Peter Gilliam - Musical Fourier (

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The Fourier Transform is a wonderful piece of math that is out of reach to so many people because it's often needlessly over-complicated for an introductory level. This video is NOT an attempt at a thorough explanation of the transformation, but rather a qualitative and relatively simple one. Additionally, I used this project to experiment with a higher production quality content format, I hope you enjoy/enjoyed it!
The project was most heavily influenced by Grant Sanderson of 3Blue3Brown. The video was also built using a modified version of his software "Manim"
Link to interactive Windows Forum:
github.com/MrMVPeter/C-Sharp
Installation tutorial and showcase video for the forum:
• FFT Application Instal...
Link to his channel:
/ 3blue1brown
Here's a link to my Github where you can find the code for this video along with each of my other projects:
github.com/MrMVPeter
A GREAT resource from 3Blue3Brown introducing the Fourier transform.
My use of the spiral graph was inspired by him. He develops it further in this video:
• But what is the Fourie...
While I'm mentioning 3Blue3Brown, he also introduces the field of Fourier Series, an excellent application of the transform:
• But what is a Fourier ...
I didn't talk much about the Fast Fourier Transform as I had originally envisioned, which Is rather unfortunate. However, the channel "Reducible" has an EXCELLENT introductory video on it below:
• The Fast Fourier Trans...
Lastly, MIT has an excellent online lecture in which he derives the Fast Fourier Transform in much greater detail. If you don't mind lectures and you want to unearth every detail, this is the video for you:
• 3. Divide & Conquer: FFT
There is so much more free online content I thoroughly enjoyed that I haven't mentioned, but the resources above should hopefully be enough to get you started on your journey.
Background Music
Some Royalty free music provided by "FiftySounds"
www.fiftysounds.com/
- Nothing Else
- A Part of Us
- Out of Time
- Little Changes
- The Beginning
- In The Memory
Outro Music Provided by Videvo
- Plain Folk

Опубликовано:

18 сен 2021

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Комментарии : 84

@prikarsartam 2 года назад

Great video! One thing to add, harmonicity of a chord can also be identified if there exists a repeating waveform in it [which in case of examples you provided, was visually identifiable but could possibly require an algorithm for complicated waveforms], otherwise finding its frequencies can also be the way

@petergilliam4005 2 года назад

Yes and no. The music we hear nowadays is equal temperament, meaning the chords never actually have those perfect simple ratios...just close enough to trick our ears. Combine that with chords a little more complicated than I showed, it can be VERY difficult for a computer (hence 'algorithm') to see those patterns. The Fourier transform is the most reasonable way to solve the problem. But great observation! Thank you!

@prikarsartam 2 года назад

@@petergilliam4005 okay, is that why it's NOT just 3-delta functions in the frequency space of a waveform of 3 fundamental frequencies rather a NOISY-3-peak distribution?

@petergilliam4005 2 года назад

@@prikarsartam Pretty much. I didn't compute the transform on a waveform of infinite length. So the lack of a perfect delta function is a result of the wound waveform being unable to completely balance itself around the origin with the length of signal provided. Importantly, in the limit as the length of the input waveform approaches ∞, the transform graph approaches that of a Delta function graph. Oh, and yes, it's noise in the input waveform that creates the noisy three peak transform. But again, with an infinite waveform input, you'd have your Delta function . I hope that helps

@prikarsartam 2 года назад

@@petergilliam4005 thanks, you explained well!

@petergilliam4005 2 года назад

@@prikarsartam I couldn't have asked for a better question, you clearly have some background in the field. Thank you!

@KriegAdler09 2 года назад

It would help to fade out on the background music when you are playing sample sounds (chords) that are acoustically illustrating a point in your video. You may also want to adjust the audio mix so that the background music track is not as loud as your narrative track. The busyness of the music can also be distracting to your narrative.

@Trainwreck3000 2 года назад

that's what i was thinking

@itellyouforfree7238 2 года назад

How clever putting a loud background music while showcasing harmonious/dissonant chords! Very smart, thanks!

@DiracComb.7585 2 года назад

This is a very good video, a nice follow up to 3Blue1Brown’s work. Just one note, I did find at some points the background music overwhelming, and so it was hard to hear your voice sometimes. It isn’t bad enough to make you unhear-able, but it would definitely be nicer to not have to strain my ears to pick out some words. Okay, that’s enough nitpicking.

