! I was searching for some explanations of xen ideas I've found through Sethares, and your video was quite clear and objective for the matter! I hope you can continue making such great and well crafted content 🌳
Thank You! Happy that it was helpful. Was struggling to carve out some time for new videos, but there are topics I want to explore outside of Sethares framework that should accompany it quite well, such as harmonicity, subharmonic modulations and history of tuning. Should be interesting)
Ive been toying with the beating and with the harmonics of the low piano strings and this video answered all of that I was doing. By far the best video to date that I have seen on music. This video is THE foundation on which any serious music explorer should base their understanding on. Also you can attach silly puddy to nodes on the piano strings to achieve deisred harmonics and pair that with the middle (sostenuto pedal) for further control of sympathetic resonance. Thanks for all your work dude!
I must say that I've watched plenty of videos regarding similar topics, searched the reliable information in books and was trying to keep up with the latest studies and I trurly find your work like one of the most precise, legible and substentive trials of synthesising such a complex issue. I admire it much & your studies gave me the whole new perspective on many aspects
Good video! Microtonality is a topic I’ve studied since 1977, and I agree that the relationships between tuning and timbre are indeed all-too-often ignored.
In case you’re not familiar with it, I strongly recommend Bill Sethares’ book on exactly this topic, entitled Tuning, Timbre, Spectrum, Scale (Springer Verlag).
This book starts out with a similar, stretched-octave illustration.
Not super-important, but for the record:
1:25 - A minor 6th above a C is an Ab rather than G#. Similarly, a minor third is Eb rather than D#. G# is an augmented 5th, and D# is an augmented 2nd.
In Microtonal tunings, pitches that are enharmonic equivalents in ordinary 12TET typically are _not enharmonic_ , so it’s not just pedantic.
Only thing I have to add to this is that it's free to read on the author's website - otherwise quite expensive. Edit: saw that that book is linked in the sources, too - great!
This video gave me goosebumps, made me laugh and then cry. I will remember this day as my inharmonic awakening
This is fantastic!!! I have thought and theorized about artificially moving the harmonic series of synths, but have been too dumb to actually make it happen. It's wonderful to see people who know what they are doing. There is so much to learn. Thank you for these very high quality videos, this is important stuff!!
Please continue! You're doing an amazing work! Thanks for this and the other vídeos from your channel
This completely changed my understanding of harmony. Thanks for sharing.
Very great video and production ! i don't usually post comments but this deserves a lot more views !
Also the Gamelan music tuning system make a lot more sens to me now considering all the inharmonicity parameters.
Thank You! I am doing a video on Gamelan right now, hope to release it this month, it should be interesting.
@@new_tonality well consider me subscribed :d
ahhhh bohlen pierce my beloved... i find it so interesting that even inharmonic timbres can work perfectly well.
thanks! Nice video, I like what Im learning ironically just got the pdf for "Tuning, Timbre, Spectrum, Scale" by W. Sethares , as this is currently what im trying to go direction was in college! the way we engage with sound and perception generally. thank you again.
this was genuinely a profoundly illuminating video. this has began to actually answer so many of the questions that i have had for such a long time.
thank you so much.
I am very happy it helped)) thank you for all the comments!
Superb way of explaining the complex topic of music perception.
This answered questions I've had in exactly the ways I suspected, especially regarding bell/metal sounds etc., awesome stuff!
I've had some strange frequency shifter experiments sound way more cohesive than I was expecting, as long as I was careful with my timbre and used a narrow stretch of notes. Even with pure sines, you notice how much more consonant an octave is than anything near it, it's so cool how enharmonicity can change that. Simplifying quite a bit, it's like how playing a major scale is more dissonant than a diminished one... over a diminished chord, really simply.
It was maybe 2 years ago now that I started to notice something a bit off in TONS of music, it was that 5th harmonic on a fat bass under something like a minor chord that first started to commonly stand out. You notice it a ton when people distort low power chords too, I've also noticed enharmonic overtones on epianos, fm synths and low piano notes etc. etc. etc. just sounding off for the longest time.
it's really strange to me how most people just wing this without really knowing what's going on, I felt lost with it for the longest time, especially when trying to get more creative with sound design, which is still tricky and limiting. I really wonder how many others struggle with this and how they deal with it, whether they know what's going on or not.
