minutephysics - 2025-07-18
Thanks to the Acoustical Society of America for sponsoring this video! Start your career in acoustics today with the ASA career toolkit: https://exploresound.org/acoustics-careers/ Get your very own ‘Harmony/Dissonance‘ t-shirt here: https://store.dftba.com/products/dissonance-tee And check out my friend Aatish’s interactive website here: https://aatishb.com/dissonance/ Further watching: - https://www.youtube.com/watch?v=1Hqm0dYKUx4 - https://www.youtube.com/watch?v=spUNpyF58BY References used for this video: - Tuning, Timbre, Spectrum, Scale by W. Sethares, 2nd Ed. 2004 - Tonal Consonance and Critical Bandwidth by R. Plomp & W. Levelt, 1965 - Auditory Patterns by H. Fletcher, 1940 - On The Sensations Of Tone by H. Helmholtz, 1875 - https://www.pharmacy180.com/article/sense-of-hearing-3587/ - https://www.sfu.ca/sonic-studio-webdav/handbook/Consonance.html - https://sethares.engr.wisc.edu/consemi.html#anchor149613 - http://hyperphysics.phy-astr.gsu.edu/Music/cirmem - https://en.wikipedia.org/wiki/Piano_acoustics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics provides an energetic and entertaining view of old and new problems in physics - all in a minute! Created by Henry Reich Produced by Joshua Chawner 00:00 - Intro 01:57 - Contents 02:13 - 1) Dissonance of Pure Sine Waves 07:42 - 2) Dissonance of Notes with Overtones 11:28 - 3) Dissonance and Scales 15:29 - 3.5) Is any of this true?? 19:06 - 4) Dissonance in Chords 22:36 - Conclusion 24:15 - Sponsorship from ASA 25:03 - 5) Caveats and T-shirt!
finally a video from my favorite YouTuber: half-hourphysics
7-minute abs
@rykemapowhat.
@@Ruzzzz57 *ads i hope
@rykemapohuh
😂😂😂😂😂😂😂
Finally a video which explains dissonance in music without stopping at "because Greek philosophers liked small ratios"!
Looks like it's the other way around - Greek philosophers liked small ratios because they associated them with harmony
Well, there are two other videos about dissonance that just came out by Levi McClain and Marc Evanstein which cover the same topic
Why does western music use the harmonics from strings and pipes?
Because greek philosophers liked small ratio's and their theory for harmony gave an easy guideline for creating music that worked well with strings and pipes.
@@amyntas2868well, why should we limit our discussion of dissonance with Western music? What you provide is an explanation, but not a very insightful or helpful one. It's also incomplete. Because originally only the fifth was considered consonant, and in Pythagorean tuning thirds are out of tune.
@@BryanLu0I kind of messed up my theory. I meant to suggest that the reason western music uses so many string and pipe instruments might be because of the effects of having a theory.
I do not know if they had any other type of music theory before the greek philosophers but I just assume they didn't.
If this was the first theory, the process of writing music just became a lot more accessible because a writer has a place to start, no matter the validity of the theory.
If then the theory somewhat works for strings and not for bells, writing for string instruments gets a comparative advantage over bell instruments and the culture slowly shifts acordingly (more string music, less bell music).
The theory doesn't have to be perfect or even good for this effect to work. It just has to be the best available and work better for some instruments than others.
"I had 5 minutes, I'll watch a minutephysics video!" - Last words.
Youtube is getting out of hand when even watching minutephysics requires a substantial time investment. 🙄
@@Don2006wut
you can see how long it is though
and also youtube didnt use to have shorts it was all other videos
Literally me, now finishing the video 25 minutes after my lunch break already ended.
Just want to say I had to go and now have come back and finished the video to its full length. Thumbs up.
This is unreal. I have been told countless times that "we don't know why but we think humans just like hearing tones with simple ratios". This explanation makes so much more sense and offers such a more nuanced and interesting view of harmony. I want to immediately start playing with additive synthesis to find some interesting new chords.
Additive will get you there but you might like to try FM. Additive will take longer to build a complex timbre that you can then explore. With FM you simply set an inharmonic ratio between the carrier and modulator and then your index (modulation depth) will decide how many harmonics you want to work with. Building your timbre that way is intuitive and will give you complex results fast that you can then explore. I’m excited to create some interesting timbres and resulting chords/scales with FM after seeing this vid.
