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.
A small room's lowest modes. The first few axial standing waves of a room, drawn in plan, with the frequency of every mode below 160 hertz listed underneath. The low modes are far apart in frequency, so some bass notes are loud in one corner and absent in another. The sound buttons play these two octaves above their real pitch, because a room's lowest modes are below what most speakers reproduce.

Room acoustics

  1. 1 The room is part of the instrument
  2. 2 How long a room rings, and where the formula stops
  3. 3 An instrument points
  4. 4 The room chooses the harmonic rhythm
  5. 5 Where a room stops being a room
  6. +4 more
9 essays · timbre The major scale as a cycle. The twelve semitones drawn as a cycle, with the notes of the scale filled in. The gaps between filled positions are the step pattern, and reading them round the circle is what makes the scale's asymmetry obvious.

The diatonic set

  1. 1 Seven of the twelve, chosen unevenly
  2. 2 Five notes, and no semitones
  3. 3 Two sizes of every step, which is why the names work
  4. 4 Every interval a different number of times
  5. 5 The same algorithm made a Cuban rhythm
  6. +4 more
9 essays · scales Chords as stacked intervals. Each of 4 chords — major, minor, diminished, augmented — drawn as the semitone distances above its root, with the nearest simple frequency ratio beside each note where the 5-limit table has one. Where the chords are triads they differ only in the size of the two stacked thirds, and that difference is the whole of their character.

The triad

  1. 1 Three notes at once, and why these three
  2. 2 The interval that inverts to itself
  3. 3 Three is the largest agreeable number
  4. 4 The inversion that cannot end a phrase
  5. 5 The root an ear supplies
  6. +4 more
9 essays · harmony How far the voices have to move. Three chord changes with their voices joined by the assignment that moves the least in total. The distance is computed over every way of pairing the notes, so a change that shares two of its three notes shows as two flat lines.

Voice-leading

  1. 1 The shortest move, which is what a chord change is
  2. 2 Chords as a space
  3. 3 Two voices that stop being two
  4. 4 A melody that can accompany itself
  5. 5 What the rules cost
  6. +4 more
9 essays · harmony 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. +3 more
8 essays · instruments 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. +2 more
7 essays · instruments 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
  6. +2 more
7 essays · instruments Struck, a suspension's roughness falls whether or not it resolves, and the step itself sends it back up. One 4–3: C5 prepared over a C chord, tied over G3, D4 and G4, and stepping to B4, each moment 1 s. Roughness, Plomp–Levelt over eight partials of every pair weighted by the product of their amplitudes. Sustained: suspension 0.327, resolution 0.325. Struck, with a T60 of 12 s at middle C: suspension 0.149, resolution 0.054, and with the note left hanging 0.024 at the same moment.

Suspension

  1. 1 A tied note is the oldest thing in its own dissonance
  2. 2 A trill is half a consonance unless it borrows its own resolution
2 essays · harmony A meantone keyboard is a stretch of the chain of fifths, and every split key lengthens it by one place at an end. 14 keys hold the positions from A♭ to D♯. That is 10 major and 10 minor triads; major keys E♭, B♭, F, C, G, D, A, E; minor keys with a raised leading note C, G, D, A, E.

Split keys

  1. 1 A split key buys one of everything, and two buy C and E
1 essay · tuning

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