Vocal Harmonies and the Piano

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). Continue reading “Vocal Harmonies and the Piano”

Music Theory 000.1 – Part 6: I’ve Got Rhythm

This is part of my series on Understanding How Music Works. If you haven’t yet, you may wish to start at the beginning.

I think it’s well past time we talked about time, y’know? As I first thought (months ago) about writing this post, I realized that music, of all the arts, has a special relationship with time. I also realized that my goal here was to explain things simply, thereby understanding it well enough myself. And I have not always kept it simple. So I’ll break this post up into the abstract/philosophical part (to get it out of my system) and the simple/practical part. Continue reading “Music Theory 000.1 – Part 6: I’ve Got Rhythm”

Music Theory 000.1 – Part 5: Tonics and Intervals

This is part of my series on Understanding How Music Works. If you haven’t yet, you may wish to start at the beginning. This post, finally, is about how two or more notes interact within a piece of music — when there is a “home base” note and some interval relationships between that note and the others in the piece.

The most succinct and accurate definition I’ve encountered for “music” is “organized sounds and silences.” That broad definition encompasses just about everything that’s seriously regarded as music, and even most things that many people don’t regard as music. Things like John Cage, Daft Punk, Schoenberg, Stomp, turntablism, and Ke$ha. But we’re not going to deal with these outliers yet; we’re going to start by looking at one way that we humans organize sounds (and silences) into music that is so common that we might reasonably conclude that it’s physiologically hard-wired into us. Continue reading “Music Theory 000.1 – Part 5: Tonics and Intervals”

Music Theory 000.1 – Part 4: Pattern-Recognizers and Meaning-Makers

This is part of my series on Understanding How Music Works. If you haven’t yet, you may wish to start at the beginning. In my last post I said that this post would be about how two or more notes interact within a piece of music – “what happens when there’s more than one note?” But I have one more digression to take before I do. There are some ideas that form an important context to any meaningful discussion of how musical sounds work together. I’m going to try to cover them here, in just enough depth that we can get back to talking about pitch-classes and harmonies.

Human beings, you see, are pattern-recognition machines and meaning-makers. It’s not just how we understand music; it’s how we make any sense at our environment at all. So let’s be more explicit about what it means to be pattern-recognition machines, and what it means to be meaning-makers, before we talk about the patterns we observe in music and the meanings we ascribe to them. Continue reading “Music Theory 000.1 – Part 4: Pattern-Recognizers and Meaning-Makers”

Music Theory 000.1 – Part 3: Pitches and Octaves

This is part of my series on Understanding How Music Works. If you haven’t yet, you may wish to start at the beginning. Here, I discuss a certain perceptual phenomenon that occurs, to the best of my knowledge, in all humans with normal hearing. This phenomenon has profound implications for how music works. But first, a definition…

We humans seem to perceive regular cycles of compressions of air, happening at a certain range of amplitudes and frequencies, as a “pitch” or a “note.” Translation: when something pushes the air molecules tight together, then apart, then together et cetera, not too much and not too little, at a regular pace that’s not too fast and not too slow (let’s say 200 times per second for an example), we hear that as a steady, even sound that doesn’t seem to “move” up or down; that’s what we’re calling a “pitch” or “note.” Continue reading “Music Theory 000.1 – Part 3: Pitches and Octaves”