On a side note this also gave me major insight into Pelog and Slendro temperaments. I always used western timbres to explore those tunings. And while they work, I never knew that the physics and resulting overtones of exotic instruments actually serve those tunings.
@@CharlesFerraro Interesting! I do a lot of FM but I hadn't thought about it in this context. Now you mention it, that's probably why FM produces such nice bell sounds. Will give it a go!
@@CharlesFerraro what does FM stand for?
@@reminso2952 frequency modulation
@@reminso2952FM stands for Frequency Modulation. When people say FM synthesis we’re actually talking about phase modulation or linear FM. Not exponential FM like cross modulation between audio rate oscillators or really fast vibrato.
I admire that you don't "dum down" your content. This is top notch educational material for those who pursue knowledge and understanding. Thank you
as a science obsessed music student THANK YOU
THEY ABSOLUTELY SHOULD TEACH THIS IN COLLEGE
Opposite side here as an art-obsessed STEM student. Minutephysics still goated.
They should teach THIS AND THAT!
I don't really agree that this should be taught. It's an amazing subject, fascinating, has wonder explaining power beyond western music which is always a plus. But you'd have a much easier time teaching students by showing them what different musical styles favor and train their ears, let them intuitively develop their hearing
there are some inaccuracies- too many to list, but overall it is well done.
@@MooImABunny Yeah, too bad it's impossible to teach both concepts as some kind of "major" area of study... shame... I guess the kids will never learn anything :(
As a music theorist who is definitely not a physicist, I find this to be probably one of the most understandable videos of yours in this complexity range
As someone here for the physics and is close to musically illiterate, I wish this was how music was explained from the start! This makes music theory a lot more approachable.
I studied music for several years, and I can confidently say this video should absolutely be mandatory viewing in any harmony class. In 30 minutes it covered more ground than a full semester of a university-grade class.
As a person who thinks like a physicist and has never been able to understand the FIRST THING about music, I understood almost NONE of what this video said.
@@michaelcherokee8906yeah i have no idea what half the terms in this video mean. I don't know what sharp, flat, major, minor, octave, scale, cords, consonance, dissonance, and such even mean.
@@ArcaneOverride Well damn.
Everyone is complaining about the length. But that Video was so packed with information that you more than kept up the pace. I'd love to see more videos like that
Add me to this list, too.
Feels like they're more joking about the length, instead of genuinely complaining.
^, though some people are actually mad. i adored this video especially as a violinist
Im complaining about length
It is too short
Complaining isn't the same as wondering or pointing out.
As a musician this video was incredibly interesting. Very cool to hear an interval that I knew was an octave, but still sounded dissonant
Music educator and microtonalist here. 1/3 of the way through, and very good so far. Two terms I wanted to "sub out" or clarify, to avoid confusion:
Discordance and concordance = the sensory acoustic roughness/fusedness of sounds outside of context, rather than dissonance and consonance, which almost always involve "resolution" of what came before, relevance to the scale, or relationship to the tonic, etc.
And partial = frequency component of a complex sound, rather than overtone. In general music knowledge, overtones are generally understood as harmonics above the fundamental, whereas the word "partial" is used on some commonplace inharmonic spectra, including bells, and piano, where the lowest partial is the lowest frequency component with a strong peak. In bells it is generally an octave below the second partial, and a minor tenth below the third. In piano tuning, the beating of coincident partials is usually the primary thing to listen for to get a note "in tune".
If you use "partial" numbers instead of "overtone" numbers, the maths and labelling are both simplified, essentially the same. You can say a 4:7 (or 7:4 if you like) ratio is the distance between the 4th and 7th partial, and where the 7th partial of the lower note is equal to the 4th partial of the upper note. There will be a (first order) difference tone equal to the 7-4=3rd partial, and a (first order) summation tone equal to the 7+4=11th partial.
Great points, agreed. But still a very good video even with those slight misses.
Oh great, now I apparently have to subscribe to your channel, too! 😂
Thank you for existing, and thank you for adding your comment!
