Music notes

Miscellaneous notes about computer music

Ode To Joy

This is a handy quicky test:

 int odeToJoy[] = { F2S,QUARTER, F2S,QUARTER, G2 ,QUARTER, A3 ,QUARTER,
                    A3 ,QUARTER, G2 ,QUARTER, F2S,QUARTER, E2 ,QUARTER,
                    D2 ,QUARTER, D2 ,QUARTER, E2 ,QUARTER, F2S,QUARTER,
                    F2S,DOTTED_QUARTER, E2,EIGHTH, E2,HALF,
                    F2S,QUARTER, F2S,QUARTER, G2 ,QUARTER, A3 ,QUARTER,
                    A3 ,QUARTER, G2 ,QUARTER, F2S,QUARTER, E2 ,QUARTER,
                    D2 ,QUARTER, D2 ,QUARTER, E2 ,QUARTER, F2S,QUARTER,
                    E2 ,DOTTED_QUARTER, D2,EIGHTH, D2,HALF, 
                    E2 ,QUARTER, E2 ,QUARTER, F2S,QUARTER, D2 ,QUARTER,
                    E2 ,QUARTER, F2S,EIGHTH,  G2,EIGHTH, F2S,QUARTER, D2 ,QUARTER,
                    E2 ,QUARTER, F2S,EIGHTH,  G2,EIGHTH, F2S,QUARTER, E2 ,QUARTER,
                    D2 ,QUARTER, E2 ,QUARTER, A,QUARTER, REST,ETERNITY } ;

Digital filter

 filter ( input, tunefactor, damping )
 {
   lowpass  += tunefactor * bandpass ;
   highpass  = input - lowwpass  - damping * bandpass ;
   bandpass += tunefactor * highpass ;
   notch     = lowpass + highpass ;  // Optional!
 }

Another Low-pass filter

Calculate each output-signal sample as the sum of the input signal and the previous output signal with scaling. This defines a low pass single-pole filter:

  Yn = Xn.(1-T) + Yn-1.T

Where:

• X_n is the input
• Y_n is the output, Y_n–1 is the output from the previous loop.
• T is our frequency control: 0<T<1

Physically, T is the amount of decay between adjacent output samples for a 'step' input. You can directly specify the value of T or derive it from the time constant of the filter, d, which is the number of samples it takes the output to rise to 63.2% of the steady-state level for a lowpass filter. T=e^–1/d.

Instead of multiplying by 1–T, it is more convenient to divide by the F=1/(1–T):

  Yn = Yn–1 + (Xn–Yn–1)/F

You can determine the digital filter’s parameters using the following steps:

1. Choose a value for F. Suppose F==8, so you can do a right-shift instead of a divide.
2. Calculate T = 1–1/F = 1–1/8 = 0.875.
3. Calculate the time constant as d = –1/ln(T) = –1/ln(0.875) = 7.49 samples.
4. Multiply that into your sample rate: 22000/7.49 = 2.9kHz