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Why do we perceive some pairs of notes as pleasing and others as harsh? (Understanding FM #3.5)
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- čas přidán 3. 07. 2024
- While preparing for the 4th instalment in my FM series (czcams.com/users/playlist?list..., I realized that I really need to first talk about why we find some pairs of notes as pleasant, harmonic, or stable; and why others are discordant, unstable, and seem to fight against each other.
So I offer this small digression, not officially part of the FM series, but still important background before we get to the question of picking frequencies for carrier & modulating oscillators.
Your video about sidebands has single-handedly multiplied my understanding of FM a thousandfold. Thank you for making this series, it's a true treasure trove.
@oxar050 - Wow! I'm so glad you found it so helpful!
I'm loving this series. Keep it up.
Agree, this fm series is cool!
It really is helpful. Thank you! I love FM sounds and this series is a boon of knowledge.
So well addressed. I can’t wait for the next one!
I’ve only now undertaken creating my first modular. I had lots of clocks divided in my brain and hoped to lean on sequencers for the laborious task of setting the frequency for simultaneous notes, one by one by ear. As a NON-musician, I was hoping that all the tech would work like magic. At my age, I probably don’t have the time to become a musician. With my background I’m knowledgeable about module functions and patching principles and always think in terms of voltage and math relationships. This video is a masterclass for me. It’s a revelation for me in terms I can understand. More “music” here I come. Thank you so much!!!
Thank you, it is really nice of you to say. I suspect you are coming at this very much like I was when I got into modular. It's an exciting way to learn...also expensive...but what are you going to do?
Thank you. Like a teacher I could listen to endlessly ;-)
Loving this FM series! Thanks!
Glad you enjoy it!
oh heck yeah. x.5 episodes!
Very neat to notice during your animated traces, that the sum waveform of the 3:2 appears to resemble a bit of light folding applied to a sine wave. I suspect that the end result is similar because they are simply 2 different ways of adding the same harmonics.
@CatFish107 - Or possibly a bug in my code LOL. I'll look at it.
The BEST CZcams channel! Thank you for the time and energy you put into each of these videos! PLUS, you are a wonderful presenter!
Thanks! My days in radio have paid off! :)
Thank you, amazing video!!
Oooofffff, this is definitely my new favorite youtube channel. Great content, sweet narration, lovely visuals... NICELY DONE!
Wow, thanks!
It has been a minute since I made one, but that is one of the techniques I used to create binaural beats brainwave entrainment. I knew instantly that those two tones were going to 13 hz apart and if you listen to it long enough your brain will focus in on that 13 hz beating and sync with it through the process of entrainment. 13 hz happens to be in the Beta range and is a good dominant brainwave state for alert regular waking consciousness. It is more often used for frequencies that are inaudible like lower than 10hz. 13hz is within the audible range for many. I had never thought about the additional beats that are being generated by the harmonics, but it makes sense. Some people suggest that particular frequency ranges of tones are best to use to create the effect and also with the binaural beats many people recommend that the 2 tones be panned hard left and right. I am not sure why this would increase the effect but maybe there is a biological reason I do not know of. The effect is definitely created when the two tones are combined as you illustrated, whether the tones are coming into your brain from your left and right ear, or not. Something is happening 13 times per second when those two notes are playing at the same time and if you give your brain long enough it will sync into that cycle. Even if it doesn't hear it as a sound, it does as a rhythm.
I do understand these simple examples, and have for years. And it all rapps up in this simple to understand package.
The assumptions:
1. We attach great importance on lower frequencies. Thus we name the note after the first frequency in the harmonic series, and a cord after lowest note.
2. We finde "simple/who number" frequency ratios pleasing. Especially 1/2 therefore we have the octave as the building blocks and consider the note to be the same if the frequency is doubled or hafted.
3. Sadly the maths do not add up. We cannot have 1/2, 1/3 and 2/5 at the same time for all 12 notes. Since we have chosen the Octave as the most important the best we can do equal temperament. (we can do better if we only use 7 notes and don't care about the octave, just intonation)
But the think is... When you start to look at tuning, a song og just a single instrument playing, then you have to "look over" some details for the story to keep making sense.
Ok our brain likes simple intervals and it hates two frequencies that are close to each other. (do to beating). But we tune in equal temperament, thus some of the frequencies are a little of. On a instrument like the Guitar your not even able to tune to a perfect equal temperament tuning (unless true temperament trets and some luck). Thus when actually playing the guitar non of the frequency ratios are 1/3 and 2/5, the best you can hope for is for a clean octave 1/2.
