Acoustics & Music Theory
why it sounds like that
Concept

Satb — where it appears

The four voice compasses of choral writing — soprano, alto, tenor and bass. They are the ranges every part-writing figure here enumerates inside, and they are what makes a four-part exercise a finite problem rather than an argument about taste.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Which note a chord would rather have twice. Every complete four-part voicing of each chord inside the SATB ranges, grouped by which member sounds twice and scored for roughness — 480 voicings for a triad. The order for a major triad is root < fifth < third, which is the rule every part-writing treatise states. For a minor triad it is fifth < root < third, which is not. The numbers printed under each bar are the mean error, in cents, with which the four sounding notes fit a single harmonic series, and that measure separates the three far more sharply than roughness does.

The note that sounds twice

A triad has three notes and a four-part texture has four voices, so one note is doubled — and the voicing model used here leaves the choice free because the rules have an opinion about it. Asked properly, the arithmetic agrees with the treatises for the first time in nine essays: root, then fifth, then third. For a minor triad it does not agree, and for a symmetric chord it correctly has nothing to say.

intervals · The triad The staff holds 11 positions and nothing fits in it. Each clef's eleven staff positions — five lines, four spaces and the space either side — as a bar on an axis that counts letters, with eight ranges laid underneath. The clefs step through the axis in thirds and cover fifteen positions of offset between them. Every range drawn is wider than eleven positions: the four voices span 13, 12, 13, 13 and the four instruments 24, 24, 25, 23, so the best clef for each still leaves 1 to 7 positions off the staff. A clef is a choice of which end sticks out.

The clef is an integer

The first essay on notation found that the staff's vertical axis counts letters rather than pitch, and named the clef as a question it was leaving open. Paid, it is arithmetic: a staff holds eleven letters, no voice or instrument is that narrow, and the eight clefs of European practice step through the axis in thirds — a spacing that buys everything a set of fifteen would buy on a wide range, for eight.

scales · Notation

Named alongside it

The objects these essays reach for when they reach for this one.

ClefDiatonic setDoublingInversionLedger lineNotationPart-writingRangeRoughnessStaffTranspositionTriad

All concepts