As a professional engineer in acoustics and signal processing, this is one of my new favourite videos of all time. It manages to perfectly explain and demonstrate one of the most complex aspects of music with minimal effort for the viewer. Truly wonderful and masterful.
Good, I'll watch it. Thank you, I needed to see that. Music fan, musician, singer (the last two started when I picked up the bass guitar at 50 and 64 they made me buy a mic. Recently started adding key bass/keys. Been in this current gigging cover band for 7 years, over 250 performances.) Also a techno-geek, I've known about ADSR envelopes since I was in high school and bought an electric organ that also had a synth.
@@nathanwahl9224That's how I got into this mess. Started making music from my room at 14, had a side channel that even did some numbers back in the day. Then I got into a Music Bachelor's for composition, and that's how I got to know synth design and development. First with Pure data, then using raw code and eventually writing my own filters and other signal processing stuff. I've been going strong on synth development and designing tools for musicians for years now. I still make my own music whenever I can though.
Perhaps you can help me? How would I construct a "sound laser"? That is, a speaker are precisely spaced group of speakers made out arrays of ultrasonic transducers.
It's supposed to work like 5G cellular and phased array telescopes in that the ultrasonic frequencies combine only along a single line (single speaker array) or at a specific 3D location (using multiple speaker arrays) to create the desired output sound through the mixing of these ultrasonic frequencies at the receiver (ear for audio).
The problem is I suck at math and I don't know any of the necessary maths to implement this.
Do you know of any pre-written libraries that I can use to program a FPGA to make a custom DSP for this purpose?
If you do know of such a library does it take into account the non-linear aspects of the receiving medium? Ideally I would like it to work with both ultrasonic transducers (human ear receiver) and small radio transmitters (for disconnected speakers) or perhaps even other forms of information transmission without the need for a specialized receiver.
You were correct!
This video is so fascinating cuz if you fiddle with additive synthesis enough you get the intuition for this kinda stuff but you put it into words and visuals so clearly. Incredibly well made video
hey wangeline! you make banger music
@@22222Sandman22222 thank u!!
the only intuition I have about additive synthesis is how to shitpost using harmor
omg HAIII WANGLE LINE!!!
Crazy that Marc Evanstein, Minutephysics, and myself all made in depth videos on basically the same esoteric topic all within the same week of each other. Im sure it takes all of us months to produce these videos as well which is even crazier. Exact same sources too. Bill Sethares is clearly in the air! Glad his work is getting the recognition it deserves.
Yeah, this is weird!
@@marcevanstein "No, it's not weird, stop believing things that cause dissonance!"
I have been studying this exact rabbit hole for the past month! I was hyped when your video dropped, but I was still wondering about dissonance curves, then this video! Absolutely wild how that happens.
I'm subscribed to all three of you and I've also been reading Bill Sethares's book, so it's been a pretty good week.
I believe that collective unconsious is a real thing lol it has to be, stuff happens so synchronously way too often like that
Audio system engineer here. I've spent the past several weeks preparing lessons and lab plans to teach this stuff as fundamental context for mixing. This might be one of the best videos I've ever seen of these concepts.
Brilliant work. Thank you!
Wow... Just wow! Such good video and audio production and editing. Congrats! One my top fav 10 YT ever
THX's Deep note makes so much more sense now. They started with dissonance and then expanded the notes to every harmonic to get that satisfying resolution. Perfection
what were you listening for before?
I would love to see the THX sound animated into the graph!
@@WarttHog what do you mean animated into the graph? it's a glissando that resolves into a major chord.
@@opticalreticleeach frequency in the final note starts out a little journey from a random starting point
@@WarttHog https://youtu.be/52YXKcz4tmE?t=288 This video on the Deep Note has one, and also gives you the backstory!
This explains why sometimes playing the same chord on different instruments make such a big difference
There is a video here, which explains why bells music usually sounds dissonant. There they said, overtones are different and they create lot of of dissonance. https://www.youtube.com/watch?v=0BNtaNNfUR8
yeah, and why writing covers is such a pain
And then there’s the question of how different key instruments are tuned, fretted instruments, non fretted… etc
overtones
I did a paper on this in college, and it was one of the most fun projects I did. I used the dissonance graph at 3:35 and applied it to sheet music, looking at total dissonance between all note (and some number of overtones) played at each time, and looked for patterns of consonance and dissonance in the song.
