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This video ROCKS! such explanation Greetings from Brazil

Duuuuuuude! I knew about the reasons for JI ratios being what they are, but I never thought to apply that knowledge to highly anharmonic sounds. In hindsight it is soooo obvious, but I just never thought about it! Thank you!

Love your videos. If I can offer some friendly criticism, when you are comparing the guitar string being stopped at the ends, and the metallophone bars being stopped at some distance from the ends.... this is not the main reason for inharmonicity in the metallophone. Pitched western instruments with high harmonicity of their spectrum, such as marimba and vibraphone, also have their bars suspended at points a short distance from the ends. The difference in spectral properties between different metallophones, including between different western ones, is related to bar shape. The point of suspension is important of course but mainly affects the damping of different modes, it does not shift vibrational modes higher or lower for example.

2:49 i prefer 26tet because it has 7/4 and 11/8

wtf why are the major seconds and minor sevenths dissonant aren't they two stacked fourths and fifths

Hello!! This is an very cool and informative video, I enjoyed it very much. I just wanted to add another reason why tonal percussions produce inharmonic frequencies. In strings (as well as air, for example in flutes), the speed of sound is constant. Since frecuency and speed of sound give you wavelength, and the ratio of wavelength to the length of the medium give you the resonances, then you get these resonances at integer ratios from the fundamental. But for sound traveling across a 2D surface, like a metallic plate, there is a slightly different type of wave that's "creating" the sound, called a "bending wave". An interesting property of bending waves is that the speed of sound can _change_ at different frequencies. Look up the video of throwing a stone on a frozen lake, and you get this sci-fi laser sound. This is a quick downward sweep caused by high frequency waves traveling faster across the ice and reaching our ears first. So for bells, metallophones, etc., the speed of sound varies at different frequencies, again changing the wavelengths of proportional frequencies to non-proportional wavelengths, which causes these shifts in the spectrum to a non-harmonic spectrum.

What an amazing, well-researched video. Thank you so much!

Do they also make these instruments tuned to chromatic (or pentatonic etc) scales? Nothing against the traditional tuning. I just advocate for compatibility. I think people from all over the world should be able to play in tune with each other.

this video is goated thank you so much

A TikToker trying to understand this video would be like a rat trying to understand a closed cycle staged combustion methalox engine.

I had no idea that equal temperament was not harmonically perfect, the way you showed it with the green and yellow lines totally blew my mind. I'm just a casual musician so my understanding of music theory is far from academic. This is incredibly helpful

Wow, this was absolutely fascinating! I had always suspected (like many others I assume) that perception of consonance had to do with a mix of culture, beating and periodicity, but this overview was SO rigorous and well thought-out, and the 3rd clair de lune example honestly opened up a whole new world of harmonic possibilities for me! I would have never thought that you could approach the combination of tuning and timbre in this way (although upon reflection it is similar in nature, but much more extensive, to the end of Messiaens first prelude). It does beg the question for me however, how we would go about accessing these timbres? One way is of course digital synthesizers, but acoustically, pinning down these kinds of partials exactly seems like a daunting task for physicists. Certainly it should be possible, similarly to how gamelan instruments are tuned (like you mentioned in a video of yours) or how church bells are tuned in Europe. How feasible would the construction of such instruments be? Is that a topic you have expertise of? To maybe rephrase the question, do you think you could actually physically construct a piano-equivalent instrument that could play the 3rd clair de lune example?

Very informative thank you

this is basically everything i wanted to do (but didn't know how) when i was reading Tuning Timbre Spectrum Scale by william sethares

Please dont forget Sundanese Gamelan.

In section 7, example 3 was my favorite, it's bell like and sounds beautiful. And it complies with your explanation of the Java/Bali tuning system derived from the overtones of the pitched percussion instruments used in that music.

Does someone knows a text about what he is explaining but in spanish? I can understand some of the information but i guess because the name of the terms are different in spanish I miss a lot of info and it gets harder to follow 😢

9:52 eldritch horror

Excellent video thanks.

This reminds me of how Gamelan music uses instruments that resonate non-trivially, lending themselves to entirely unique tuning systems. When I first learned that, I wondered if timbre could be used to solve pitch drift but, having other things on the mind, put that thought away. I'm very happy to see that others have not merely toyed with this idea, but have successfully implemented it. Bravo!

9:00 in my understanding you have artificially re-mapped the overtones to fit the 12-tet (12 tone equal temperament) notes frequency intonation eliminating the perfect ratio overtones. But, what when such a music is reproduced through any physical mean? Do the perfect ratio overtones come back?

Indonesian musician who can tune gamelan with keyboard/synthesizer is DWIKI DARMAWAN. He is one of the best jazz keyboardist/piano in Indonesia! 😊😊😊

"Timbre" is pronounced "tamber"

for point n.7 of your video, did you generate the streched tuned scale AND your stretched spectrum sample within your app? would love to know how you generated the scale to match your stretched tuning and mapped it to your DAW. Very very interesting work you are doing, kudos

love this! question for future development: could your app create not only a single sample, but a scale that relates to a fundamental and is constructed based on its harmonicity/inharmonicity? Big congrats for your work, it is truly inspiring!

A spectral synth engine like SUMU from Madrona labs might prove interesting to use with the concepts outlined, as you can import spectra into their additive synth directly

All of your videos are extremely detailed and have a lot of work that have gone into them. congratulations on amazing work

Haha this video is amazing! Although it probably will make people with perfect pitch go into a catatonic state 😅

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.

11 minutes to explain what might take up to a year in class!

4:33 I don't hear the guitar as out of tune tbh

yippee 22/32 intonation!

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.

Can I please have a link or URL for the Gamelan Bali site (7:30). Thanks.

"Balinese gamelan has specific tuning peculiarities." Please, please, please, do a video on those peculiarities, or on Balinese gamelan in general.

amazing

Let's make every interval pure through making every note impure! Surely this cannot be serious?

Shut Up And Play Your Synthesizer.

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)

Amazing presentation.❤❤

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...

I love your english speech. Your speech and intonation are clear 😊😊😊

Superb way of explaining the complex topic of music perception.

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!

Is it possible you have removed a few videos? I am looking for one that you did that uses the same graph as 17:56 of this video. I can't find it.

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