A dream of mine is Harmor 2 btw., taking everything to the next level with several more approaches to programming the overtones according to tunings (And tuning support, obviously), doubling up on the phaser, simulating a sort of pseudo-distortion, flanger and chorus baked into the routing rather than being post-fx, nore versatile and clean resynthesis that let's you clean up the spectral image in the box.
Lowering that 5th harmonic to be minor is an amazing sound btw., works SO well for retro planed chord house and jungle etc., working with other tunings amps up how it sounds kinda ''off''. It's nothing crazy like a bell that comes with a bunch more weirdness, so it's very easy to be musical with. It's great cause you may want a deep and warm character, it's really easy to get muddy or even run into the lower interval limit, but this is one way to get more clear harmonic info down there.
Wow these videos are really the perfect place to go after getting a beginner to intermediate understanding the harmonic spectrum. Keep it up!
That is so true, finally people start to re-realize this fundamental fact about tuning and normal modes…So simple yet modern music theory systems give no attention to for hundreds of years.
this is a really well made articles!!thank you for making this
Good video. It deserves more play than RUclips has been giving it, so I linked it from the description of my only popular video -- which isn't all that popular, but hopefully anything is better than nothing.
Excellent video - interested in aligning tunings with frequencies for the "ultimate" reference vocabulary...I'll check out your other vids.
Oh my god you are so cool I love this SO MUCH!!! I'm still a noobie in microtonality, as I haven't figured out how to make digital microtonal instruments yet. I've been bingewatching content about microtonality tho, and if your other videos are like this, your channel is extremely bingeworthy. My jaw literally started cramping because my mouth was agape for so long! OMG I love you and what you make.
Привет!
I may be 2 years late to this but this video was super interesting. Just like you said, seen tons videos on temperment and tuning systems but nothing touched anything you covered here. You also confirmed a suspicion I had about the low notes on the piano sounding slightly dissonant... I just assumed it wasn't properly tuned. The spectrogram visualisations were very helpful to understand the concepts you are presenting, all around well crafted video. Also side note, you may know this by now but we don't actually pronounce the b in "subtle" for some reason.
High praise! This is good shit
such a good channel i stg
thank you so much for making these
Nice video. I would have loved if you played in equal temperament with equal tempered spectrum, i.e. 2:1 octave, 2^(1/12) semitone and corrected spectrum to fit equal temperament as well. Keep it up!
I picked up on that point you made about the partials of individual notes in polyphonic music lining up on the spectrogram, and wondered, what if instead of creating a stretched timbre and playing with a stretched scale, you simply compose in regular 12-TET and a regular harmonic sound (like piano or synth), and then stretch the whole kaboodle, pitches and timbres, by running the whole thing through something like a frequency shifter or a spectral stretching plugin. I've also tended to find that detuning individual instruments, especially electronic ones, against eachother can bring a whole arrangement to life, such that notes and harmonies beat off of eachother in a manner similar to the chorus effect, but across the whole stereo mix space. EDIT: Also, subbed!
doing research on computer music, very helpful!
Very informative thank you
Amazing video. Fascinating subject and excellent presentation.
Very informative and clear explanation Thax!
I'm really enjoying your videos, and learning a lot. Thank you! One thing that's still a mystery to me is how my brain is able to receive two separate square waves of different frequencies one after another, each with a completely different (though related) spectrum, and based on the partials from the cochlea, say to itself, "ah yes, those both sound like square waves". Brains are incredible!
That is a topic for another video that I was making but had to scrap it and do more research)) But my impression from reading literature is that it is evolutionary beneficial to be able to discern harmonic sounds from environment, as human and animal voices are harmonic. So we have a pattern matching neural network just for that purpose. That is why we can also tell harmonic sounds from inharmonic and inharmonic sounds can sound dissonant just by themselves. So how close the sound is to harmonic spectrum is another dimension of consonance / dissonance to play with.
