Your explanations are great but I still want to point something out. Objects in space (such as air) can only occupy one place in space at a time. So there is no superimposition of waves in the real world (at least at macroscopic scale).. It is true that we do hear harmonics but that is only because of the way our ears do natural Fourier transformation on the waves they receive, as you explained. However, harmonics are not real in a physical sense (unless you have a multitude of little speakers producing sine waves which result in one and the same block of air moving in a square wave fashion). I might be wrong, but whenever someone explains this it seems they forget that an object's movement cannot be described by more than one wave at a time. You mentioned speakers in an earlier response. From what I could gather, different parts of a speaker move differently, but there is no superimposition of waves in one and the same part of the speaker.
Aa! This is so cool, I played the Gamelan as the child ( Saron and Gong Agung player) and now i understand why foreigners find it so fascinating! You have made a wonderful video, thank you very much. Come to Indonesia when you can, and I hope you watch the live Gamelan shows in Jogja and Bali 🙏🇮🇩 thank you very much
I may be dumb but I don't understand modes of vibration. In what sense does the guitar string vibrate at two frequencies at the same time? Must I imagine small waves on a big wave? Or do the different types of vibration succeed each other in time? What I want to avoid is a confusion between abstract mathematical decomposition of the Fourier series and an actual physical phenomenon.
It a very good question that I dont know how to explain well)) Different frequencies are present at the same time and are largely independent from one another. Small waves on a big wave is a good picture. You can also think of a loud speaker, it can produce almost any spectrum, certanly several notes at the same time and it is a single surface. Vibrations of that surface is a sum of all individual vibratios. If you havent watched my older video "Spectrum and hearing" you can give it a shot. There is an example how several sinewaves can result in a sqare wave and how it is decomposed back into a sinewaves inside our ear.
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.
In western tradition there is no such thing as impure note)) FM synthesized sounds or church bells are not considered impure though they are inharmonic. I woudn't say it at the time of making the video but now I think only harmonic sounds are pure in a true sense. Thus this approach is the same thing as tempering tuning but that coverts dissonance from spectral interference into dissonance from inharmonicity.
I fell in the music theory hole. Started with getting recommended what pop songs are not in 4/4 time signature -> every time signature explained as Nintendo Music -> Forgotten Isle - Super Mario Odyssey -> this video.
In the stretched spectrum experiment where the partials were shifted further apart, there really is a physical beating effect, you can see that the amplitude modulates and visually reflects the beating that can be perceived by ear, I think this is most noticeable since it is only slightly off from the standard octave (partials being out of phase due to inharmonicity, creating beating in amplitude), in experimenting with tuning I've found that correspondingly stretched just-intonation ratios for the stretched octave sound quite stable and consonant musically, and that certain irrational numbers as pseudo-octaves, such as phi squared, the square root of 6 or 7 etc, can sound consonant as though the roughness is masked, the waveforms seem to lack any periodicity while also lacking glaring beating or roughness issues; in some ways these sound to me somewhat reminiscent of Gamelan tunings. It is interesting to conceive of beating frequencies in tuning as being a reflection of low frequency brainwaves, tying in to the concept of entrainment in music this can also be related to rhythmic or melodic qualities, such as a vibrato between two close pitches being perceived as pleasant while the two played simultaneously would be dissonant, or the same with a melodic accent ("neutral intervals" being an example). An important consideration for theory on dissonance is the objective physical nature of sound and vibration as opposed to subjective interpretation, that dissonance can be measured and displayed with accuracy, and that people can be incorrect in judging what is more or less consonant (in this sense a person with a preference for 12TET over pure harmony could be said to have an incorrect harmonic calibration of the ear, having been entrained to the tempered harmonic deviations)
Yeah I think there should be more correct mathematical description of beating as an amplitude variation. In literature, the most simple formula for equal amplitudes is used, and I agree that it seem to miss a lot of what is actually happening. So there is definitely a plenty of room for improvement
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...
The just intonation isn't praticable because the half tones in each interval are differents! The perfect music equal temperament must have an universal half tone to avoid equally all just intervals!
