Quick post today, just to record hypotheses I’d like to test. I’m back onto the “math of musical pitches” thing, but I’m promising myself I won’t get too lost down this rabbit hole. Not this time.
Pianos and digital keyboard instruments are tuned to 12-Tone Equal Temperament (12ET), where each half-step is exactly the same interval as the others. It’s a tuning system that confers certain advantages, such as flexibility in the use of tonal languages to exploit enharmonic ambiguity to pivot to other tonal centers. Such advantages come at the cost of the “sweetness” or “purity” (terms to be defined) of harmonic intervals. It’s a halfway-decent trade-off.
Ensemble vocalists and similar groups (such as a string quartet) tune their performances “by ear,” using subjective aural experience to shift notes microtonally to achieve harmonies that are deemed optimal, somehow. Hypothesis: the subjective judgement of what’s optimal for an individual performer has a physiological/biological component and an acculturated component; probably the biological component is weighted somewhat more strongly. Another hypothesis: what’s judged as optimal is usually some kind of just intonation; probably 5-limit tuning as (opposed to Pythagorean (3-limit) tuning or 7-limit tuning). (more…)