Wonderful explanation here - instant subscriber! ❤
Many thanks for an amazing video with quite interesting content. May I ask a few questions:
- what kind of mathematical approximation did you use for the sensory dissonance as a function of ratio between two sinusoidal signals?
- when you produce the sensory disonance of two tones with 6 partials each, what metric do you use to you combine their contributions?
- given these two tones with their partials how do you select the pairs to consider?
Formula for a dissonance between a pair of partials:
d = min(L1, L2) * ( exp(-3.5 * s * (f2 - f1)) - exp(-5.75 * s * (f2 - f1)) ) where d - dissonance, L1 and L2 - loudnesses of partials 1 and 2, f1 and f2 frequencies of partials in Hz, s = 0.24 / (0.021 * f1 + 19). And to convert amplitude to loudness I used a formula 0.25 * 2 ** log10(2*(10**8) * amplitude).
To find dissonance of 2 notes with complex spectrum I do the following: 1) I combine partials of 2 notes into single spectrum of 12 partials. 2) iterate over all pairs of partials to find their dissonance using the formula. Note that I didn't include "opposite" pairs, i.e. if I have a pair partial1 - partial2, I do not include pair partial2 - partial1. 3) sum up all those dissonances
Iterated this process for every cent in an octave to get dissonance curve that is then normalized so it's maximum value is equal to 1.
This is excellent content, thank you.
Fantastic video, thank you very much, I learned a lot! Quick question: I’d like to plot chords and scales against the sensory dissonance diagrams you show around the 17:41 mark. Is there a place I could find those with numerical values?
Also, when compared with the graph at 01:47, why I am not seeing a peak around the tritone area? I would expect one that would reach higher than that of the major second, don’t you think?
And again, thank you so much, awesome content!
Hi! I'm very glad that you liked it! I uploaded data as .txt files for dissonance curves for Harmonic spectrum with different number of partials, drive.google.com/drive/u/2/folders/1Pxa73JSmhpFod5Qof8Z7G4PxLeh9In6w
There you can see that additional partials create additional dips in dissonance curve. With 7 partials the dip on triton occurs! So according to this theory, tritone it is kind of consonant!
I think that happens because classical simple ratio approach to explain dissonance is just not really fully correct. It is just an observation rather than finished theory. Also we are used to think that tritone is very dissonant but actually it isn't, it can sound quite smooth even dreamy and mystical. Lydian mode for example does have sharp fourth and it is the brightest of all modes. Late romantic composers use triton all over the place, it is also very common in blues and it sounds great.
@Objective Harmony Thanks a lot for the files! Yes, I did notice the dip, pretty surprising I must say. I was a little skeptical at first about tritone intervals feeling dreamy, but after experimenting a little, I have to admit that my perspective has changed. Cheers to you for broadening my horizons! On a side note, “Farewell” is a phenomenal track!
@@FuturisticCaveman Thank You for kind words!
Hyper piano when!
Well done! 😮
( trying to not use all-caps )
this is actually quite mind blowing
because i thought that it's strictly simple intervals,
This is kinda like non-euclidean music :0
except it's now non-... pythagorean??? lol :3
Haha this video is amazing! Although it probably will make people with perfect pitch go into a catatonic state 😅
Superb video !
Gonna have to pull out an older meme for this
Me: Mom, can we have Für Elise?
Mom: No, we have Für Elise at home.
Für Elise at home: 9:49
well thank you _so_ much. I think this is the first “music theory” video I've encountered that seems to actually talk about the theory of music rather than some culture-specific mumbo-jumbo. I'm also thankful for the explanation of why pianos sound so bad to me (and, I think, why Balinese gamelan sounds so good).
I _think_ it's also a good sign that this one takes more than a single viewing to take in. ;)
Thanks again.
quality content!
