Demystifying spectral analysis through additive synthesis - Ep. 06

What does it mean to perform a spectral analysis/Fourier analysis? In a frequency spectrum, what are the fundamental frequency and harmonics, and how are they perceived by our ears? If you're unfamiliar with any of the concepts used in this video, watch my previous videos (link below). Starting with the first video, I explain concepts so basic that anyone could understand it :) Complete series starting with basic concepts: https://www.youtube.com/watch?v=4_PIxS4A0cU&list=PLa-whSjdwzxGD-juVFGo4yA4E8VmmpRZ- More about spectrograms: https://www.youtube.com/watch?v=q7MotHfrWEE Versión en Español de este video: https://www.youtube.com/watch?v=o8YtWHE_FEc&list=PLc6BlWWbxqOI9xvXoMedLb8e3KLdk1YZG&index=6 Music: Ricardo de Santiago – Beautiful Chaos 0:00 Intro 1:09 Trigonometric function sine 2:02 Relation between a rotation and the sine function 2:42 Wave summation 3:53 Additive synthesis and Fourier series 4:17 Additive synthesis of a square wave 6:05 Additive synthesis of a melodica 7:32 Spectral analysis (Fourier analysis) 8:41 Frequency spectrum and frequency components 9:49 Frequency components and loudness 10:34 Fast Fourier Transform 11:30 Fundamental frequency and harmonics 12:32 Inharmonic and noisy spectra 13:05 Relationship between Spectrum, Waveform, and Timbre 14:07 Sum of components in phase vs. out of phase 14:42 Loudspeaker frequency range 15:24 Behavior of real sound sources 16:31 Clipping explained with spectral analysis 17:00 Spectral analysis in Audacity 17:37 How to select audio for spectral analysis 19:40 Analyzing varying signals 20:43 Spectrogram and multi-view in Audacity 21:05 Additive synthesis on a synthesizer 22:17 Outro Image and animation references: Car suspension: https://www.vectorstock.com/royalty-free-vector/front-car-suspension-vector-929291 Earthquake diagram: https://www.freepik.com/free-vector/seismograph-illustration-with-earthquake-waves_39652970.htm#fromView=search&page=1&position=35&uuid=d23c3593-9584-4981-acfe-dd355be41388 Light Refraction: https://www.theguardian.com/music/musicblog/2011/aug/26/dark-side-moon-pink-floyd Radio Tower: https://www.freepik.com/free-vector/radio-tower_759860.htm#fromView=search&page=1&position=0&uuid=7fcc617d-5501-4660-a78f-881261f59822 RC Circuit: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-8/high-pass-filters/ Hydrogen density probability: https://www.reddit.com/r/coolguides/comments/hqkkya/this_so_the_probability_distribution_diagram_for/ Interactive unit circle: https://www.geogebra.org/m/nv9vex3X Circle, spiral, and sine animation: https://www.geogebra.org/3d/m4z9ejpt Fourier series square wave image: https://mathworld.wolfram.com/FourierSeriesSquareWave.html Fourier series sawtooth wave image: https://mathworld.wolfram.com/FourierSeriesSawtoothWave.html Fourier series triangle wave image: https://mathworld.wolfram.com/FourierSeriesTriangleWave.html Piano: https://www.freepik.com/free-photo/music-instrument-store_51589620.htm#fromView=search&page=2&position=19&uuid=e5fbd306-f688-477c-b8eb-3bc5930e68e9 Guitar: https://www.freepik.com/free-photo/acoustic-guitar-protective-case-dark-background-top-view_94082662.htm#fromView=search&page=2&position=10&uuid=fb185a25-91a8-42d6-b43f-8331dc063c06 Violin: https://www.freepik.com/free-photo/violin-wooden-textured-table_20989339.htm#fromView=search&page=1&position=9&uuid=608dad9d-c839-41e8-9eaf-b61e0d63ae52 Bass reflex speaker: SVS PB-2000 Bass reflex speaker diagram: https://en.wikipedia.org/wiki/Bass_reflex FFT butterfly algorithm: https://en.wikipedia.org/wiki/Fast_Fourier_transform#/media/File:DIT-FFT-butterfly.svg Bell: https://pixabay.com/photos/bell-church-sky-religion-3652226/ Cymbal: https://unsplash.com/photos/a-close-up-of-a-cymbal-on-a-stage-fTxJC395FpA Electromagnetic spectrum: https://commons.wikimedia.org/wiki/File:EM_spectrum.svg