Hello, first-excuse my improvised English! Without the partials of each sound I have the following idea. In the standard music equal temperament the relation netween two sounds in the half ton is K= 1.059463... Or we have there a just octave divised by 12. In the equal temperament of Serge Cordier based on the just fifth K= 1.059643... Between these both K we can construct aproximately 178 different equal temperaments and listen how it sounds. Can you make a video with this subject? It will be a stretched equal temperament without any just interval.I try to experiment this way, but I am 75 years retired violinist and I don't have software nor hardware for do that... Please try my idea!
Hi! I see what you mean, equal temperament that treats all intervals equally and does not use particular just interval as an anchor. I am finding myself more and more in Just Intonation camp as time goes on, but I will think about your idea. Thanks for commenting!
so the only way this wouldn't be a true solution to the puzzle is that if we defined "perfect" music as that which uses sounds that coincide with the harmonic overtones we find in nature
At the moſt fundamental leuel, it ſeemeth pꝛetty cleare that harmonicity trumpeth the other theoꝛies. The 12 tet noꝛmal verſion is beſt, but the ſecond example of 12 tet with inharmonic overtones is definitely ſecond beſt in terms of the intonation being right. Examples 3 and 4 one could onely like if one was a very peruerted perſon. Examples 3 and 4 ſound like one is very deeply tripping on drugs and is deuill poſſeſſed. Example 2 ſoundeth baſically in tune but with very meſſed vp timbre, but in tune neuertheleſſe. If one's bꝛain hath been trained to aſſeſſe intonation by hyperfocuſing on the pꝛeſent moment, then the place in the bꝛain which pꝛoceſſes and compareth things to the "harmonic template" within, getteth ignoꝛed. Inſtead a hyper fixation on beating oꝛ lack thereof taketh place It is in the place of the bꝛain which is attentiue but deeply relaxed and not ſqueezed into the pꝛeſent moment, looking to ſee if ſomething in a giuen moment is wꝛong, where the ſoule of man can compare againſt the "harmonic template" which hath moꝛe to do with the coherency of the tuning ſyſtem as a whole, and not a given inſtance of a particular cloſe harmonic note being matched oꝛ not. Foꝛ example I would ſay Pythagoꝛean tuning is moꝛe conſonant than 5 limit tuning becauſe the ſyſtem of tuning is coherent while the 5 limit ſyſtem is not. In all theſe demonſtrations ſaue the laſt one, real muſical context was excluded from the equation. Playing examples like this but in Pythagoꝛean tuning with coꝛrect ſpelling, and with 5 limit tuning, and maybe 1/4 comma meantone. And ſeeing with the harmonic ſpectrum noꝛmal oꝛ ſtretched, howe diſſonance is perceiued then. Another thing which was not mentioned by thee noꝛ the ſtudies that thou didſt pꝛeſent, is to compare different types of beating. There is harmonic beating, and inharmonic beating. And there is likely a difference in perception as long as it is compared within the context of muſicke.
Thanks for comment! Not sure why Pythagorean tuning is more coherent than 5 limit? I think the problem is that tuning is naturally dynamic and we cannot squeeze it in the static box. When choirs or orchestras play by ear they never stay in any one tuning exactly but move around just ratios as they are the only ones that can be sung or played by ear exactly. Is it because of harmonisity or interference I don't know those contributions seem to be intertwined. I lately started to think that one cannot say that inharmonic timbre is a single pitch, a single pitch can be only harmonic. Thus there are several pitches playing at the same time in inharmonic sound therefore the coloring of unison is precieved.
I'd be curious if the presence of beating is affected by cleanness/harshness of a sound. If you have two sine waves with very close frequencies, it's definitely there. But is that also the case with for example distorted guitars or harsh metal vocals? If no, what about all the sounds inbetween on the clean to harsh spectrum?
Yes, I think it is connected. In literature they call it roughness of the sound and generally speaking it is fast amplitude modulation. Not sure how exactly that works, but in cade of overdriven amps there is definately a difference when you play notes of a fifth separately into two amps and when you play them into one amp. Amp seems to magnify roughness for all intervals apart from the octave, probably cause it creates more of inbetween harmonics or somethg like that))
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.
This is a very interesting channel and I'm glad I found it. However, I wonder if your claim about our brains containing a harmonic template is jumping the gun a tad. First, the mechanism of sound production in our speakers and headphone create harmonics just from natural imperfections. Are you sure that there is not any non-linear responses from our sound equipment first that allows interference between harmonics coming from non-linear distortion and the inharmonic partials you inserted? I'm genuinely curious about the answer to my question. I unfortunately don't have the best audio equipment to test this out myself yet. If the effect I describe is insignificant, then harmonic template generation in our brain raises many other questions about how it can biomechanically arise from something within our brains and how the brain does some sort of multiplication of frequencies to sample in the fourier/wavelet transformed signal, or how it measures peaks of autocorrelations.
