Good day Gentelmen.

I'm reading the csound book chapter about gen functions and there are all
these mentions about chebyshev polynomial functions, quasi-guassian curves,
Fourier transform etc. Now i have no idea what those are and of their use in
csound or anywhere else (well i kind of know that fourrier has something to
do with adding sines to make a complex wave, but the math is beyond me). My
math backround is mostly non existant (6th-7th grade? not even sure), so i'm
not sure how much of it i have to know to further my csound knowledge, i
guess i could function with the knowledge that i have now (for music
purposes), somewhat, but as i stated, i want to know as much as i can. So
with that in mind it's kind of hard to read some sections, where i don't
even understand what is being talked about.

My questions is, do i, and how much do i need to know those exotic terms in
csound and where should i start. I'm currently reading Musimathics first
volume where it lightly touches aspects of trigonometry (haven't read it all
yet) and trying to brush up on some basic caveman algebra in youtube videos.





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Well i have nothing against learning math, i actually want to learn it very
much, since i want to break that  damn curse that plagued me from my
childhood, where i thought that i'm just not talented (a term i don't use
anymore) enough to understand math (i also thought that math is just useless
dry formulas). The main problem however is that i'm not sure how, where and
how much effort has to be put in... hm, i don't even know what i need to
know, there are many branches of math and all of them would take me a life
time (which i don't mind, i just want to at least use it in this lifetime he
he). 

I actually tried to read various books on algebra, geometry and studied a
bit of math in college (terrible experience not knowing anything and getting
shouted at by the lecturer). But i am always missing some things, feeling
confused and don't understand where the particular math is used in real
world.  

And John, did you mean The Audio Programming Book?



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musimathics by gareth loy is an excellent book in my opinion. the second 
volume is also about fourier transform, if i recall correctly.
	j


Am 28.04.2014 13:19, schrieb Askwazzup:
> Good day Gentelmen.
>
> I'm reading the csound book chapter about gen functions and there are all
> these mentions about chebyshev polynomial functions, quasi-guassian curves,
> Fourier transform etc. Now i have no idea what those are and of their use in
> csound or anywhere else (well i kind of know that fourrier has something to
> do with adding sines to make a complex wave, but the math is beyond me). My
> math backround is mostly non existant (6th-7th grade? not even sure), so i'm
> not sure how much of it i have to know to further my csound knowledge, i
> guess i could function with the knowledge that i have now (for music
> purposes), somewhat, but as i stated, i want to know as much as i can. So
> with that in mind it's kind of hard to read some sections, where i don't
> even understand what is being talked about.
>
> My questions is, do i, and how much do i need to know those exotic terms in
> csound and where should i start. I'm currently reading Musimathics first
> volume where it lightly touches aspects of trigonometry (haven't read it all
> yet) and trying to brush up on some basic caveman algebra in youtube videos.
>
>
>
>
>
> --
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>
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>
>
>
>


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joachim-3 wrote
> musimathics by gareth loy is an excellent book in my opinion. the second 
> volume is also about fourier transform, if i recall correctly.
> 	j

Oh yes, i love it, though i'm not sure if i will be able to crack the second
volume with my current knowledge. And even though there are no exercises in
the first volume, i try to write down and play around with the examples, but
i feel that one has to write out many more exercises to get a good
understanding on the subjects.



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So, getting back on the original question. How about those funky terms
(Chebyshev polynomials etc). Will i need to know calculus to crack them, or
is precalculus trigonometry enough. 



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  2 
  3 ; Select audio/midi flags here according to platform
  4 -odac  ;;;realtime audio out
  5 ;-iadc    ;;;uncomment -iadc if realtime audio input is needed too
  6 ; For Non-realtime ouput leave only the line below:
  7 ; -o gen13.wav -W ;;; for file output any platform
  8 
  9 
 10 
 11 sr      =       44100
 12 
 13 kr      =       4410
 14 
 15 ksmps   =       10
 16 
 17 nchnls  =       2
 18 
 19 
 20 
 21                 instr   205                                             
 22 
 23 ksweep  linseg  0, p3*.5, .49, p3*.5, 0 ; INDEX SWEEP FUNCTION
 24 
 25 aindex  poscil3 ksweep, p5, 2           ; SOUND TO WAVESHAPE
 26 
 27 atable  tablei  aindex, 26, 1, .5       ; WAVESHAPE aindex
 28 
 29 knorm   tablei  ksweep*2, 27, 1         ; MAKE NORMALIZATION Fn
 30 
 31 kenv    linen   p4, .01, p3, .02        ; AMPLITUDE ENVELOPE
 32 
 33                 outs            atable*kenv, atable*kenv        ;
NORMALIZE AND IMPOSE ENV
 34 
 35 endin
 36 
 37 
 38 
 39 
 40 ;8192 POINT SINE
 41 
 42 f   02  0   8192    10  1
 43 
 44 ;WAVESHAPING FUNCTION
 45 
 46 f   26  0   1025    7   -1 256 -1 513 1 256 1
 47 
 48 ;AMP NORMALIZING FUNCTION
 50 f   27  0   513     4   26 1
 51 
 52 
 53 
 54 i   205 0   3   20000   440
 55 
 56 i   205 4   .   .       220
 57 
 58 i   205 8   .   .       110
 59 
 60 
 61 

Since i already created the topic, i will waste no more space on a new one
and ask about this instrument above.

