#2871977  08/10/17 04:44 AM
Re: Simple differential Equations
[Re: J. Dan]

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Registered: 11/01/01
Posts: 11973

My experience was that High school covered Algebra and Trigonometry as requirements, though most people who were college bound in any kind of technical field elected to take Calculus....which was sort of the cliff notes version of Calc at an engineering University.
My Engineering degree required in order: Calc 1, Calc 2, Calc 3, Differential Equations, Partial Differential Equations. Sort of separate from those but still required was Statistics. Problem with the Diff EQ classes was that they were very general since all of the various Engineering Disciplines may apply them in different ways  so you may be using it for Thermodynamics, Engineering Mechanics/Dynamics, etc....so they kept it very general in terms of applications.
Now some of the EE classes were basically math classes except offered by the EE department and more applicable. As an example, Diff EQ covered Laplace Transforms, which I found to be less applicable than the Fourier Transforms covered in EE classes. We also had to take a Computer Science class that really didn't involve a single computer all semester and was also all math. It was covered Decision Tree, Game Theory, Shortest Route (Travelling Salesman Problem) etc.
Anyway, at undergraduate level, they just weren't very good at digging into specific music related applications. I took a semester of analog electronics for obvious reason. While we did spend adequate time on things like OTA's for VCO/VCF/VCA, enough for me to be able to design circuits, the professor spent most of the damn semester covering a Tunnel Diode. I'll probably never touch a tunnel diode my entire life. 18 hours of calculous and DE, physics, statics, thermodynamics, etc... I don't remember a single problem or test question relating to music.
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#2871988  08/10/17 05:39 AM
Re: Simple differential Equations
[Re: RABid]

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Registered: 01/28/12
Posts: 2497
Loc: Australia

Well I only have certificates that say for a period of three hours on one day many years ago I was able to demonstrate a pass level in mathematics. All that has since evaporated.
But the bass player I have played with for many years is a lecturer and researcher in bio chemistry. I guess he has a working knowledge of differential equations.
But we both ocassionaly miss chord changes and contribute clams, to our mutual amazement.
So Dear Abby, should we spend more time working on differential equations and less time learning the songs?
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#2871990  08/10/17 05:39 AM
Re: Simple differential Equations
[Re: Theo Verelst]

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nobody seems to know much about what they're doing, except try everything out they can get their hand on, maybe ? That's me. Always wanting something new.
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#2871996  08/10/17 06:07 AM
Re: Simple differential Equations
[Re: Synthoid]

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Registered: 02/27/10
Posts: 3567

Right, it's like this: many processes in nature that involve acceleration (and velocity and displacement etc), have mathematics corresponding to the physics that involve Differential equations. It's like saying the rate of change is coupled with an excursion, in the case of a free hanging swing for instance, and the interesting part is that those DEs are real algebraic equations, with an infinitely accurate solution for a broad class of physical, mechanic and electronic systems.
You could say that a big part of a synthesizer makes sound waves that can be thought of as coming from DEs that are built in the electronics, that's just a matter of one of the ways of designing electronic circuits. Alternately, you can go into approximation techniques that deal with difference equations, nd in some cases you might want to look at (simple..) functional integrals to get exciting waves.
The whole of a sound field, finally, scientifically speaking is like a model of air molecules in 3 dimensions, which can in certain (long known) DE models be computed through, either in approximations or in some modes as algebraic solutions (which is like "infinite accurate" and of mathematical interest).
The processing that usually takes place in Digital Signal Processing, has left the direct connection with these facts in many ways, and that might be "new", but it's hardly accurate.
My interest is at a higher level at the moment, excluding Physical Modeling (I've looked into and like). Harder to explain, but it's like a physical system like a piano has certain fixed properties, in terms of wave making elements, and I hear those get raped (by lackof a better word coming to mind) all the time, in more than one way, while in fact there are also relatively pure differential equation related considerations, like phasing effects, that could make more faithfully reproduced sounds more edible to the human perception.
T.