@petergilliam4005 2 года назад

Ha, I felt so bad about my voice over that I think I was subconsciously trying to cover it up. I totally agree with you and I appreciate the feedback

@DiracComb.7585 2 года назад

@@petergilliam4005 As far as I’m concerned, your voice is great for narration, and your pacing is good. Keep it up 👍

@Michallote 2 года назад

I loved the music! Made for a constant reminder of what was all of this useful for haha

@adheensheikh6896 2 года назад

@@DiracComb.7585 It was a joke

@davidstork5604 4 месяца назад

And words of gratitude to 3b1b, which first showed this way of interpreting the Fourier transform.

@finxy3500 2 года назад

adding two sound waves is not convolution. Convolution is multiplying two functions' Fourier transforms then inverse transforming. you can also think of it as using one wave as a weight function for the other in the time domain. en.wikipedia.org/wiki/Convolution Might be confusing that you refer to addition as convolution, or did I misunderstand something?

@petergilliam4005 2 года назад

In retrospect, that was a huge mistake on my part. Aiming for an elementary explanation, I meant convolution in the traditional English semantic form. But I totally understand that it conflicts the the relevant mathematical definition.

@Firigion 2 года назад

@@petergilliam4005 As a non native speaker: what does convolution in coloquial english mean? Never heard of it outside the mathematical/physical sense. I assume it's not "to make something convoluted".

@sofia.eris.bauhaus 2 года назад

@@Firigion i think he just means "becoming messy/complicated".

@00_002 2 года назад

The video quality is amazing, makes me wonder why this video only has

@petergilliam4005 2 года назад

Thank you! I was expecting ~40 views, so I'll take what I can get. There's a lot I can and plan to do better though.

@LoganMarcosSchmidt 2 года назад

Music in background makes distinguishing the harmonic vs inharmonic sounds you’re playing hard. Distracting

@Sjoerd-gk3wr 2 года назад

this was a very good video, make more of them and i'm proud to say i am your 23 subscriber.

@petergilliam4005 2 года назад

Thank you! I can't actually say I'm too proud of this particular video, the topic could have been more distinct and the voice over could be miles better. But I really hope I can rectify myself

@metacarpo10 2 года назад

That was awesome, i knew about the fourier transform but that draw you made by wrapping the wave in a circle around the origin just shined a light in my brain about the transform i never had thought before, now the formula actually makes clear sense to me, very nice very nice thank you very much!

@rohitkasgar4840 2 года назад

Well, as a guitarist myself, and having a keen interest in maths, this is a delight!

@GimbertLane Год назад

Beautiful video. Thanks

@fidelcertuche8002 3 месяца назад

Thanks for this valuable insight!!!

@filledmug 2 года назад

A pleasant and musical video ❤️

@lekonda5526 2 года назад

Wonderful. I really loved it. Just one thing. I think it would be even greater if you'd lower the intensity of the backroundmusic. Thank you :)

@petergilliam4005 2 года назад

You're totally right, I'm sorry

@afrigal2420 20 дней назад

love it!!

@averagemilffan 2 года назад

Very well done!

@clod2529 2 года назад

Great video, very informative.

@ThankYouESM Год назад

I've been trying a whole lot to create a Python random music generator for far too long with still no progress.

@shaheenainpour1610 Год назад

very helpful video thanks! one thing that's hard for me to understand is at 5:48 when you're describing a chord, I'm not clear on how the 4:5:6 ratio relates to the frequencies 554, 698, 831?

@quadrannilator 2 года назад

Thank you

@felipevale7993 2 года назад

amazing

@brendawilliams8062 2 года назад

Thx. Very nice

@Dziaji 2 года назад

Great video. The only problem is that the background music is too loud. In order to hear the words clearly, I had to turn up the volume to the point where the music was too loud.

@petergilliam4005 2 года назад

Sorry about that, i agree

@Dziaji 2 года назад

@@petergilliam4005 it's ok. I just wanted to point it out in case you didn't realize because some people are audio nazis and they literally will not watch a video that doesn't have properly mixed audio. It would be a shame for people to miss out on this because of a reason like that.

