Acoustics & Music Theory
why it sounds like that
Concept

Engraving — where it appears

The craft of laying music out on a page, and specifically of deciding how much horizontal room each note is given. Its rules are a compromise between showing duration as distance and fitting music onto a page, and both halves are measurable.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

What the engraver used here gives a note, measured off the page. The horizontal distance VexFlow allots each duration, read back off a formatted system rather than quoted from a manual. It is not a power of the duration: it is a constant of 58 points plus 15 points a crotchet, and the constant is 93 per cent of the width the shortest note here gets. A note four times as long as another is about 2 times as wide, not four. The floor is the notehead, its stem, its accidental and the space a reader needs to see them as separate events — which is a claim about legibility and not about time at all.

The axis that is not a time axis

Eight earlier essays have measured the staff's vertical axis to a position. Its horizontal one has never been asked about, and the answer is that it is proportional to nothing: measured off the typesetter used here, a note gets 58 points before its duration is considered at all and 15 points a crotchet after — so the constant is 93 per cent of what the shortest note gets, and a note four times as long is not four times as wide.

scales · Notation How much music each notation fits on a page. The two axes multiplied. Vertically, a system is as tall as the staves the range needs; horizontally, a system holds as many notes as fit once the shortest is wide enough to read. the staff, seven to the octave: 3 staves to the system, 4 systems and 38 notes to a system, 152 notes to the page — 46 seconds at 100 beats a minute, so a page turn every 46 seconds; a chromatic staff, twelve to the octave: 4 staves to the system, 3 systems and 38 notes to a system, 114 notes to the page — 34 seconds at 100 beats a minute, so a page turn every 34 seconds; a whole-tone staff, six to the octave: 2 staves to the system, 7 systems and 38 notes to a system, 266 notes to the page — 80 seconds at 100 beats a minute, so a page turn every 80 seconds. a whole-tone staff, six to the octave holds 2.33 times what a chromatic staff, twelve to the octave does, which is a difference of 1.00 page turns a minute — and a page turn is a thing a player with two hands occupied cannot do.

How much music a page holds

Nine earlier essays have measured notations, and every one of them is a page — a two-dimensional object read in a fixed order by a reader who has to turn it. One measured the vertical axis and another the horizontal, and multiplying them gives the one design constraint on notation that is not about legibility at all: a chromatic staff turns pages a third more often than an ordinary one, and a proportional spacing rule turns them nearly twice as often as a columnar one.

scales · Notation Every standard rastral size against the two bounds a reader imposes. Print the notes larger and the eye-hand span stops fitting inside one fixation, so the reader has to saccade ahead faster than the eye can move. Print them smaller and a notehead stops subtending enough angle to be identified. Both bounds come from the reader and neither from the music. At 100 beats a minute with 2 notes to the beat, the acuity bound sits at 1.63 millimetres and the saccade bound at 7.5 — so the saccade rate is nowhere near binding and acuity is doing all the work, which is the opposite of what the eye-hand span suggests. 5 of the 9 standard rastrals clear the acuity bound: rastral 4 and larger. Those are exactly the sizes used for parts, and the ones below are used for study scores — which are read at a desk rather than played from at a stand, and a shorter viewing distance moves the bound with them.

The page is read by an eye

A sight-reader's eye sits a fixed number of notes ahead of the sounding one and a fixation takes in a fixed number of millimetres, and the spacing rule converts between them. Two bounds follow, from the reader rather than from the music — and the one everybody would expect to bind does not. The saccade rate has enormous headroom at any playable tempo, and what decides is acuity.

scales · Notation

Named alongside it

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

NotationStaffLegibilityReadingTempoAcuityDurationMicrotonalityPage turnProportional notationRhythmSaccade

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