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#2871998  08/10/17 06:10 AM
Re: Simple differential Equations
[Re: Synthoid]

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Registered: 08/11/06
Posts: 596
Loc: NJ, USA

There are many musicians who are famous, and a bunch more who are not famous but are seen here on this forum, who know even less about music theory than I do, and who may not even read music well. But they kick my a** musically, and no one is lining up to pay money to hear me sight read on the sax. Some of them might be able to improve their musicianship with some extra music theory knowledge, but not by understanding differential equations.
Now if they want to start designing airplane wings, or perhaps design some type of gear, those diff EQs would come in handy.

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#2872003  08/10/17 06:30 AM
Re: Simple differential Equations
[Re: harmonizer]

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Registered: 10/23/14
Posts: 279

In any but the most simple (ordinary?) cases you'll need chaos theory rather than differential equations to describe music (and musical sounds).

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#2872007  08/10/17 06:42 AM
Re: Simple differential Equations
[Re: harmonizer]

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Registered: 11/16/15
Posts: 226
Loc: USA

My interest is at a higher level at the moment, excluding Physical Modeling (I've looked into and like)..... When you cause something to vibrate or resonate (pluck a string, blow into a bottle, etc.) You don't need to know the mathematics to appreciate the resulting sound. Some people were curious enough to mathematically describe it though. A model of a single piano string can be described by the second order partial differential wave equation. But to model the full sound of the piano from first principles, one needs to add the effects of all the other strings (damped and undamped), the soundboard, the driving function (hammers) and then couple in all of the boundary conditions. Do you think anyone did this mathematically prior to building the first piano to ensure it would meet their expectations?
Edited by JazzPiano88 (08/10/17 06:44 AM)
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#2872010  08/10/17 07:14 AM
Re: Simple differential Equations
[Re: Theo Verelst]

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Registered: 05/12/13
Posts: 1033
Loc: Montreal, Canada

it annoys me that there's this whole world out there of discussions about technology and software, and nobody seems to know much about what they're doing, except try everything out they can get their hand on, maybe ? T. Theo, you're tremendously lucky if you can have a higher level of understanding of the science and math behind your passion of sound and music. The lack thereof certainly doesn't make any of us here any less competent to create, listen, and enjoy what we make, and hear, even if provided to us by the keyboard manufacturers. Most of us also drive cars without understanding the physics of aerodynamics or the intricacies of combustion yet still can discuss what features we like or do not like about our vehicles. Most of us take medications without understanding the cellular mechanism of action yet still can discuss side effects.
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#2872012  08/10/17 07:18 AM
Re: Simple differential Equations
[Re: stoken6]

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Registered: 04/03/08
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Loc: Chicago, IL

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#2872037  08/10/17 09:03 AM
Re: Simple differential Equations
[Re: Ulf]

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Registered: 07/25/08
Posts: 10938
Loc: St. Louis, MO

In any but the most simple (ordinary?) cases you'll need chaos theory rather than differential equations to describe music (and musical sounds). This was partially my thought as I was reading Theo's last reply, although chaos theory would only be a small part. Given Theo's example of modeling a piano, I suppose he's thinking you can more accurately calculate mathematically the phase relationships of the waves from each of the strings to a particular listening position, also calculate sympathetic resonance, calculate reflections and resonances from the surfaces within the piano, calculate reflections in the room.....and on and on and on. My guess though is that it's almost impossible to figure out, before even developing the necessary DE's, to even comprehend all of the possible interactions involved and come up with a better result than a properly executed sample with high quality mic's, A/D's, D/A's, etc.
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#2872236  08/11/17 02:21 AM
Re: Simple differential Equations
[Re: Theo Verelst]

Senior Member
Registered: 10/23/14
Posts: 279

In fact some of the A grade records I know to be advanced engineering and science feats.
Absolutely. There's no doubt that excellent, educated and interested musicians and engineers have helped develop a lot of the music technology we now take for granted, just because they had a vision for their art.