Well what did you notice
@@greaws It's been a while but I think it was basically showing (at least in the song i looked at) that sets of measures would alternate between ending on more dissonant chords and more consonant chords for the sort of tension and resolution feeling. So maybe the first 8 measures end in higher dissonance, and then the next 8 end in lower dissonance.
Sounds like a cool research
@@acmhfmggru You completely missed the point. Musical dissonance doesn't mean detuning. It's just that a major 5th is more consonant than a minor 6th. That mild dissonance is what builds tension and makes music interesting.
@@acmhfmggru You must be really fun at parties.
0:30 I'm unreasonablely mad that you didn't resolve the suspended chords... My head hurts
Your explanations of how overtones are what determines tuning and how consonant/dissonant different sounds are are excellent.
As someone who has no idea about music theory or playing an instrument, I feel like I need an entire multipart lecture to understand this video fully.
Just realize that in general, while this stuff is the underlying principles of what you hear, literally nobody looks at stuff to this depth. Much of it has become simplified by being rule-based, what works, what doesn't, and what doesn't work when you want it to not work on purpose. You don't have to know how to build a watch to tell the time.
I was just watching Marc Evanstein's recent video on making consonant tritones, and I'm so happy to see another one of my favorite YouTube creators investigating this!
Watching this video is a weird experience for me!
same. the idea of visualizing dissonance and consonance using graphs is still so clever and intuitive to me.
@@marcevanstein what a conincidance, right?
12:30 this realization sent shivers down my spine!
When learning piano as a child, at first I had a cheap keyboard before my parents bought me a proper e-paino. I remember messing around with the few melodies and chords I knew at that point and playing them in the different sounds the keyboard could produce. When playing them with the bell sound, it always sounded ... 'off'. But I never knew why.
Now you finally got me the answer to this deep buried question in my head.
As a guy, who is passionate about both physics and music, this video generally is a masterpiece!
Experiencing audio as we grow, as we learn and develop, the way all that is etched in our brains and the way our consciousness and understanding of it evolves… that’s one of the (few) truly miracles of life I’ve experienced and I realise I can’t share that with a lot of people. Your comment made me smile.
I’m really glad I stuck around for the caveats at the end. As a musician with a focus in percussion, I was going to mention how critical materials are in getting the timbre/consonance you are chasing within in ensemble. The shell of a drum, the fiber of a head, and even the wood choice and geometry of the stick, all play a huge role in your sound, before you ever tune the instruments themselves. Cheers to a great video!
As a musician, I feel like I'm not supposed to learn this. Knowledge like this only tortures me in this artistic process.
As a tone-deaf STEM major trying to understand music theory, this is the single best video on the topic I have watched, with 12tone's video explaining major scales to an alien being a close second.
Music theory is a lot of math. If you can teach yourself, you can learn music theory from qualified tutors or books. I would recommend starting with the ABRSM books "Music theory in practice".
You’re not tone deaf. You instantly recognize your mom’s voice on the phone and even know if she is a bit sick. Your ears are excellent.
I hope you don't mind me asking, but do you experience these sounds in the same way? Even if you can't discern the tone or the relationship between the notes, can you feel the dissonance when it's there?
@@cmhieksesDo you know this person?
Yeah there is no such thing as tone deafness. It's just a colloquial way of saying someone has an untrained ear.
The Physics of Dissonance is a sick name for a metal band
more for a math rock band tbh
How about The Psych(ology) of Dissonance?
PsycoDiss
@@uncopinothey get all the good names
Playing tonight live:
Dissonant Physick
( I spelled physic the old timey way on purpose, for obvious reasons)
What's really amazing to me is that you can play a dissonant chord and then a series of chords or notes after that can make it seem less dissonant and actually "fit" the music.
This is the definitive overtone video. I love learning about stuff like this for years, and there is so many I didn't think or learn about! Well done, this is the video I'll send to anyone wondering. Thank you so much!
I’m 11 mins in and just smiling away. 11:36 The graphical representations are so clear. I love seeing overlapping overtones as two notes rub into their calm
Octave Homes.
