That's not exactly true. In digital signal processing, delays and filters are effectively one in the same. This is because you implement digital filters using digital delays. For example, the simplest low-pass filter is just a summation of the current and previous sample: y(n) = x(n) + x(n-1).
“Filters are delays” doesn’t imply “delays are filters”. In particular, the type of effect known as a delay (e.g. a delay guitar pedal) isn’t a filter, certainly not in the musical sense, which is the relevant sense here.
> “Filters are delays” doesn’t imply “delays are filters”.
Purely logically, no, but that's not really the practical sense we're talking about. And by introducing a digital delay, you do induce a filter on the sound. So if you have a delay, then you have a filter.
> In particular, the type of effect known as a delay (e.g. a delay guitar pedal) isn’t a filter, certainly not in the musical sense, which is the relevant sense here.
I think it's best to reconsider my original comment. I was arguing that it isn't useful to suddenly rename subtractive synthesis as a "transformation", because you could just rename all of synthesis "filtering". But that's not useful, and synthesis just means building up sound from parts. I.e., it's best to work at a given level of the parts and think about things like waveforms, envelopes, LFOs, pulses, triggers, delays, reverbs, etc., most of the time.