Would have loved to hear the difference between stretched octave vs harmonic octave on stretched partials, with timbres with more rapidly descending amplitude of partials compared to fundamental
Great. Octavas on piano are not just, there are bigger than the theoretical one, because of the piano's inharmonicity and equal temperament. With violins, cellos etc, it's different. Furthermore, octavas on piano are not equal, they are bigger the higher the pitch, so do all other intervals (major 3rd etc)
Well, the only way the timbre of an instrument can align perfectly to the harmonic series is to generate them digitally. So synthesizers shouldn’t have this problem. That being said having such perfect alignment makes the timbre sound artificial. The inharmonicities of physical instruments are what makes them sound natural :P
@@adiaphoros6842 That's not true, there are many instruments without inharmonicity such as violin, viola, cello, flutes, etc actually most of them are "correct". For the naturalness in piano, it's actually not the inharmonicity but the overlap of several almost tuned chords, eg., A,A+1%,A-1%. The longuer pianos have less inharmonicity, hence are easier to tune and still have this almost tuned chords, a bit like many violins with vibrato playing together; and they sounds better and not less natural.
4:33 I don't hear the guitar as out of tune tbh
Is it possible you have removed a few videos? I am looking for one that you did that uses the same graph as 17:56 of this video. I can't find it.
No, all the videos are up. Perhaps the Gamelan video you talking about?
Would you know of any tool that can stretch the spectrum of a sample I have? It would help a lot, say I want to have a brass-like thing.
Check out dynamictonality.com, I stumbled upon them recently but didn’t have time to play with them myself. Seems like Sethares ideas in vst form, so should be super useful
Did Stockhausen experiment with this? It sounds really familiar.
Sorry, not familiar with that
@@new_tonality No problem. I would recommend you checking a bit from that composer, he used similar stuff. Maybe his Gesang der Junglinge is worth checking it.
1:40 I would recommend using something else than red and green for data visualisation, a good portion of the population has color vision problems with this exact pair. Purple and yellow are a pretty safe pair.
Thanks for the tip!
@@new_tonality If you ever have to illustrate a scientific paper, this tip saves you one round of reviews!
18:43 I have a quick question about this part... how did you choose the partials for the 12TET spectrum? It looks like there's a lot of complicated stuff going on with the frequencies and amplitudes here... did you use some kind of optimisation code? Only I'm trying to write exactly that at the moment, but I'm struggling a little to get it right!
I didn't actually reconstruct spectrum from tuning. Sethares has a chapter on how to do that in his book, but I haven't read deeply into it.
To get a spectrum for 12TET I use a formula from Sethares book that look like this partial_frequency = fundamental_frequency * 2 ** (Math.round(Math.log2(partial_index) * 12) / 12). Here 12 is number of steps in the octave for 12TET and 2 is the octave ratio (so increase it if you want to stretch the spectrum). From that formula you get a lot of partials that have the same frequency that have to be filtered out. That is because that rounding in the exponent collapses partials to the closest note of 12TET. So all partials are actual notes from 12TET. Amplitudes I think where just 1 / partial_ratio_to_fundamental
The spectrum on its own does not sound very good. Some partials are just dissonant (those are just notes from 12TET in the end of the day). But first 6 sounded good. So the way I generated the entire spectrum was:
1. generate 6 partials using the formula
2. copy spectrum and transpose it to the second partial of the original spectrum
3. repeat step 2 for third, fourth, ... partials
4. combine all 6 spectrums into one
5. filter out partials with the same frequency
That's it, result sounded good so I went with it.
@@new_tonality Ah, I see - yes, that formula does make sense to me, and I also understand about the partials that end up on the same frequency. I've been working some more on my code and I think I've managed to get the original spectrum you mentioned, which you found was quite dissonant. I really like your idea of using six partials and copying the spectrum to each one, so I'm going to try that. I am writing code that will read random or specific files from the set of Scala files (over 4000) and make "chimes" out of them by generating a good spectrum first.
I don't know yet how Sethares does it but the way I construct the spectrum from an arbitrary tuning is very much like the formula above, except I'm careful to round each partial to the nearest scale ratio in the tuning list - and to get the higher ones I have to also keep adding equaves (in case this is a non-octave scale). Pretty fiddly, but I think it's working sort of OK. I think your ideas will really help make it sound more pleasing to the ear, so thank you very much!
I would really like to listen to what 10:12 sounds like with harmonic (12 TET) tuning + stretched spectrum. Like what does it sound like when the dissonance is the note's 'fault'.
