Hi,

I am confused about how it's called what I am looking so that is why the messed title.

I am looking for a compressive list of the mathematical qualities of different instruments.
For example, I know the harmonics of each instrument are different and sometimes pretty particular.


And also that there are many other values as envelopes and very cool stuff as the Karplus-strong string synthesis formulas that recreates mathematically the sound of a guitar, obviously it's not perfect but actually this is very cool and interesting I hope you can help me to find more formulas or algorithms like this one.

So first I need to find a list something like this

Code:

instrument  tonic    harmonic1 harmonic2 harmonic3 ..... harmonicx
Violin      0.8 db   0.5db     0.35db    0.3db     ..... 0.xdb
Guitar      0.9 db   0.5db     0.35db    0.7db     ..... 0.xdb
Piano       0.7 db   0.6db     0.55db    0.2db     ..... 0.xdb
....        ....     ...       ...       ...       ..... ......
instrumentN n0       n1        n2        n3        ..... xn 

And second anything like the Karplus-strong string synthesis (formulas, codes or scripts) I am not looking for a closed app or vst.
http://amid.fish/javascript-karplus-strong (Javascript demo using the web audio api)

 

Last edited: Jul 10, 2021

From theory to practice! The Karplus Wave is in the Reason - Europe VSTi.
I made a soundset with 200 presets and used the Karplus-Strong Wave very often.
It sounds exceptionally good and is a real step forward for me.

Chapter 4: The Synthesis of Sound by Computer // Section 4.9: Physical Modeling
http://sites.music.columbia.edu/cmc/MusicAndComputers/chapter4/04_09.php

The TAO Soundbank By Che For The Europa by Reason Synthesizer (Free)
https://www.kvraudio.com/product/tao-soundbank-by-che-for-europa-by-sonic-sirius

 

About the subject, do you know the right name for that particular set of harmonics of different instruments? i am sure someone compilated all the info in a webpage, I saw these data each time in many books, but just as example, few instruments as in the picture.

 

For more about harmonics, we recommend Yoshinori Ando's Instrument Acoustics and Atsushi Hashimoto's The Science of Instruments (Blue Backs series).

Sorry / some Links for the Google Translator:

www.lehrklaenge.de/PHP/Akustik/Obertonspektrum1.php
www.oberton.org/obertongesang/die-obertonreihe/
www.bonedo.de/artikel/einzelansicht/eq-frequenzen-und-frequenzbereiche-von-instrumenten.html
https://die-orgelseite.de/registertabelle.htm

 

Last edited: Jul 11, 2021

@BEAT16 it's the same that I found before, just mentions to certain harmonic arrengement, what I didnt thought about was something called instrument character in orquestration, that are the different timbres or playing modes of instruments that also change the harmonic arrangement, I was also looking for formants, that is sort of a natural 3 band EQ for human voice, I chant almost eveey day, and I play with different timbres, I can't do singing overtones but I was amaze I can do so much change in the harmonic spectrum, also I still dont know the reason of what I call metallic voice, that in the spectrum shows a second arrangment of harmonics starting from a perfect fifth, more than 40 harmonics in that way. I will post about when I know more about.

 

Last edited: Jul 12, 2021

Hello @GabsIT, I think it's exciting that you can still research and discover something.

Instrument EQ frequencies and frequency ranges // Use spectra / tone ranges in Hertz for equalizing
Which frequencies are characteristic of individual instruments?

https://www.bonedo.de/artikel/einzelansicht/eq-frequenzen-und-frequenzbereiche-von-instrumenten.html
https://translate.google.com/transl...en-und-frequenzbereiche-von-instrumenten.html

photo hosting

 

How this it's applied to my research/app it's quite simple but maybe hard to explain.

1.- Current music theory it's based in linear harmonics, harmonics that happen naturally in strings.

2.- TET12 it's a standard just to being able to play in any key, sacrificing perfect harmonics using instead tempered frequency approximations.
3.- In a normal scale of 7 notes in TET12 there is always a wolf sound, the tritone, for example in C mayor it's the B, this by maths and ear sound dissonant.