And when you actually look at a song, that you think sounds pleasing to the ears the frequencies are all over the place. You have human singing, drums, base, guitar/piano coming in and out multiple time each second all with there own harmonic series. And it is even difficult to talk about frequencies because they are chaining so fast, so when looking at a EQ you have easily >10 significant frequencies at any giving time and finding the simple frequencies ratios becomes very hard.
So my problem is that there are quiet a long distrance from theory to practice. All the simplified examples makes sense to me, and when making actual music the octave, perfect fifth, Perfect fourth etc. are super useful. But in practice the simple ratios are nowhere to find, it seems to me to be an oversimplification.
Just read first few chapters of Gareth Loy's Musemathics.
As a side-topic to this, it would also be super-exicting (at least for me as none-traditional musician), to learn more about the psycho-acustic behind frequency combinations and western versus asian/african scales. I mean, asian/african music often sounds more or less unpleasing to western ears (and vice versa), but thats just how you grow up. But the science behind this would be really interesting especially for someone, who didn´t went to a music university. Probably there is already a lot of material on the web about this... But you have the ability to bring those things in a brief way to a good "level of understanding" for people! Thanks a lot for your big effort!
For example, Rytis Ambrazevicius has some papers about dissonance vs roughness in the Lithuanian tradition
I love your videos a lot! thank you for your hard work
Critical Bandwith theory and Sethares Theory of Dissonance has entered the chat
Such nice explanations.. thanks!
thank you for your interesting videos
thank you!!
Very clear and concise 👌
Glad you think so!
Video Idea
Hi Jeff,
I really like your channel, I think you are an excellent educator.
I'd like to suggest a video idea, which is related to the subject of "sound", or more precisely how the sound is physically created to our ears from voltages.
Recently, I came to understand the connection between waveforms (like square waves) and their impact on speakers. For instance, a square wave causes the speaker's magnet to rapidly switch between zero and full strength, creating a "ticking" sound. Multiply this "tick" 440 times per second and you get the A note. I haven't found any videos that illustrate this well. You could also add explanations for other wave types.
Another idea, perhaps for the same video, is to explain the speaker movements and their effect on the amount and types of harmonics in different wave types. For instance, why there are no harmonics in a sine wave, more in a triangle wave, and even more in a sawtooth wave.
I hope you find these ideas interesting and consider making a video about them.
Thanks
Wow, I'm so glad the algorithm recommended this video! Now I'm checking out all your older videos and so far loving every one! Thabks so much for making them!
I wonder if there can be FM done with inharmonic spectrums
There absolutely can, and I'll be talking about that in the next video - which I'm starting work on today :)
This is awesome. What is patch, oscillator?
Yo hol up there's a relationship between volts and octaves?
With modular synthesizers, yes. Everything in modular is just voltage, including pitch, which is measured at one volt per octave. I have a video about it (including volt-per-octave) here: czcams.com/video/RXQFrs4f8tU/video.html
An oscillator is a bit of hardware or software that outputs a repeating waveform, like a sine wave or a square wave. A 'patch' is the organization of the various pieces together.
I'm not sure I understand your point about Eurorack. My sequencer and my quantisers can be used in any scale I choose. Actually it seems to be (the default behaviour of) MIDI that seems to keep us all stuck in 12EDO.
I'm also not convinced about the ratios anymore. Or not perfectly satisfied, anyway. A 12EDO fifth really doesn't sound _that_ horrible, despite involving irrational ratios, and small amounts of frequency shift applied to non-sine waveforms (which results in inharmonic harmonics…) can sound good, too. So … the explanation is not complete.
You are absolutely right about quantizers, etc. My point was just that since the default definition of pitch in eurorack is simply "1 volt per octave" that leads to a simple implementation that is equal tempered. But, get a microcontroller involved, and you can set it up any way you want. I did actually have an extra paragraph in the original script just about it, but I felt it was more noodly than I really wanted to get there. Good catch.
@@SoundVoltage The reason it jumped out at me is that one of the reasons I like eurorack as a playground is the logarithmic analogue pitch representation, which lets me do microtonal (and root-varying) things without, say, writing code (which is too much like my day job). And since I like listening to things I _haven't_ been listening to all my life best … well. ;)
If a 12EDO fith would sound horrible, the system would be unusable. There is a tolerance-range for the exact tuning. Plucked strings don`t have perfectly "harmonic" harmonics either, for example Piano and Guitar.