Also, surely the harmonic spectrum is natural in the sense that a wave with period x also has periodicity of n*x for all integers n. I wonder what would happen with aperiodic (either time-changing frequency or something more subtle) notes.
Great video! I'm wondering how much of the math about the harmonics of the low piano strings is off because of the fact that the frequencies are calculated as integers instead of decimal numbers. There's much less integers between lower octaves than higher ones so therefore much less accuracy.
for example if that low frequency was 32.3, it would round down to 32, but doubled (64.6) would round up to 65. This would lead to the same deviation you show, without any actual octave stretching. Every octave higher would have half as much deviation as the last since there are twice as many integers and thus a finer grain.
Good point. The number for inharmonicity seemed a bit high, but the practice of octave stretching in piano is mainstream, ear can detect beating if octaves are perfect 2:1. So the inharmonicity is definitely there but more accurate FFT in the video would be better for sure.
This video is fantastic! Just one question, if we use this measure of dissonance, wouldn't it imply that, for example, f played against 7f would be perfectly consonant (since all overtones coincide) just as a unison or octave? Wouldn't this be a bit problematic with our understanding of consonance?
Not sure what you mean by 7f, but yes generally speaking it can be at odds with conventional understanding. One thing that I am not mentioning in this video is that we could say that inharmonic timbre by itself is more dissonant than harmonic. But than we can say that unison or octave can be dissonant)) which also has problem with conventional understanding. I think that because dissonance is such a complex phenomena I should in future use the word roughness instead, as it is much more specific and is only one of many parts comprising dissonance. You can use app that I develop to experiment with that yourself at newtonality.net/lab. Its in early stage, but I’ll post updates.
That would be wonderful if you could upload the stretched octave version of Fur Elise as a video. I enjoyed listening to it and found it beguiling.
That is a cool idea! I think I should do some recordings🤔
That is a cool idea! I think I should do some recordings
@@new_tonality so glad to hear! I’ve subscribed and enjoy your thoughtfully explained music theory videos. I hope you keep exploring more subjects in depth!
you’ve got a good head on your shoulders, I can tell
So if I have produced an FM sound in Serum that sounds very good but has dissonant harmonics, what can I do to fix them? I tried lowering/raising the octaves, semitones of the oscillator but it distorts the sound. Cutting annoying frequencies using the equalizer doesn't solve much and still denaturalizes the sound...
9:52 eldritch horror
Hey, do you know about 18.911 notes in octave EDO ?
No, not sure I've heard about it before
at 6:26, that interference frequency is 5 hz, not 10, cause it's half the difference between the frequencies, not the difference itself. have you also done any research on the effects of the higher interference frequency (which is halfway between the original frequencies), or do you think that's probably irrelevant to how we perceive harmony?
Yes you are right, thank you for correction! The research and results are done for the correct beating frequency so they should be valid. I just screwed up when making the video))
There is one more facet here: bass. A lot of intervals in bass cannot be played simultaneously as frequencies are very close to each other. With that in mind bass has its own rules (especially sub bass). Maybe a topic for another video?
This is similar to what William Sethares writes about.
Yep, his work blew my mind when I found it))
i love your videos ((':
Anyone knows synths and synth sound libraries that can be or are finetuned to work with each other? To point at the gamelan video, it seems you _do_ need a master tuner who can tune different instruments to work with these inharmonic, metallic sounds. It ain't no simple task, you can't just grab a couple of different gamelan samples and push some subbass under it, it seems.
Around the @16:30 mark you mention that the bandwidth of critical bands is larger in the low frequencies, and smaller in the high frequencies. I believe this is incorrect, the effect of which being that humans have increased* pitch perception in the low frequencies rather than in the high frequencies.
I meant critical bandwidth, the bandwidth within which two pitches are indistinguishable. A bit confusing, I agree
A TikToker trying to understand this video would be like a rat trying to understand a closed cycle staged combustion methalox engine.
That shirt is the fashion/stylistic equivalent of dissonance.
The problem is it doesn't sound good, like a lot of other music experiments.