Math 101?
  • Hello all,

    I was wondering if someone could point me in the direction to brush up on my math skills. It seems that Audulus is a lot easier to understand if you're good at math, and it's been a long time since Ive been in school! LOL!

    Sometimes I feel lost when others comment on certain mathematical functions they've applied to using Audulus.

    Any insight on the TYPE of mathematics I should brush up on would be a huge help!!! I know there are a lot of sites out there to help with reviewing math skills, I would just like some ideas on the type of math which would best help me to use some of the more advanced features of Audulus.

    Cheers from NY!!!
    Thanks in advance,

    Tom
  • Hey Tom.
    A whole lot of the math I'm using in Audulus I figured out by poking around in Audulus. And most of that is arithmetic and simple logic. I cribbed a few fancy formulae from Wikipedia with only the foggiest notion of what's going on.
    I think there are better answers to your question but one cool thing about Audulus is whatever resources you find can be tested and manipulated in Audulus with visual or audible feedback.
    If you want to get more specific, I'll help as best I can.
  • The first round of math you will need to grasp with audulus is the following:

    1. Converting a 0-1 range to an audible frequency range which is typically 50-18000 hz
    2. Amplitude manipulation where 1 represents full volume
    3. Pitch manipulation where double a note is an octave, 1.5 times is a fifth each and also harmonic theory.
    4. Logic signal flow, using math and sensor objects to manipulate signal flow, particularly with the less than module.

    That is a good starting primer IMO. You get more advanced with the math module where you can define your own wave forms as mathematical formulas. Here we get heavy into trigonometry.

    Ken
  • What do you mean by "sensor objects"?
  • So are you saying is it's trigonometry and algebra I need to review? There is a good site called "Kahn" or something like that. All free and you can find anything to review their. I will post it.
    In the meantime, anyone else care to chime in?
  • Sorry was thinking stuff like env follow for example, modules that detect a condition and return a true or false. Basically Boolean operations.

    Ken
  • Algebra, yes, maybe. It is more about logic flow and basic knowledge of audio physics. Trig comes more into play when using math to create the waveform itself. A good example of this would be the expressive piano patch which can be found in the forums.

    Ken
  • A few points based on my experience..

    1) Basic arithmetic is fundamental really, multiplication, division, multiplying by fractions to scale values will suffice for most usage scenarios.
    A better understanding of Algebra and relational operators will also help.

    2) Use the metering nodes wherever you can, plug values in and see what happens to them. Use trial and error until you understand whats going on.

    3) If you want to make your own waveforms then you need to understand the maths behind periodic objects. Trigonometry is essential for this, find tutorials on Sine, Cos, Pi etc.

    4) Quadratic equations and Logarithms can also be useful if you want to understand how midi notes relate to frequency and how to scale linear values to curves.

    5) If you want to strengthen your intuitive understanding of how it all fits together then I would also recommend learning a programming language. It will really help you get how logic flows through a system. Codea app on the iPad is really good for this.


    However I must say points 3 to 5 are only relevant if you want to really geek out on this stuff and do really specific and niche things. For 99% of things you will just need points 1 & 2, you can get a lot done with just basic maths.

    I would also recommend avoiding the math expression node while you are learning all this. It doesn't really seem computationally more efficient and ultimately makes it more difficult to work out what is going on if you come back to a patch you made a while ago. Using the math nodes is better because you can insert metering nodes in and see what is happening to the numbers as they flow from node to node. Move onto the expression node once you feel more confident with the maths.
  • +1 for above. Expression and trig will create unique waveforms in an efficient manner. But before you get there basic logic flow and smile signal manipulation will be what you need to master. After that is understanding how math can affect amplitude and then how math can affect pitch. Some interesting math affecting audio signal would be aft8 patches on the forums. For example how subtracting the resonant low pass filter from the original signal makes a resonant high pass filter. And the band pass filter usage. These are also great examples of nested sub patches.

    And this also brings us back to the best thing to do to learn practical usage of these principles is to explore the patches submitted to the forum by other users. They will show you practical examples of the concepts you are trying to learn. As a computer programmer who programs accounting software and a music theory geek these were invaluable for me in learning best practices for some of the things I wanted to accomplish. It also saved me reinventing the wheel when others had already built working examples of things I was experimenting with.

    Ken
  • So Algebra, Trig...and Logic as it applies to computer science?
  • Yes, more or less, that is a more succinct way to put it...

    Ken
  • I'd say algebra, Boolean algebra and a bit of trig.
  • We could put together a set of patches to illustrate some of the fundamentals -- an extension to the default set. Anyone interested?
  • That would be great! I have a strong background in analog synthesis. As well as additive and FM. So I understand the synthesis concepts. But doing the math in Audulus, rather than twisting a knob, is foreign to me. Thanks for all of the great suggestions! Looking forward to trying out some of the illustrative patches you've suggested.
  • I'm revisiting as I have some free time to do some studying. any suggestions or patches as described above?
  • And of course as I'm sure you've discovered already in Audulus some of the simplest math nodes are basic synth building blocks you are already familiar with; addition is mixing, multiplication is amplifying and so on. I often find creating patches with the oscillators running very slowly so I can see the output in the waveform display and then speed it up to hear it.
    When the Expression node became available I had great fun hacking little bits of formulas from websites and getting them to run in Audulus. I really don't have the math skills to fully understand what's going on but many of my crazy patches are still up here somewhere!
  • tombitondo,
    These are all great suggestions.
    The only additional thing I might add is to find yourself the simplest graphing calculator app that you can find that will handle and plot trig functions (particularly sin and cosines), log (etc.), typical algebraic functions as a function of x (i.e., f(x)), Boolean expressions and conditional statements, and simple number theory operations such as modulo.
    Start out by plotting A*sin(2*pi*f*x), where f is the frequency and A is the amplitude. Then, play with it and all of its parameters using the above list of operators. Turn A or x into algebraic expressions, add two sin waves together, multiply them together, plot as many algebraic expressions as possible, etc.
    With what you learn through your review and research elsewhere, including what you gain from audulus, you will quickly become familiar with most of the standard concepts in audio synthesis and processing......a picture is worth a thousand words.....your ears will complete the picture in audulus.
    I, unfortunately, can not currently recommend which app might be best for you. I currently occasionally use Grapher, which is currently included on Mac, and PocketCAS, both of which are capable of higher level math than you need (I have a strong mathematical background) but very short on user instructions and also glitchy (particularly Grapher), which often confuses me also.
    What you should do is peruse the App Store for graghing calculators at the high school or entry college level.....read the user reviews, they're quite informative and useful in deciding if the app is good and will meet your needs.