@@johannalvarsson9299 I actually tend to dislike (that's a big strong. Disprefer maybe) pianos, precisely because they are so jangly and out of tune sounding. But my point is that the idea that there is a tolerance-and I agree that there must be one (a) on physiological grounds and (b) if 12EDO doesn't drive everyone insane-then the story about frequency ratios _cannot_ be the exact story. Irrational ratios and very small differences in particular do not _automatically_ sound extra bad, as the naive interpretation of the maths implies. At very least there are things to be said about windowing in the frequency domain or shunting beat frequencies into places where they are inaudible. But it's also possible the whole description is not really right (just as the popular mythology of 12EDO is a big fib).
If you see what I mean.
Sorry, but my brain prefers the beating 13 times a second…
You explained the qualities that differentiate the two chords, but you didn't explain why we find one pleasing and the other harsh. What about music that uses dissonance deliberately? Anyways, it's not a big deal because you probably were meaning to explain why we can tell a difference and why one sounds organized and the other sounds not-organized.
Why do the minor 2nds in this song sound so badass? czcams.com/video/pjl5AKpsDoU/video.htmlsi=-xx22cNEzhjwF6go
I'm not even sure those are minor seconds, but for sure it's possible to use them for emphasis, as a dramatic break from what was "normal". Music doesn't have rules so much as strong suggestions, and some of the best results comes from breaking them. Great song! I mean, they're no Tool or anything... :)
meat circuit incompatible signal. EROORORORORORRRRR
Have you tried turning it off and on again?
@@SoundVoltage every night, lol
ensisted maths. also and you cover it, the same maths largely works for beats. moreover you cover the psychoacoustic "it's something else, missing a fundamental" (enter Ogg chat), The only real issue I have with this video is the assumption that all humans "enjoy" this: Abstract composers, jazzers, and indeed just the living exceptions strive to go further down any road that IS NOT THIS, be it via feel, dissonance, rubato, inferred tones, microtones, or just a really well designed synth patch or prime numbered beat patterns and a 10 gamelan jam, all of differing tuning.
You discuss the audio bubble gum core of cheawble tree saps not the bad for you and delicious man made flavourings we truly crave. So, other than a 100% disagreement about that being "pleasing", have to agree with everything you said. decent video. good level. easy to access.
And totally, utterly wrong about what is "pleasing". ;)
Teaching people something new is generally best served focusing on the 90% case. Yes, there are free-jazz-squee-squonkers and microtonal noodlers, and people making whole pieces out of the sounds of broken glass. And I like a lot of that. But it's not where you start the lesson.
And though I said in the video that this sort of thing is "used sparingly", it's a fair criticism to say that I should have at least mentioned that there are people specifically looking to break these "rules".
However, if the viewer is one of those people, then this gave them a few tools they can explore deliberately instead of just turning knobs until they get the crunchy sound they want. THis is going to come up more in the followup video more specifically on FM, I'll mention it then.
@@SoundVoltage to be perfectly fair. your knowledge was 100% and frankly 110% spot on. my hat was and is doffed. But the label "pleasing" still grates.
It's so sheeple. Platoon arms.
might I suggest the term "relieving" since it really only has this role when in the face of "tension".
well met. You are spreading knowledge and that is ever a good thing.
I'll agree 100% on tension and relief/resolution. :) Thanks for watching!
i wanted to like this video but atm the like count is 420 so i can't ❤
I appreciate the sentiment, but since I'm at 425 of so now?? :) LOL. Glad you're enjoying the videos!
Adding all this negative connotation is so misleading and is one of the worst practices in music education. You could leave all of that out and keep all the other descriptions and explanations in and be left with the result you should have produced. "Our brains don't like that" should be something like "the difference tones are too close for our perception systems to integrate, so we hear something different, which is this cycle of 13 swells per second, which is perceptually summed into a new, emergent pitch," or some thing like that... It isn't bad, it isn't ugly, it isn't poop, our brains just don't function in a way that allows accurate perception of those small intervals............
Yes, this. I am not interested in the prescriptivism that I find entirely too prevalent, and have enjoyed this channel's other videos in the series for their descriptive approach.
@@oiartsun I have to say, the delivery and overall straightforward writing really lend to an enjoyable educational experience. I'll probably watch some more videos on this channel because of that alone.
@@oiartsun No one says that our brains hate video below 60fps, they just say it's lower quality video... No one calls the impossible task of perceiving above 60 or even 200fps something that "our brains don't like" because the real stimulus moves too fast for our perceptual systems to fully perceive and integrate informationally... You get what I'm saying