a common format for storing signals digitally is sample values of the distance magnitude of a vibration over time, like positions of a membrane between two bounding values

• stateless: have only parameter values that need not be kept
• stateful: have parameters for values that need to be kept between function calls. for example, carryover values that fall outside the currently processed range and are used in the next one
• processing one input sample at a time: can affect multiple samples only with state and delay after accumulating samples
• segment to segment: processors might depend on preceding or following values
• one to many: output creates a longer signal
• many to one: a longer signal becomes a shorter one

• analog hardware devices for synthesizers with keyboards or sequencing
• software sequencers where instruments, synthesizer sounds, recordings and effects can be layed out and played back
• software environments like fruity loops, reaktor, reason and others
• lv2 or vst plugins as effects and synthesizers
• taking audio recordings and prepare their ordered playback in a program like ardour or cubase
• connecting hardware devices with midi and puredata and the user interfaces that it can create
• preparing sample arrays using a general purpose programming language and writing to sound files

• harmonic: a harmonic is a wave with a frequency that is a positive integer multiple of the frequency of the original wave
• time series: a series of data points indexed (or listed or graphed) in time order. most commonly, a time series is a sequence taken at successive equally spaced points in time
• a sound program is a potential for sounds to occur. elements can appear and disappear like entering and exiting a dimension. there is always some kind of seed, for example the literal arguments in program code
• amplitude: the magnitude of the difference between a variables extreme values. the amplitude of a periodic variable is a measure of its change over a single period
• scales, a comprehensive study
• clipping: limiting values to a maximum
• digital image processing is a subcategory of digital signal processing
• envelope: a path of loudness transition
• every linear time-invariant system can be represented by a convolution
• frequency: number of occurrences of a repeating event per unit time
• low frequency: less rapid change between sample values
• phase: relative shift or progression of a repeating event
• sequencer: configures the starting points and durations of sounds
• vocoder: splits into frequency bands and removes bands
• wave < instrument < composition

• more links

  • amplitude
  • artificial reverberation
  • beat interference pattern between two sounds of slightly different frequencies
  • negative frequency
  • phase
  • rhythm

• 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

• 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

• "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 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 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