@ogrenciadasukaradag3412 Год назад

HELLLLLLLOOOOO. Can I ask you how or which app did you use to apply Fourier transform and obtain those frequency domain graphs? I NEED IT FOR A MATH PROJECT. PLEASE HELP ME

@Mahdi.alkawaz 2 года назад

The style is clearly similar to 3b1b..but daaaamn so well produced video

@NovaWarrior77 2 года назад

very berry underrated

@Electromowls Год назад

Hi Peter that was an excellent video. I had trouble in understanding translating the time waveform about the origin, is it polar coordinate transformation of the sine wave ? I didn't understand the part where you mentioned about the degree of freedom to change frequency about the origin. Can you please clear that by siting any reference ?

@jaroslavhorvat6307 2 года назад

on the right side we can see change in frequency, on the left we can see change in speed of whole animation implying change in speed of sound

@empireempire3545 2 года назад

like for the program!

@bijoydas6044 2 года назад

🙏 Sir , Please Make a video on How Fourier Transform is the another case of Laplace Transform ?

@petergilliam4005 2 года назад

I actually have done a lot of work on such a project. I think the Laplace transform deserves a good video...it's just a bit of a messy creature. I'm not sure how I want to show him to the world

@mukhtaarjaamac8763 2 года назад

3blue 1brown is the best

@petergilliam4005 2 года назад

No arguments there

@delfikpro7375 2 года назад

Maybe reupload the video with less loud background music before it surpasses 10k views? Would be a great video

@PretTy_Fish 2 года назад

I noticed a typo in the video description: you spelt the channel name "3Blue1Brown" as "3Blue3Brown". Aside from that, the video is well done.

@philcrookes4225 2 года назад

I enjoyed the creativity in this video and learned a few things, although I share the view of others that the piano soundtrack detracts from the experience. (Thanks nevertheless)

@ogSquink 2 года назад

Please consider reuploading the video without background music. It's incredibly distracting and at times quite grating to the ears!

@frankargenti 2 года назад

Isn't this an exact copy of Grant's work?

@IsYitzach 2 года назад

Hardly. It's an extension and application of his work. And I'm sure it was made with Manim.

@timbeaton5045 2 года назад

@@IsYitzach He says so in the description:- ' The video was also built using a modified version of his software "Manim" '

@petergilliam4005 2 года назад

The original vision of this video was supposed to focus more on the FFT, but I found more and more of that getting cut. And in retrospect, it wasn't as original as I wish it was, I hope to rectify that in the future

@ilikemorestuff 2 года назад

How'd you get yer hands on 3blue1browns rendering engine?

@mixnik 2 года назад

It's a python library named "Manim"

@pocolilman1111 10 месяцев назад

Can't believe you don't have over 1000 subs... hope I can help.

@JazzfireflyNZ Год назад

Great video. Thanks for making it! My only criticism is that the background music was a bit too loud (and stylistically perhaps not everyone's cup of tea)

@georgen9755 Год назад

domain ???

@jursamaj 2 года назад

At least twice, you mispronounced dissonant like dissident. Pretty sure I heard a few other such problems. Otherwise, this is a pretty good addition to 3b1b's version.

@petergilliam4005 2 года назад

Omg, doing the voice of for this video was a nightmare. I suddenly forget my native language when the mic is turned on. That's in part why I had the music a little loud. I hope it gets easier, thanks for the feedback

@plekkchand Год назад

Consequently, not consequentially.

@Zildawolf 2 года назад

Majro seventh :)

@solaokusanya955 8 месяцев назад

10:35 I do not understand it please,please

@MarkCassano Год назад

Loved this until around 9:00… that visualization (rounded graph) makes zero sense to me. No clue what you are doing, but it’s pretty to look at.

@kasunb1738 4 месяца назад

great explanation , please get rid of the background music :-D

@user-vu7th7pp1o 5 месяцев назад

I hope I'm well known 😅

@tim40gabby25 2 года назад

"Dissonant", not 'dissident'. Just saying. Chart typo Major 7th needs fixing. Good video :)

@spiralofinspiration3653 2 года назад

I don't understand

@petergilliam4005 2 года назад

I could have done better with the explanation in retrospect, I hope it wasn't a total waste of your time

@cmyk8964 2 года назад

dis-son-ant. dis as in disparate, son as in sonic.

@truthseeker7815 2 года назад

Ok, this is the lowest

@petergilliam4005 2 года назад

Yeah, I'm not proud of it myself either

@truthseeker7815 2 года назад

@@petergilliam4005, the amount of subs is influenced by random factors more important than quality. I met 5 new math channels 2 days ago, and all of you are masterpieces

@lekonda5526 2 года назад

@@petergilliam4005 Why that?