Audio frequency increment yielding wrong results

Question

I am writing something in the ChucK programming language, which is designed specifically for audio time functions (in this case, hertz). I'm having a really difficult time with a mathematical calculation; I'm not very good at mathematics, I hope I can get help here.

The operation I'm attempting to perform is as follows, given these variables:

F: Input frequency in hertz
I: Incrementation to next F
R: New frequency in hertz

In pseudo-math, it would read like this:

(output) F
R = F + I
F = R

Where I is 1/12 of the power of F, I think. To summarize, if F is 110 hertz, and the same note on the next octave up is 220 hertz, the range between the two is split up in 12 parts, exponentially, which makes up a full musical scale.

I feel my mathematical formula is incorrect, as I am getting F = F *2 instead of what I am aiming to do. But I don't really understand where the problem is.

In code, it looks like this:

110 => float OscFrequency => fbOsc.freq; // 110Hz, or "A -1" musical note
// stuff to set up look
while ( now < stop ) {
    ( OscFrequency + 1 ) - ( Math.pow ( 1, ( OscFrequency / 12 ) ) ) => float stepExponent;
    // other irrelevant things happen here
    OscFrequency + stepExponent => OscFrequency => fbOsc.freq;
}

Full code.

If this were written in a more common language like Java, it would look something like this:

float OscFrequency = 110.00;
// snip
while (now < stop) {
    float stepExponent = (OscFrequency + 1) - (pow(1, (OscFrequency / 12)));
    // other irrelevant things happen here
    OscFrequency = OscFrequency + stepExponent
}

The output looks like this:

[chuck](VM): sporking incoming shred: 1 (fizzbuzz.ck)...
"-----" : (string)
stepExponent:  110.000000 
Result:  1 
OscFrequency:  110.000000 
"-----" : (string)
stepExponent:  220.000000 
Result:  2 
OscFrequency:  220.000000 
"-----" : (string)
stepExponent:  440.000000 
Result:  3 
OscFrequency:  440.000000 
"-----" : (string)
stepExponent:  880.000000 
Result:  4 
OscFrequency:  880.000000

I've been trying to get this thing to calculate properly for a couple days, without success. Can you offer any advice as to where I might be miscalculating the value of F (a.k.a. OscFrequency)?

---

I've tried a number of other formulas, neither of which yield correct results:

• OscFrequency + ( ( Math.pow ( OscFrequency, 12 ) % 12 ) - OscFrequency ) => float stepExponent;
• ( ( OscFrequency + stepExponent ) ) => OscFrequency => float fbOscFreq;

Answer 1

In Java, you can do this one of two ways. You can calculate the increment and add it to the original frequency:

// This is 2^(1/12) - 1
final float HALF_NOTE_STEP = 0.05946309435929526;
float OscFrequency = 110.00;
// snip
while (now < stop) {
    float stepExponent = OscFrequency * HALF_NOTE_STEP;
    // other irrelevant things happen here
    OscFrequency = OscFrequency + stepExponent
}

Or you can multiply directly without calculating the increment:

// This is 2^(1/12)
final float HALF_NOTE_MULTIPLIER = 1.05946309435929526;
float OscFrequency = 110.00;
// snip
while (now < stop) {
    // other irrelevant things happen here
    OscFrequency *= HALF_NOTE_MULTIPLIER;
}

Or you can do it without a loop:

float OscFrequency = 110.00;
OscFrequency = OscFrequency * Math.pow(2.0, (stop-now)/12.0);