Acoustics & Music Theory
why it sounds like that
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Series — page 3

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
Ode to Joy as a path. Ode to Joy plotted as 30 notes against the 8 scale degrees it uses, one column per note. Its largest melodic interval is 2 semitones and it spans 7; the mean absolute step is 1.24 semitones. Beethoven, Ninth Symphony, finale, 1824 — the theme as first stated, eight bars.

Melody

  1. 1 A melody is a walk, not a set
  2. 2 The leap that pays itself back
  3. 3 The shape that survives everything else
  4. 4 The register where the series becomes a scale
  5. 5 The note that is sharp because of where it goes
  6. +3 more
8 essays · scales A phrase is a number of seconds, and the bars follow the tempo. Phrase durations for 1, 2, 4, 8, 16-bar phrases at seven tempos, on a logarithmic seconds axis, with the 2 to 8 second window shaded. The window is a property of the listener and does not move; which bar count falls inside it is decided entirely by the tempo.

Phrase

  1. 1 A phrase is a number of seconds
  2. 2 One of these eight-bar phrases accelerates
  3. 3 Where a phrase ends
  4. 4 A boundary at a stated level
  5. 5 The level the tempo chooses
  6. +3 more
8 essays · form Where each family's tone-hole lattice stops reflecting. The cutoff frequency of an open tone-hole lattice, from Benade's formula, for four woodwind geometries: clarinet 1824 Hz, oboe 2990 Hz, flute 1690 Hz, bassoon 506 Hz. Below its cutoff a note's wave turns round at the first open hole and the instrument is a tube of that length; above it the wave passes through the whole lattice and radiates from the far end, so the upper part of every note's spectrum leaves the instrument from the same place whichever note is fingered. That is what gives a family one recognisable voice across its range.

Tone holes

  1. 1 Above a certain note the holes stop working
  2. 2 One hole doing a dozen jobs
  3. 3 The hole that spoils a note
  4. 4 The vent a cone cannot place
  5. 5 A hole is a short tube
  6. +2 more
7 essays · instruments E(3, 8) as a cycle. A rhythm drawn round a circle, one equal arc per step, with the struck steps filled. On a circle the pattern has no beginning, which is why the same necklace of onsets is several different named rhythms depending on where a listener decides bar one is.

Cyclic rhythm

  1. 1 Rhythm is a circle, and the bar line is a choice
  2. 2 A cycle cannot cadence
  3. 3 A cycle that says where it is
  4. 4 The cycle that outruns the memory
  5. 5 Repetition buys least where it is needed most
  6. +1 more
6 essays · rhythm Three ways a note starts, on one pair of axes. Every instrument in this collection, with how long its note takes to speak measured twice: across, in periods of the note itself; up, in milliseconds. The three clusters are three different pieces of physics. A wind instrument accumulates energy in a resonance, so its wait is the resonance's Q — 27, 26, 26, 19, 37 periods here. A bowed string is at full amplitude the moment Helmholtz motion begins and what takes time is the bow reaching a force inside Schelleng's window, which is 3.0, 3.8, 5.1, 7.6 periods. A plucked or struck string is at full amplitude at once and the only duration in it is the exciter's own contact, under a tenth of a period. The two axes do not agree: the slowest instrument in milliseconds is an alto saxophone at 159, and in periods it is an alto saxophone at 37.

Onset time

  1. 1 A note takes a number of periods to speak
  2. 2 The higher note speaks sooner and takes longer
  3. 3 The hardest place is also the latest
  4. 4 A note starts twice
  5. 5 What the tongue actually removes
  6. +1 more
6 essays · instruments Six named proportions, as blurred as the durations that make them. Six proportions between two parts of a piece — 1 : 1, 4 : 3, 3 : 2, golden section, 2 : 1, 3 : 1 — placed on one axis by the logarithm of the ratio of the longer part to the shorter, and drawn as bars one criterion wide (d′ = 1) for a listener timing both parts with a Weber fraction of 7%, 15%, 35%. Bars that overlap are proportions that listener cannot tell apart. At 7%, 4 of 5 neighbouring pairs stay apart; at 15%, 3 of 5 neighbouring pairs stay apart; at 35%, 0 of 5 neighbouring pairs stay apart.

Proportion

  1. 1 A proportion is only as fine as its two durations
  2. 2 A return is shorter than its first hearing
  3. 3 A count is not an estimate
  4. 4 A form is sharp at the bottom and vague at the top
  5. 5 A golden section is a coin toss with six coins
  6. +1 more
6 essays · form Second order and fourth order, from the same sequence of wavenumbers. Frequency against wavenumber for a string and for a bar, with each object's own wavenumbers marked on the axis. A string's equation is second order in space, so frequency goes as wavenumber and the straight line carries its modes at 1, 2, 3, 4. A bar's is fourth order, so frequency goes as the SQUARE of wavenumber and the parabola carries the same kind of sequence to 1, 2.757, 5.404, 8.933. Both sequences of wavenumbers are arithmetic — a string's are the even multiples of π/2L and a bar's the odd ones, except that the first is 3.011 rather than 3 — and squaring an arithmetic sequence is the whole of why one object has a fundamental and the other has none. Every number is derived from the boundary condition; none is measured.

Struck bar

  1. 1 A bar's partials are the odd numbers, squared
  2. 2 One cut cannot place two partials
  3. 3 The tube shuts on the partial the arch placed
  4. 4 The four ways a marimba loses what its arch placed
  5. 5 A bar and its pipe are one object
5 essays · instruments

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