The observation is that the closest of the natural harmonics, the more harmonic that sound the melodies, this is interesting when playing EDO4 or EDO8 (equal interval of frequency, not tempered)

Example:
EDO4 using freqs 440 550 660 770 880
EDO8 using freqs 440 495 550 605 660 715 770 825 880
This fits exactly with the harmonic progression of strings, naturally it sounds rare and too perfect no dissonance when playing pure tones (sin waves without any harmonics)

Now there are many mathematical relations but the most obvious thing is that the waves encounter at certain points, as analogy, if the frequencies are beats per seconds, so no sound but rhythm instead this is much more obvious, rhythms must match at certain points a bmp 120 with something in bmp121 will naturally sound odd or out of rhythm.

From here it's obvoius that 12TET is restricting some interesting and natural frequencies that are more harmonic than what 12TET a example of this happens around the seventh or sixth and the second and minor third.

But doing experimentation with sine waves I realize that all this perception of harmony is directly related to harmonics so I suspected that other kind of harmonics could exist and could be interesting to find the logic instead of trying blindly and in fact existed, non linear harmonics could be classified as 2D harmonics 3D harmonics and beyond so the mathematical relations are there for multiple dimensions and this is fantastic as inclusive is not well known as happen with "making plasma from grapes"

So using these other relations as example I can create a slider to move slowly following a mathematical pattern.

So this is a second experiment, using other set of harmonics non linear, the perception of harmony will be affected? what about the middle ranges between linear and non linear?

I found this using pure sin waves, without any trace of the harmonic that produce the fifth, any frequency close to it not sound wolf at all, this surprised me so I presume 2D harmonics could be very interesting.

and more natural findings, speakers, mics, and almost all audio use a 2D surface to create pressure waves and that naturally create non linear harmonics, and has no relation with linear harmonics, so most probably I will find much more interesting things as it's not a random set of harmonics but instead a very present one.

4.- Harmonics never have the same amplitude in organic or natural medium.

This is also important as this also dictates harmony if the tonic has less amplitude that the third harmonic will be obviously be perceived as a fifth of the original sound (following human perception of the amplitude that is also non lineal, near subsonic and ultrasonic the perception of amplitude is severely diminished)

So I also need real data here, real examples, it's not about creating a square, saw or triangle wave using harmonics, it's also not about using human voice formants data that it's incomplete as it only tells around where the peaks are in the harmonic spectrum, (anyway better than nothing) so the more accurate the data the better the results.

This is why I asked in the top for something like this

Code:

instrument  tonic    harmonic1 harmonic2 harmonic3 ..... harmonicx
Violin      0.8 db   0.5db     0.35db    0.3db     ..... 0.xdb
Guitar      0.9 db   0.5db     0.35db    0.7db     ..... 0.xdb
Piano       0.7 db   0.6db     0.55db    0.2db     ..... 0.xdb
....        ....     ...       ...       ...       ..... ......
instrumentN n0       n1        n2        n3        ..... xn 

and much better a full digital approximation to natural instruments and with the data I could easily find patterns transposing it into any of the other sets that I am using.

I already found the formants, and a basic demo I still need to find some sets of harmonics per instrument I repeat, data as this preferably more than 20 harmonics

Code:

instrument  tonic    harmonic1 harmonic2 harmonic3 ..... harmonicx
Violin      0.8 db   0.5db     0.35db    0.3db     ..... 0.xdb
Guitar      0.9 db   0.5db     0.35db    0.7db     ..... 0.xdb
Piano       0.7 db   0.6db     0.55db    0.2db     ..... 0.xdb
....        ....     ...       ...       ...       ..... ......
instrumentN n0       n1        n2        n3        ..... xn 

 

Last edited: Jul 12, 2021

There's a nice paper about that:
https://www.researchgate.net/profil...strument-Sounds.pdf?origin=publication_detail

It focuses on analysis rather than synthesis but the concept can be re-used for sound synthesis as well. And since you're free to choose your own favorite samples, this looks like a flexible means of classification.

 

Thanks! I though pretty similar as in the paper, harmonics only had 3 notable values, frequency, amplitude and phase (no idea how this apply to natural instruments, but a must in electronic ones) reading I also remembered that some old languages had a noise generator so only 4 possible values, adsr could be manipulated per value, per harmonic or to all the set, that is what it's described in the paper, i didn't thought about the maths bit adding the phase probably will be an improvement, I don't know yet if phase could be detected juist by sound

 

Last edited: Jul 12, 2021