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Harmonics Explorer

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Re: Harmonics Explorer

#11

Post by laszlokorte »

Prcmaker wrote: post #9

I like the thing, but it misses what I enjoyed teaching about these most: phase. Many people know white noise is nominally 'all frequencies at the same intenisty', yet those taught Fourier mathematics are also taught that the same recipe makes a pulse. The difference is all in the phase information, and why I maintain to this day the Nyquist-Shannon sampling theorem, as typically applied, is incorrect.

Yes phase information is really important. Try this:

1. Fourier Transform an Image 2. Set all magnitues the the spectrum to 1.0, but do not change the phase 3. Inverse Transform and look at the result 4. Now try the same, but this time keep the maginutes unchanged but change all phases to 0°

Spoiler: When changing all amplitudes the image is still regocognizable, when changing all phases, it is not. See example: [1]

But in what sense are you saying the Nyquist-Shannon theorem is incorrect (when applied)? It only says something about the most general case of perfectly reconstructing a signal.

For getting an playful and intuitive understanding of time/frequency transformations my fourier-cube visualization might be useful [2]

[1]: https://static.laszlokorte.de/phase.png [2]: https://static.laszlokorte.de/frft-cube/

Re: Harmonics Explorer

#13

Post by brk »

xeonmc wrote: post #8
lioeters wrote: post #6

Earlier quoted context omitted.

That reminds me, I saw a video recently of a choir practice where they sang "brighter" and "darker" based on the conductor's hand position. It was fascinating how the singers could control the brightness of their voice while holding the same note and frequency. When they went bright, it sounded closer to "eee" or "iii". When they went dark, it sounded like "uuu" and "ooo". From that, I learned that the lyrics of a so…

You may find this interesting: https://www.youtube.com/watch?v=vC9Qh709gas EDIT: also this https://www.youtube.com/watch?v=FdldD0-kEcc

You may also find this interesting: https://www.youtube.com/watch?v=3oxe4mlsQos&t=120s

Re: Harmonics Explorer

#14

Post by AlecSchueler »

lioeters wrote: post #6
mcqueenjordan wrote: post #3

This is really cool. I used to do a lot of overtone ("harmonic") throat singing and playing with this tool reminded me of those days. For anyone curious, vowels are mostly just how we perceive different harmonic distributions. Put differently, harmonics are the basis of what it means to pronounce a different vowel. The human voice is basically just a harmonic chord, with different distributions of the 2nd, 3rd, 4th,…

That reminds me, I saw a video recently of a choir practice where they sang "brighter" and "darker" based on the conductor's hand position. It was fascinating how the singers could control the brightness of their voice while holding the same note and frequency. When they went bright, it sounded closer to "eee" or "iii". When they went dark, it sounded like "uuu" and "ooo". From that, I learned that the lyrics of a so…

A lot of great music has been written with this in mind, I would highly recommend Stimmung, for six vocalists and six microphones, by Karlheinz Stockhausen.

Really the whole piece is created from a framework of phonetics, loose vowel sounds as well as names taken from the "magical of otherworldly" traditions of various cultures as well as words taken from the composer's own poetry.

Re: Harmonics Explorer

#15

Post by rock_artist »

Prcmaker wrote: post #9

I like the thing, but it misses what I enjoyed teaching about these most: phase. Many people know white noise is nominally 'all frequencies at the same intenisty', yet those taught Fourier mathematics are also taught that the same recipe makes a pulse. The difference is all in the phase information, and why I maintain to this day the Nyquist-Shannon sampling theorem, as typically applied, is incorrect.

Without entering the broader discussion in the comment. I've also missed the ability to change phase for each harmony.

Re: Harmonics Explorer

#16

Post by divan »

xeonmc wrote: post #8
lioeters wrote: post #6

Earlier quoted context omitted.

That reminds me, I saw a video recently of a choir practice where they sang "brighter" and "darker" based on the conductor's hand position. It was fascinating how the singers could control the brightness of their voice while holding the same note and frequency. When they went bright, it sounded closer to "eee" or "iii". When they went dark, it sounded like "uuu" and "ooo". From that, I learned that the lyrics of a so…

You may find this interesting: https://www.youtube.com/watch?v=vC9Qh709gas EDIT: also this https://www.youtube.com/watch?v=FdldD0-kEcc

Thanks for sharing! Didn't know human voice can do this.

Re: Harmonics Explorer

#17

Post by lioeters »

AlecSchueler wrote: post #14
lioeters wrote: post #6

Earlier quoted context omitted.

That reminds me, I saw a video recently of a choir practice where they sang "brighter" and "darker" based on the conductor's hand position. It was fascinating how the singers could control the brightness of their voice while holding the same note and frequency. When they went bright, it sounded closer to "eee" or "iii". When they went dark, it sounded like "uuu" and "ooo". From that, I learned that the lyrics of a so…

A lot of great music has been written with this in mind, I would highly recommend Stimmung, for six vocalists and six microphones, by Karlheinz Stockhausen. Really the whole piece is created from a framework of phonetics, loose vowel sounds as well as names taken from the "magical of otherworldly" traditions of various cultures as well as words taken from the composer's own poetry.

Ooh nice. I'd heard of Stockhausen - attended a performance of his works once - but this is new to me. Very strange music with a wide range of harmonics produced by vocalizations of vowel sounds. Sometimes nasal, other times chant-like, machine-like, and even reminiscent of insects at night.

https://www.youtube.com/watch?v=3hPkJW95jsw

Re: Harmonics Explorer

#18

Post by rcxdude »

laszlokorte wrote: post #11
Prcmaker wrote: post #9

I like the thing, but it misses what I enjoyed teaching about these most: phase. Many people know white noise is nominally 'all frequencies at the same intenisty', yet those taught Fourier mathematics are also taught that the same recipe makes a pulse. The difference is all in the phase information, and why I maintain to this day the Nyquist-Shannon sampling theorem, as typically applied, is incorrect.

Yes phase information is really important. Try this: 1. Fourier Transform an Image 2. Set all magnitues the the spectrum to 1.0, but do not change the phase 3. Inverse Transform and look at the result 4. Now try the same, but this time keep the maginutes unchanged but change all phases to 0° Spoiler: When changing all amplitudes the image is still regocognizable, when changing all phases, it is not. See example: [1]…

I'm not sure the original poster meant, but the sampling theorem is often misunderstood, there's a good article I recommend to most anyone who has the choose a sampling rate which goes into those misconceptions: https://neuron.eng.wayne.edu/auth/ece4330/practical_sampling...

Re: Harmonics Explorer

#19

Post by bigbillheck »

Prcmaker wrote: post #9

I like the thing, but it misses what I enjoyed teaching about these most: phase. Many people know white noise is nominally 'all frequencies at the same intenisty', yet those taught Fourier mathematics are also taught that the same recipe makes a pulse. The difference is all in the phase information, and why I maintain to this day the Nyquist-Shannon sampling theorem, as typically applied, is incorrect.

In the domains that I'm familiar with we never get to measure phase, only intensity. (https://en.wikipedia.org/wiki/Phase_retrieval)

Re: Harmonics Explorer

#20

Post by djmips »

xeonmc wrote: post #12

If you want to go above 13 overtones or make other waveforms, I quickly whipped this up for square/triangle/sawtooth/impulse trains: https://www.desmos.com/calculator/eioaj93rzr

Very nice.
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