What i understand:

aindex reads half the table until value ".49". Since all the partials are
above just 0.5, when poscil reaches the .49 mark, the  atable  offset value
of ".5" kicks in, and aindex is able to scan all the partials.

What i don't understand:

Is how does that offset kick in only when aindex reaches the ".49" mark and
why does one need "knorm" table? I tried to remove knorm and nothing
changed. 



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On 4/28/14, 7:53 , Askwazzup wrote:
> Well i have nothing against learning math, i actually want to learn it very
> much, since i want to break that  damn curse that plagued me from my
> childhood, where i thought that i'm just not talented (a term i don't use
> anymore) enough to understand math (i also thought that math is just useless
> dry formulas).

this is an excellent start, forgetting about what you have been told
about your abilities and just diving in. as others have said, once you
can open up to it, there is no end to fascination.

if you are going to work with computer music, though, you've pretty much
got to have some understanding if you want to do more than tweak
controls that others have designed. nothing wrong with this, and the
musical output can be very nice this way. but you have to be kinda lucky ...

i'd suggest you start with something that interests you. as you may or
may not know, there are only about a zillion ways you can apply math to
the making of interesting sounds to listen to.

you will probably have to keep going back, to learn building blocks, but
this too will end eventually. and then you'll know ...

but as long as you keep working at it, you will grow. and your music
will change too ...

jpff wrote
> Depends what you want to do with them!  Their interesting properties  
> come from calculus.
> 
> They are generated by simple recurrence relations
> 
>      T_0(x) = 1
>      T_1(x) = x
>      T_{n+1}(x) = 2xT_n(x) - T_{n-1}(x)
> 
> or the more complex
> 
> T_n(x)=cos(n arccos(x))
> 
> but what makes them interesting is
> a) they are orthoginal (weight sqrt{1-x^2} )
> b) they are useful in approximating other functions.
> c) etc
> 
> The wikipedia page is rather long and too complicated I guess.
> 
> If you are starting to get maths for audio really you should start  
> with the complex numbers.

Tried to follow what you wrote in the first paragraph, but most of what i
kind of understood is that the function redefines itself . Don't know much
about recurrence or what does orthoginal mean, but thanks.

Complex numbers as in PI, E, sqrt2?


\js wrote
> you will probably have to keep going back, to learn building blocks, but
> this too will end eventually. and then you'll know .

Yeah, i pretty much had to do it this way with music theory, since i started
out from 0. I guess this will be the same - no work no gain. 




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On 4/28/14, 10:32 , Askwazzup wrote:
> no work no gain.

i know it's not particularly popular, but this has been my experience.

Michael Gogins-2 wrote
> If you are serious about learning math, take some courses with good
> teachers. Finding the good teachers is the hard part. The reason I say
> this
> is that to learn math you have to do the problems at the end of each
> chapter, and it take extraordinary self-discipline to do that on one's
> own.
> 
> What you need for understanding audio signal processing in reasonable
> depth
> is algebra, polynomials, Fourier transforms and digital filters, and the
> beginnings of differential equations.
> 
> One book that looked good to me A Digital Signal Processing Primer
> http://www.cs.princeton.edu/~ken/.
> 
> Here's the analog box I was talking about:
> https://code.google.com/p/analog-box/.
> 
> The YouTube video about digital sampling is
> https://www.youtube.com/watch?v=zakAgGXTClU. There are a number of good
> videos by Erik Bardy.
> 
> Regards,
> Mike

Thank you Michael, i will look it up.