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#2872243  08/11/17 03:37 AM
Re: Simple differential Equations
[Re: Ulf]

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Registered: 05/10/11
Posts: 745
Loc: Budapest, Hungary

On the other hand, Fourier analysis really really helps understanding what overtones are and how they work, which is IMO necessary for good sound design, EQing, mixing etc.
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#2872448  08/11/17 07:00 PM
Re: Simple differential Equations
[Re: stoken6]

Senior Member
Registered: 09/09/13
Posts: 178

Interesting topic...during my engineering days at university, I took DiffEQs.
And while I could do the mechanics of thirdorder partial differentiation in polar coordinates, and get the right answer, I'll be damned if, then (30+ years ago) or now, I could explain what it meant.
Maybe if there was mathematica or some other graphic representation of what it was, it might have gelled.
Still, to the OP's point, it probably wouldn't have helped my shoddy skills on keys or synthesis.
Suffice it to say, shortly thereafter, I was asked to leave the college of engineering, where I went to the "weak side" of campus and got a business degree.
And yet, I ended up in an engineering field. Go figure.

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#2872452  08/11/17 08:36 PM
Re: Simple differential Equations
[Re: dje31]

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Registered: 12/04/12
Posts: 1471
Loc: San Diego, CA USA

Nobody whips out their DE and PDE handbook to design complex sounds. No musical person ever even thought to. This thread is absurd.
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#2872453  08/11/17 08:41 PM
Re: Simple differential Equations
[Re: dje31]

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Registered: 11/16/15
Posts: 226
Loc: USA

The fun (partial) DiffEQ stuff happens in the complex analysis.
The proverbial: "Two Pi eye times the sum of the residues" to solve otherwise really difficult integrals.
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#2872455  08/11/17 09:02 PM
Re: Simple differential Equations
[Re: JazzPiano88]

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Registered: 03/11/07
Posts: 282
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#2872457  08/11/17 09:10 PM
Re: Simple differential Equations
[Re: MotiDave]

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Registered: 11/16/15
Posts: 226
Loc: USA

Nobody whips out their DE and PDE handbook to design complex sounds. No musical person ever even thought to. This thread is absurd. On the other hand, viewing the FM equations shows how the HF modulation index increases the harmonic content, acting like opening an analog filter. Yeah it was serendipity, after the fact, that Chowning stumbled onto it. But once it was understood, the rest of FM synthesis was at least partially driven by the mathematical understanding.
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#2872458  08/11/17 09:24 PM
Re: Simple differential Equations
[Re: waygetter]

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Registered: 11/16/15
Posts: 226
Loc: USA

Feel fortunate Otherwise you'd be living in a cave. Or at least the 50's... The diffusion equation, which is the basis for semiconductor fabrication is a partial differential equation describing how the doping impurities diffuse into the bulk
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#2872545  08/12/17 11:20 AM
Re: Simple differential Equations
[Re: JazzPiano88]

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Registered: 12/04/12
Posts: 1471
Loc: San Diego, CA USA

Nobody whips out their DE and PDE handbook to design complex sounds. No musical person ever even thought to. This thread is absurd. On the other hand, viewing the FM equations shows how the HF modulation index increases the harmonic content, acting like opening an analog filter. Yeah it was serendipity, after the fact, that Chowning stumbled onto it. But once it was understood, the rest of FM synthesis was at least partially driven by the mathematical understanding. maybe I misunderstood the OP, as that would be the normal expectation whenever OP posts. But I understood his thesis to state that if we used advanced mathematical equations to communicate musical sounds throughout the musical community, said communication would be improved. I boldly present my alternate thesis: The effectiveness of communication of a particular sound (tone, properties, modulation, etc.) is inversely proportional to the extent of mathematical equations included in the communication. At the lower limit, an attempt to communicate exact "sounds" only in terms of complex multiparameter multiorder mathematical equations will result in a effective communication quotient of zero.
Edited by MotiDave (08/12/17 11:20 AM)
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#2872551  08/12/17 12:33 PM
Re: Simple differential Equations
[Re: MotiDave]

Senior Member
Registered: 08/13/14
Posts: 74

I mean seriously: Everyone who knows a bit about both differential equations and about music is aware that knowledge or aptitude in the one field doesn't improve knowledge or aptitude in the other. However, people who know about both may find the interrelations interesting.

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