Well, I cannot be sure as I haven't done measurements to check that)) but I think the non-linearities in audio gear are too small to explain perceived effect. I am using monitor speakers that would've been useless for mixing if they had such huge nonlinearities. The way that brain determines harmonicity in the sound is actively studied and as far as I can tell there is no consensus. Two theories that I came across is autocorrelation and comparing against harmonic template. Perhaps both mechanisms are at play. In my view it is probably something akin to how AI recognises patterns. I remember seeing some images in early days of AI when neural network was trained on pugs and when given different images it kept finding pugs everywhere (in clouds, in smoke, etc). We also have this ability with recognising faces everywhere. But that is a hypothesis of course))
Have you ever considered developing in the VCV Rack environment? If you’re not aware of it, it’s a Eurorack-like modular synthesis software that’s open source and has a thriving development community from what I’ve seen (only an end-user myself). A configurable xentonal CV quantizer and accompanying additive oscillator module would make this tonality system incredibly accessible for modular-focused composers like myself. It’d also make it significantly easier to experiment with xentonality without necessarily understanding the underlying theory; the modules could “do all the math for you.” Considering how new this theory is, I think it could be great to get people interested through such a broadly-used system, just so people can get these harmonies in their ears for the first time without needing a robust (and niche) microtonal production workflow in place to do so. In any case, I know I, for one, am excited to see these concepts used extensively and hope to contribute some xentonal electronic music in the future!
Out of the tens of thousands youtube videos I’ve watched over 18 years this might be one of the most interesting. So well researched well presented, well edited, and well written. I will be sharing I hope your channel blows up man this is great
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.
Hello Seva! I am glad to tell you that your video is a great help for me, as I am currently writing a paper about balinese gendèr wayang and the musical compopsition within. The graphs you have used showing the dissonance distribution are very interesting. I have two questions for you in hopes you can help me. - at 14:21 you have shown the dissonance curves following the example of Plomb & Levelt, but adapted to different instruments in slendro. You have mentioned getting the data from casadamusica. However I would like to find the "median" tuning for gendèr barung and the gendèr panerus. Can you explain further how you created the dissonance spectra? - I have seen that you have created your own xentonality app. (It is so well done, congrats!) The direction of my paper is a different one, since I want to condense the basic rules of gendèr wayang into a PureData patch witch a visual and interactive landscape for learning purposes. However I would like to refer to you and your great work. So: is it okay for you if I put a ink to your xentonality app in my paper? Thank you for all your time and effort!
Hi! So the way I did it for the video is I recorded several samples of individual notes of one instrument from casadamusica library and analysed their spectrums in audacity. It is prone to error as you pick and choose which partials you consider impacting tuning and which not. Many partials in spectrum are just a part of attack so they dissappear from sound very quickly but audacity will still show them in the spectrum. The way I would do it now is that I would have longer samples (around 10 seconds) and look at their spectrograms. This way you can see which partials stay in the sound for the longest time, such partials should be considered as playing role in the harmony. Then note down frequencies of such partials for each note and find their relationship to fundamental (frequency_of_partial / frequency_of_fundamental). You will have a collection of ratios for each note that should be similar so you can average between them. Sometimes some notes have a partial that is not present in other notes, I just removed them to make life easier. In the end of this process you get an "average" spectrum for some instrument in the ensemble. Then I would've put it into the old version of newtonality app (xen-jmju0jgyc-sevader14.vercel.app/lab) to get the dissonance curve. Hope that helps))) Yes absolutely you can site my work, I am very happy that it is helpful! Send the link to the paper when you publish it, would be interesting to read)) You can also use the code of the newtonality app in any way you want, it is opensource on Github.
Buenisimo!, todos esos estudios que citestan estan sesgados porque si consideramos a la disonancia como un fenomeno universal Shoenberg estaria equivodaco, y como es tan respetado academicamente los estudios al respectos se sesgan. Pero el ejemplo que pones delos 4 audios es muy claro y alli no puede haber condicionamiento cultural. Lo mismo pasa cuando tocas un acorde mayor con la tercera mas baja, suena mas agradable y deberia sonar mas disonante si solo se tratara de la cultura, y no sucede. Ya no se puede sostener semejante mentira po mas tiempo, tambien hay estudios en bebes que confirman que la consonancia disonancia es un fenomeno universal.