14:22 i actually did notice it was a little sharp, glad to know my musician ears are still working all these years later
Same
I was wondering about those with perfect pitch, or those like you who are tuned to it it probably felt discordant. Us laypeople just nod our heads, "Ah yes an A note"
@@Corfal It doesn't have anything to do with perfect pitch, because is the interval between that A and D that sounded out of tune, in my case (having AP) I noticed that the A was out of tune but I didn't noticed that the D was in tune, I wasn't paying much atention on the moment but someone with a good Relative Pitch would notice inmediatly, with Perfect Pitch you are actually more unlikely to get it right.
@@Corfal as someone with perfect pitch, an out of tune interval is more obvious than an out of tune note. I noticed the interval was out of tune before I even thought about which pitch was out of tune and in which direction
that awkward moment when you're 15 minutes into a video and realise you weren't paying attention and have to restart.
I was paying attention the whole time through. It is so interesting!
THAT'S LITERALLY ME BRO LMAO
That awkward ADHD moment when you're 15 minutes into a video for the 4th time and realise that you yet again lost track at the same point you did the last 3 times
It's ok though, you're listening at 3x speed so you can restart to get back to losing track again quickly enough
Also an awkward moment when you didn't follow the hint to use headphones and at some point you figure it out that… it might actually be this very video's sound that made your cat start running around like crazy 😅
the dissonant sound samples clearly disintegrate focus!
Saw Marc Evanstein's video, "I Fixed the Ugliest Musical Interval... and Broke Everything Else" a couple of weeks ago when it came out
Seems like a very similar concept! I'm intrigued
Beautiful harmony of mathematics, physics, biology, and arts through an amazing combination of visual and auditory demonstrations! Thank you for this video.
The bit of info 18:20 explaining why those non-western scales exist was mind-opening! The fact we built scales based on overtones of the instrument being played makes so much sense
Marc Evanstein released a video just a short while ago that also discusses this subject! Really neat to see two well-researched and -presented videos about such a fascinating topic, and I'd be interested to see more exploration of it soon!
yeah, I think the first guy to do it was a very small mostly inactive channel called New Tonality like 5 years ago, and then suddenly it seems there has been a surge in interest in this subject. Yet another guy called Levi McClain mentions some of these concepts in the video he made just 2 days ago on microtonal pianos (also based on Sethares book hahaha). These ideas have really gained traction (and rightfully so!)
Your art style plus a video about dissonance is giving serious 12tone vibes
12tone was heavily inspired by Minute Physics to create their own style. It's no wonder you're getting vibes.
I was thinking the same thing.
That uncanny amazing feeling when the rabbit hole you've been down the past month culminates in not only a video summarizing all those findings, but an interactive website doing the exact demo you're trying to build.
This is one of the most influential lessons I’ve experienced - seriously. Been playing guitar off and on for a few years but haven’t understood music in my own way until now. Having a physics background and a deep love and appreciation for music have been longing for a marriage and this video has been that catalyst. This is my fourth time coming back to keep understanding deeper. Please do more videos like this! I’d love to see the relationships between chords and keys and how they are arranged in the dissonance contour plot
One thing that is worth considering is that integer multiple overtones aren't necessarily just a quirk of western musical instruments. In particular, distortions occur whenever there are imperfections in how the pure tones are produced by the instrument or heard by the listener. When a pure sine wave is distorted -- such as 'clipping' the peaks -- the distortions appear as integer multiple overtones. This is why if you listen to two pure sine waves, with one steady and the other slowly rising in pitch, you'll still hear that the 'beating' resolves at perfect intervals far from 1:1, as though there are phantom integer overtones.
While the idea of non-western instruments having arbitrary overtones while still achieving harmony is compelling, I think it neglects to consider how integer multiple overtone harmony already aligns with the messiness of the acoustic physics and perception, and thus is more robust to their imperfections.
One cool example of a scale based on a nonstandard set of overtones is the Bohlen-Pierce scale, which is built on the first three overtones of a pipe that's open at one end but closed at the other (3,5,7) making it beautiful on woodwind instruments.
3, 5, and 7 sure seem like members of the harmonic series to me!
First upload in 3 decades, we have been blessed with a 30 minute video!
FR
It's been 3 weeks.
@Olive_Gamer139 3 decades to us.
@Olive_Gamer139 Yeah but they were dissonant weeks.
