he asked me NOT TO PUT THE DELAY EXACTLY AT 120 BPM (if the song was at that tempo) but instead at 119 or 121 because of PHASE issues :S
I swear, I have heard and read more hand-wringing, white-knuckling, and loss of sleep over "phase" in the past three years on this forum than I had in the quarter-century I have been messing with this stuff before that

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The
whole idea behind setting the delay to the BPM is to reinforce the beat. This reinforcement in fact happens because the waveforms compliment each other. If the waves were not exactly coincident, then phase might start affecting them in slightly different ways, some good, some bad. It's when relative phase starts approaching 180° that it really stats to become a problem.
Frequency represents time (cycles PER SECOND). Therefore every tempo (also representing time) will be coherent at certain frequencies and incoherent at other frequencies.
The question is, for which frequency do the waveforms approach 180° out of phase? Some frequency somewhere is *always* going to be out of phase for any given delay time.
A little math:
119BPM = 504.2ms/beat
120BPM = 500ms/beat
121BPM = 495.87ms/beat
This means that sliding the delay by one beat either way at that tempo is the equivalent of changing the delay time by just over 4ms. To keep the math simple, let's say 4ms.
4ms also happens to be the length of a full cycle at 250Hz. A pretty important section of the mid-bass. This frequency/delay time is also an even multiple of one second, which means that any whole number BPM will be evenly divisible by this number as well. Which is all a fancy way of saying that at exactly 120BPM, the original wave and the delayed wave will be coherent (in phase) at 250Hz.
This coherency will, in fact, be true for every frequency that evenly divides one second.: 20Hz, 25Hz, 50Hz, 100Hz, 125Hz, 200hz, 250Hz, 500Hz, 1kHz, etc.
Slide the timing by 4ms (approx. one BPM at ths scale) and the coherency at 250Hz will not change, becuae all we are doing is moving things one full cycle at that frequency. However, because this is only a half-cycle change at 125Hz, 125Hz will experience 180° phase incoherency if you try sliding the timing of the delay off by a single beat. So that change will not affect 250Hz whatsoever, but will have maximum effect on 125Hz.
So, what it comes down to - as is usual with most things - is how does it actually sound. Some frequencies will be complimentary, others will not. This will always be the case; it's just a question of which frequencies and how important they are to that given sound. If a delay at exactly 120BPM sounds wrong, then slide it a bit or do something different altogether. If it doesn't sound bad (which it very well may not) then there's nothing to worry about.
This will be true regardless of the delay time; there is nothing "magical" about an exact BPM match in this regard.
G.