Sorry if I misunderstood your point, but I think that saying that consonance is 100% cultural conditioning or 100% NOT cultural conditioning is equally wrong. It plays a role though that role is not absolute. One example that comes to mind. If you ask a regular musician, which is more consonant, major chord on piano in 12-tet or the same chord in Just Intonation. I am pretty sure most musicians will pick 12-tet as more consonant, even though it has objectively more beating. Just Intonation just sounds weird on piano to modern listener. Cannot cite a study, just referencing personal experience)) As a side note, I personally disagree with Shoenberg and I don't care how respected he is)) he, as well as most academia share a modernist mindset, where aim is to destroy tradition and not get closer to truth. That is their bias.
@@new_tonality Creo que coincidimos solo que el hablar distintas lenguas nos lleva a malentendidos. Estoy de acuerdo que hay un condicionamiento cultual para el fenomeno de la consonancia, pero tambien hay un componente natural. Creo que te equivocas respecto del ejemplo del acorde mayor, al menos en mi experiencia, la mayoría de las personas a las que les hice la pregunta elige el de la entonación justa o les es indiferente. También respecto del acorde de dominante cuando se lo construye con el séptimo armónico natural. Gracias por tu respuesta! y tus videos, son muy buenos!. Por ultimo estoy convencido de que hay un fuerte relación entre las blues notes y el séptimoarmónico natural. Me gustaría saber que opinas. Saludos
It will always be amazing that this much complexity emerges from sound waves that can basically be represented fully in just two dimensions, many people don't realize just what kind of marvel they're looking at when they see a sound wave represented on their screen. I also just love blowing people's mind with an EQ, some sines, saws and noise, a bell, speed up some polyrhythms/slow down some consonant chords with perfect ratios etc., such an incredibly simple building block that leads to so many phenomena when we perceive it. I will definitely share these videos with whoever ends up being appropriately blown away by how it all works. Just think about how sensitive we are to this too... It differs so much from how we perceive colors, for example, even though you'd think it would be a very similar deal. We do perceive a far wider range of sound freqs than color wavelengths, we don't even see the equivalent of an octave, but ratios like 2/3 are present, so there's also just less of an opportunity for such consonances to stand out to us, I suppose. (Purple is fake btw., google that if you think I'm crazy) I was completely with you that example 3 sounded the 2nd ''best'' btw., the others felt more like they mixed in a bunch of messy noise that didn't have anything to do with the rest, 3 somehow sounded more organic to me as well. 16:22 Some chords like the supposedly consonant one it's about to hit over here do still have some of that chaotic quality to them to me, though. Regarding tracks that pursue some freqs rubbing together very aggressively, Joker - Tron is a classic in the uk dubstep community and a great example by using detune on synths, where it creates color in absence of more complex harmony. Still a relatively conventionally musical example as far as dubstep goes, a seriously fascinating genre you should check out even if you dislike what you've heard so far, try Kryptic Minds, for example) Would you consider doing a video about phase if you hadn't yet?
Not sure I am going to touch on phase any time soon. But you made me think more deeply about it. It indeed may impact a tuning especially if partials coincide perfectly as interference will be more pronounced. Like if some partials cancel each other out it can be percieved as less consonant. But I need to experiment with that first)) Thank you for comments, very cool stuff!
@@new_tonality Awesome to have inspired you, video or not! It's pretty hard to intuit a lot of stuff that phase can do, one of those things where I usually thow stuff against the wall until it sticks.
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.
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
I love this channel so much, easily top 3 most valuable sources of information and completely new musical perspective delight on RU-vid, thank you so much for the hard work <3 Eagerly awaiting the day Newtonality synth becomes downloadable inside DAWs :)
The fascinating thing about these "foreign", sometimes "alien" sounding tunings, is that as much as their tunings sound to us, OUR western tunings sound alien to THEM!!! I tell my students that music is just like language, what you don't understand will sound novel and out of this world, just like Chinese would sound to an American, even though both languages are made with the same structures of the mouth!!! Micro tonality is so fascinating!!!!!
( 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