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genell wrote
> Complex numbers are usually denoted by an i or a j, which is defined as
> i^2=-1
> A ordinary (not complex) number is either positive or negative, and if you
> multiply such a number with itself it is always positive (-1 * -1 = 1 and
> 1
> * 1 = 1), so there is no ordinary number that you can multiply by itself
> and obtain a negative number. Enter the complex numbers. They seem strange
> but are very useful for many somewhat advanced problems. One such problem
> is the solution to the wave equation which governs the properties of sound
> waves.
> 
> Othogonal functions (such as Chebyshev as well as sin and cos) are
> functions that in a simplified analogy are independant in the sam way that
> width, length and height are independent. You can move straight up (e.g.
> in
> an elevator) without needing to move left, right or forward,backward.
> Orthogonal functions are also useful as solutions to complicated equations
> of motions, thermodynamics and not the least sound (or quantum physics,
> which also uses the wave equation). So, in essence, chebyshev funtions are
> good for e.g. physical modelling (e.g. make tones vary in a manner
> descibed
> by how heat spreads in a solid object) or for just having numbers varying
> in a fashion more interesting than a straight line.
> 
> John's example above is how to calculate numerical values of the chebyshev
> function, and is (i assume) how it is implemented in the csound source
> code.
> Now I'll let John and his esteemed colleagues here point out all my errors
> - I'm not a mathematician...
> 
> Regards,
> Anders

Ah, i was mixing up complex numbers with irrational numbers..

Thanks, that cleared up some things (both paragraphs). So i guess part of
why we need this is because the the sinusoid moves between values of - to +
and so the calculation needs complex numbers?




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On 28/04/14 16:04, Askwazzup wrote:


It is possible to get some idea of what the filters do just be reading
up on how they were arrived at (what problems they were trying to
solve), even without the maths.

The filters have various properties
 1. How quickly they roll-off (i.e. for a low pass filter how fast the
transition is in the frequency domain from passing frequencies to
removing them)
 2. How flat the filter is in the passband (ripple) or the stopband
 3. How the filter affects the phase of different frequencies

So Butterworth filters were designed for maximally flat response in the
passband, but do not have a very fast roll-off

Bessel filters are designed for maximally flat phase response (which
means the frequencies all get delayed by the same amount in a sense).

Chebyshev filters were designed to optimise matching to a particular
frequency response *but* allowing ripple in the passband

Elliptic filters have very good roll-off, and equal amounts of ripple in
the passband and stopband.

The trick then is to relate those parameters to musical effects.

This will probably start a massive argument(!) but as a rule of thumb

A very fast cut-off in frequency implies that sharp transients in the
time domain (e.g. from a glockenspiel) will get "smeared" out.

Filters designed for optimum phase response are good for matching delays
(hence stereo image) but don't cut off as fast.

Filters with ripple will cause amplitude variation as you sweep up and
down in frequency.

regards
Alan

el 2014-04-28 a las 18:01 jpff@cs.bath.ac.uk escribió:

> I do agree with Michael about the Princeton book of audio DSP.   I  
> started there (DSP not being in the Maths Tripos) and my students,  
> both maths and non maths found it a good introduction.

yes, steiglitz is a very good book indeed.

i always recommend very specially steven smith's The Scientist and
Engineer's Guide to Digital Signal Processing. you can buy the printed
book, or download it in pdf format for free from here:

http://www.dspguide.com/



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Already reading the first chapter, thank you Luis. 

It's a shame that our lives are so short, the books that i want to read (and
things i want to learn from them) could make a separate book just out of the
titles alone. If by any chance, anyone here is a vampire... i'm all in for
the ride... just throwing that out here he, he..


Alan Peter Fitch wrote
> It is possible to get some idea of what the filters do just be reading
> up on how they were arrived at (what problems they were trying to
> solve), even without the maths.
> 
> Chebyshev filters were designed to optimise matching to a particular
> frequency response *but* allowing ripple in the passband
> 
> Elliptic filters have very good roll-off, and equal amounts of ripple in
> the passband and stopband.

By ripple you mean some sort of amplitude changes? I'm not really sure what
that means. 

Thank you, great pointers. For some reason i never thought about these
details, i just knew what a bandpass, cutoff freqauency, or resonance meant.



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On 29/04/14 12:30, Askwazzup wrote:
> 
Alan Peter Fitch wrote
>> It is possible to get some idea of what the filters do just be reading
>> up on how they were arrived at (what problems they were trying to
>> solve), even without the maths.
>>
>> Chebyshev filters were designed to optimise matching to a particular
>> frequency response *but* allowing ripple in the passband
>>
>> Elliptic filters have very good roll-off, and equal amounts of ripple in
>> the passband and stopband.
> By ripple you mean some sort of amplitude changes? I'm not really sure what
> that means. 
>
> Thank you, great pointers. For some reason i never thought about these
> details, i just knew what a bandpass, cutoff freqauency, or resonance meant.
>
Yes - the diagrams on Wikipedia are nice, for instance see
https://en.wikipedia.org/wiki/Elliptic_filter for the Elliptic filter.

All I'm saying really is that you can get an intuitive feel for what
different filters do without understanding the maths - as other people
have said messing about with an analogue synthesizer is a good way of
learning.

Of course if you need to design a filter to a particular specification,
you'll need some mathematical understanding. Even if you get a computer
program like Matlab (or Octave) to do the design for you, it will help
you to understand what the program is outputting,

regards
Alan