2023-08-30

notes on digital sound design

instruments

  • model

    • instrument

      • cluster ...

        • envelope ...

          • sine(amp, frq, phs) / filtered_noise(amp, frq_start, frq_end) ...

  • notes

    • partials summed make complex wave shapes

    • using clusters to build instruments works, because even instruments are made of some distinguishable objects

    • partials in a cluster should be similar enough to each other so they are not recognised as separate sounds, but different enough that they arent recognized as mere amplification

choosing partial frequencies

  • "The relative amplitudes (strengths) of the various harmonics primarily determine the timbre of different instruments and sounds, though onset transients, formants, noises, and inharmonicities also play a role."
  • harmonics are multiples of the fundamental (pitch) frequency. the fundamental is the frequency at which the entire wave vibrates
  • multiples and added divisions can be used
  • variables to select a partial: fundamental + divisions + shift
  • irrational frequencies have their period never restart at the same time as the fundamental again
  • mixing odd and even divisions is less harmonic

  • examples of subdivisions, times frequency:

    • 1/1, 1/1 + 1/2, 2/1
    • 1/1, 1/1 + 1/3, 1/1 + 2/3, 2/1
    • 1/1, 1/1 + 1/4, 1/1 + 2/4, 1/1 + 3/4, 2/1

  • relations to music theory

    • an octave is a doubling in frequency
    • a perfect fifth is a combination that is periodic on two periods of the lower note, a 2:3 frequency relation. the beginning of the second repetition of the fundamental is at the center of the second repetition of the other tone

  • some possible partial frequency relations

    • equidistant

    • increasing distance

    • decreasing distance

    • varying distance

    • sparse

    • dense

statistics to guide the automatic generation of data arrays for sound parameters

  • statistics are a digest/abstraction of the actual details of a pattern
  • they can be used to compare or generate patterns (monte carlo method)
  • statistics can be a target for a generator
  • it can also be used as an analysis step to make parts of patterns more similar or to blend them together
  • note that pointwise interpolation is another method to create similar patterns
  • statistics on the differences between values can also be useful

  • some interesting statistical methods

    • standard deviation: the variation from the mean (variance) with reduced bias to extremes
    • arithmetic mean: one share of the total sum equally distributed. the point where the sum of smaller values matches the sum of larger values
    • median: the center between higher and lower values. the point where the count of smaller values matches the count of larger values
    • range: the difference between the maximum and minimum
    • minimum: the minimum value in the dataset
    • maximum: the maximum value in the dataset

    • kurtosis

      • describes the distribution of numbers. for example, if values are spread out and more equally likely, or if there are peaks in the distribution, which would mean that a range of values appears in the dataset more often
      • mean((x - mean(data)) ** 4) / (mean((x - mean(data)) ** 2) ** 2)

    • skewness

      • describes the distribution of numbers. gives an indication about if there are more low or more high numbers
      • mean((x - mean(data)) ** 3) / (mean((x - mean(data)) ** 2) ** 3/2)

    • center of mass

      • the distribution of mass is balanced around the center of mass, and the average of the weighted position coordinates of the distributed mass defines its coordinates.
      • sum(n x(n)) / sum(x(n))

  • the number of unique subsequences as a potential statistic

    • the count of repetitions of overlapping subsequences of length 0..n

    • can find the subpattern lengths with the highest proportion of unique subpatterns relative to the possible unique subpatterns

    • examples

      • low: 11111 112112

      • high: 12345 112212

autocorrelation vs absolute differences

  • autocorrelation gives a degree of difference with large local difference being pronounced to differentiate it from many small differences.
  • correlation is -1 to 1
  • correlation only tests linear dependence. (1 2 3) and (4 5 6) are 1
  • mean absolute difference goes to infinity

general

  • the choice and availability of all sine configuration details before synthesis allows perfect analysis/knowledge unachivable by sound analyis with the fast fourier transform and other methods

    • this freedom is not necessarily lost even when samples are used as a basis to choose parameters, unless the goal is an exact recreation of the source material

  • even if sines can therotically represent triangles (with infinite sines), a triangle is the ideal (even if impossible) shape

    • summing sines can match the limits of reproducibility that exist anyway
    • using the ideal shapes might lead to aliasing

  • data types

    • continuous: sample -1..1; amplitude: 0..1
    • discrete: sampling-time
  • one can imagine a spectrum between harmonicity and noise, where harmonic sounds dissolve into noise
  • real human-like complexity in patterns is a variety of, and layers of, modifications over time. it is not the number of unique subsequences
  • panning effects can be left to right then again left to right, or left to right then back from right to left
  • to share parameter values, sound generators do not need to somehow trigger other sound generators (inefficient, possibly cylic). instead the values can be shared from a parent context
  • partials can be more causative/dependent/similar or more correlative/independent/dissimilar