HARM·77
a waveform is a list of partials · where each one sits, how loud it is, and when it starts
every hit leaves at the same peak, one decibel under full scale, so the reading that moves is loudness: an aligned phase row here simply plays quieter. drive bends the sum through a tanh before that, and the phases still decide what it bites: driven as hard, a spread row stays about ten decibels louder than the same one aligned
how loud each partial is
each partial, deeper · when it starts, where it sits, how it moves
when each one starts
where each one sits, as a multiple of the note
drag any bar · seven numbers per partial and every one of them is yours: how loud, when it starts, where it sits, how long it takes to arrive, how late it arrives, where its pitch slides to, and how fast it beats. the last four are what takes this past anything a struck object can do. the middle row is phase, which does not move the spectrum at all and moves the peak by nine decibels. the last row is drawn on a log curve, because the ear hears ratios: the first octave gets as much room as the last
draw one cycle · it becomes the partials
why the phases are a control and not a detail
two waveforms built from the same partial levels at different phases measure the same on a spectrum and sound nearly the same. one of them peaks nine decibels higher than the other at identical loudness. under a kick that decides everything: the aligned one eats the headroom the kick needed.
measured here over twenty four partials, as crest in decibels. phases in a line against phases spread by schroeder's quadratic: flat levels 14.21 against 5.66, rising levels 14.65 against 5.40. and where the fundamental already runs the show it is worth nothing at all: soft 1/n levels read 6.03 against 7.78, which is slightly worse.
so a layer meant to sit under a kick without eating its ceiling wants a rising tilt and spread phases. a layer meant to be the weight itself wants a steep tilt, where the phases hardly matter.