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  • It’s difficult for me to really hear any (harmonic) consonance or dissonance value when two notes are heard at the same time, but do NOT begin at the same time. As a listener, I find myself more drawn to the melodic interval than the harmonic interval of a suspension or any other moment where two notes are heard at the same time, but do NOT start at the same time.
  • When two notes begin at the same, the harmonic interval is obvious, but not so much if you offset them. If I really try to listen closely, I can hear the harmonic interval, but I think it would be irresponsible for me to assume the average listener is going to examine my music as much as I do especially if they have no musical training.
  • For context, I’m asking this question as I’m learning fourth species counterpoint. I understand you need to consider consonance/dissonance when using suspensions, but it’s difficult for me to place any value on that beyond just following the rules of fourth species. Thoughts???
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I'm going to go out on a limb here and assume you're playing on or listening to only a piano or perhaps a harpsichord. These instruments are characterized by a sharp attack that can overwhelm the sustained pitch in the listener's mind.

Here's a piece that turned me on to suspensions when I was in high school: Den Tod niemand zwingen kunnt, the second verse of Bach's Cantata BWV 4, Christ lag in Todes Banden (usually seen as "Todesbanden" but if I recall correctly the source has it as two words).

There are a couple of extended suspensions here, which you may find of interest, but the classic sequence of suspensions in the final hallelujah serves to illustrate the point. That starts at 8:30. To be perfectly clear, the point is that each time the soprano voice descends (and the alto voice holds its pitch), the dissonance is very apparent in the musical texture. The "crunchy" texture dissipates when the alto voice descends to the consonant interval, and this repeats a few times in sequence.

If you're composing at the keyboard, try a pipe organ or, if you can't manage that, a synthesizer with a sustained tone and a gentle attack.

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