If minute physics can last 1/2 an hour, then 3 weeks can feel like 3 years. :)
To add to the complexity of bells and stuff can be tuned to different overtones, which in my region is often linked fifths and minor thirds, so that the bells are consonant in arrays. The shape of a 3d object resonating changes the overtones significantly. the is no one overtone series for a bell.
It has a minor overtone series, and the minor third is very low and loud in the series. So you get a carillon arrangement of twinkle twinkle little star, and it sounds like alien music
This is excellent! Extremely helpful for composers and producers to have hard data behind this stuff. Great work and thank you.
I've studied basics of acoustics and the basics of a lot of these concepts from the science side and the music theory side, but I've never seen it all put together so clearly and concisely... very much appreciated! Thanks for putting this out there!
Excellent use of Lissajous Curves when talking about relative frequency ratios. Well Done!
One of the best video I've seen in this year. Appreciate your sound design throughout this video, especially theae ones in title screens, e.g., 23:58.
9:02 this is just the THX logo sound
Bang on! I've always loved the THX logo sound, exactly because of its mathematical simplicity. Perfect fit for someone like THX. Sounds gorgeous and impressive.
The THX deep note is similar but not quite the same I think.
@cube2fox Yeah, I think the THX sound is the sum of twenty five oscillators, each shifting in frequency over time to shift from being "out of tune" at first to being harmoniously "in-tune" at the end.
@@juliavixen176isn't this basically the same? Or at least the exact same result? The thx logo chime is slightly Frequency shifting across disharmonies, to coalesce in the harmonious blare?
@@juliavixen176 when the THX sound finally lines up, it’s as satisfying as the DVD screensaver finally hitting the corner of the screen perfectly.
12:12 completely blew my mind. How did you generate these graphs? I NEED this. You've inspired me to experiment with bells & other unusual overtone'd sounds. Such sounds come up really often in FM synthesis and it would be really interesting to pinpoint the oddly satisfying intervals for each specific sound... but I have no idea how to recreate those dissonance graphs
You can use Aatish's interactive website linked in the description. Note (heh) that if you want to modify the overtones, you need to enter the overtones of your instrument of choice using the console, which is opened by pressing F12. The website tells you the syntax of how to enter it. (Yes, it's a bit confusing, but partially because they're too lazy to do the UX :P)
Yo Exyl????????? What????????
Wth exyl???
You basically take that skewed bell curve for the start and replicate it for each overtone of your first sound (the process can also be described as convolution of the bell curve with thin-line spectrum of the overtones). Then you do the same convolution for the second sound. Then you multiply the two resulting curves together and sum up the results. This gives you a "dissonance severity" number for a given pair of sounds. You then keep the first sound fixed and vary the base frequency of the second sound, and do the calculations as described above for many "second sound base frequencies", effectively producing the dependency shown in the video. If you don't get it right yourself, give this description to ChatGPT to write a Python program for you.
@MinutePhysics - 2025-07-18
We thought the dissonance graph was so cool we made it into a tshirt: https://store.dftba.com/products/minute-physics-harmony-dissonance-tee
@jhardinger - 2025-07-18
How is the y-axis value of "sensory dissonance" calculated? Chapter 1 says "most people hear a single pitch with no dissonance". But we haven't even said what dissonance is yet.
@maximilianosotomayorga4977 - 2025-07-18
it should be possible to make a klein bottle out of the 3D graph just as 3 blue 1 brown makes a möbius band out of the graph of ordering all dyads
@dahawk8574 - 2025-07-19
An interesting visual would be to graph a SONG in its 3-dimensional harmony space. And for the follow-the-bouncing-ball pointer, why not use the Yellow Submarine as though it is spelunking through the Earth's ocean floor.
@_c_y_p_3 - 2025-07-19
Thank you. You did a BEAUTIFUL work here! This is by far the most awesome pile of knowledge on this topic! These are things musicians and sound designers know intimately, often just by feel , discovery and experimentation. But this is beautiful to have this, especially for song writing and mastering. Thank you. 🔥💚🔥
@VEGAN-2.0_VS_ANIMAL_ABUSE - 2025-07-19
Music is experienced like a game. So let's work on improving the interface.
0-11 (TL) zab, post-tonal set theory, Janko/Chromatone. Use the internet.