Acoustics & Music Theory
why it sounds like that
Depth

Series — page 2

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.
Three envelopes. How loudness changes over the life of a note, for plucked, bowed and struck. Remove the attack from a recorded piano and it stops sounding like a piano, which is the shortest demonstration that the envelope carries as much identity as the spectrum.

Envelope

  1. 1 The shape of a note, which is most of what an instrument is
  2. 2 The first fifty milliseconds
  3. 3 The note that gets duller as it dies
  4. 4 The middle nobody could have guessed
  5. 5 The collapse belongs to the bass
  6. +5 more
10 essays · timbre 4 bores of one length, and the series each supports. cylinder, cone, exponential horn, Bessel horn — every one of them 148 cm long, 5.5 mm at the throat and 62 mm at the mouth, so the only thing that differs is the shape between the two. Beside each is the series of resonances Webster's equation gives it, and the number is how far that series is from evenly spaced, in cents. cylinder: 0.0 cents, with each mode sitting at minus 0.50 of a spacing off a whole multiple; cone: 9.6 cents, with each mode sitting at minus 0.12 of a spacing off a whole multiple; exponential horn: 22.8 cents, with each mode sitting at minus 0.16 of a spacing off a whole multiple; Bessel horn: 3.7 cents, with each mode sitting at minus 0.11 of a spacing off a whole multiple.

Bore profile

  1. 1 Only two shapes make a series
  2. 2 What the mouthpiece is actually for
  3. 3 A horn has one length per partial
  4. 4 The cutoff a maker can actually measure
  5. 5 A family resemblance in the heights
  6. +4 more
9 essays · instruments One pattern, four metres. The same 12-step onset pattern read under 4 candidate metres, each scored by a preference rule set: 3 for a strong position that carries an onset, -2 for one that does not, -1 for an onset that lands off every strong position. The scores are 4/4 -4, 3/4 12, 6/8 12, 12/8 as 3+3+3+3 12, so 3/4 and 6/8 and 12/8 as 3+3+3+3 tie and the model does not choose. Nothing about the sound differs between these readings; the bar line is supplied by the listener.

Metre induction

  1. 1 The beat is inferred, and sometimes wrongly
  2. 2 The beat has a preferred rate, and it is not the notation's
  3. 3 The bar above the bar
  4. 4 The right period at the wrong phase
  5. 5 Syncopation is a number about the metre
  6. +4 more
9 essays · rhythm How much swing there is, against how fast the music goes. The ratio of the long note to the short note of a swung pair, as a function of tempo, derived from the finding that the short note holds a roughly constant hundred milliseconds. The notated readings are horizontal lines, and each is correct at exactly one tempo. Above about three hundred beats a minute the ratio reaches one and the swing has gone.

Microtiming

  1. 1 Swing is a ratio, and it is not two to one
  2. 2 The milliseconds that are the groove
  3. 3 The deviations are not noise
  4. 4 Two players and no clock
  5. 5 How late is a different note
  6. +4 more
9 essays · rhythm A note with its first partial removed. The spectrum of a 220 Hz tone with the lowest partial deleted, and the wave that remains. The wave still repeats 220 times a second, because the repeat rate of a sum of harmonics is fixed by the spacing between them and the spacing has not changed. The pitch heard is the one that is no longer in the sound.

Missing fundamental

  1. 1 The note that is not there
  2. 2 The ear makes its own sound, and it is not the missing fundamental
  3. 3 A bell has no fundamental
  4. 4 What a drum is doing instead
  5. 5 Which harmonics carry the pitch
  6. +4 more
9 essays · intervals The seven modes, brightest first. The same seven pitch classes started on each of its degrees in turn, ordered by how many of their notes are raised. Each row differs from the one below it by exactly one note, and that note moves down one semitone each time.

Modes

  1. 1 The same seven, started later
  2. 2 What a raised seventh is for
  3. 3 What a tonic costs in seconds
  4. 4 The mode with no fifth
  5. 5 One dominant among seven
  6. +4 more
9 essays · scales A string quartet's open strings are five keys of a Pythagorean keyboard. The five pitch classes a string quartet's open strings sound — C, G, D, A and E — laid out as the chain of fifths they are tuned along, outward from the A the ensemble is given, with each fifth pure. The bars give each string's departure from the same note on an equal-tempered keyboard: C −5.87 cents, G −3.91 cents, D −1.96 cents, A 0.00 cents, E +1.96 cents. Above, the strings each instrument owns: the violin G, D, A, E; the viola C, G, D, A; the cello the same four an octave lower. The cello's C2 is 0.221 hertz below the keyboard's, and the widest span of the chain, from the cello's C to the violin's E, is a Pythagorean third and two octaves, 21.5 cents wider than a just one.

Open strings

  1. 1 The tuning a string quartet cannot change
  2. 2 The cello cannot hear its own tempering
  3. 3 An open string pulls the quartet flat
  4. 4 A guitar tuned by harmonics hides a comma
  5. 5 One tuning has no comma to place
  6. +4 more
9 essays · tuning One envelope, and the three places a listener might be said to hear it. The amplitude envelope of a note with a 90 millisecond exponential attack, with the three criteria the literature offers drawn across it. The heard moment is 8.0 ms at the detection criterion, 28 ms at the perceptual-onset criterion and 94 ms at the perceptual-attack criterion. The physical onset is at zero on this axis and no criterion puts the heard moment there. The buttons play this attack against a two-millisecond one, started at the same instant.

Perceptual-centre

  1. 1 A note is heard after it starts
  2. 2 The players who have to be early
  3. 3 Playing louder is playing earlier
  4. 4 A low note cannot start on time
  5. 5 Which notes have to be played early
  6. +4 more
9 essays · rhythm 3 against 2. Two evenly spaced pulses over the same span, one in 3 and one in 2. They agree only where both grids land together, and the gap between agreements is the least common multiple — which is what makes one polyrhythm sound like a shape and another like two unrelated things.

Polyrhythm

  1. 1 Two clocks at once, and where they agree
  2. 2 A rhythm fast enough to be a chord
  3. 3 A process that enumerates its own form
  4. 4 The third pattern nobody played
  5. 5 Which of the two is the beat
  6. +4 more
9 essays · rhythm thirty-two-bar AABA, every bar against every other bar. A self-similarity matrix of 32 bars of thirty-two-bar AABA. Each cell is the cosine similarity of two bars' pitch-class vectors, with the chord's own notes weighted 1 and the rest of the key 0.5. Similarity is quantised into four bands for drawing and anything under 0.35 is left as paper. Nothing in the computation knows what a section is; the blocks and stripes are what the arithmetic returns.

Repetition

  1. 1 A piece is mostly itself again
  2. 2 The boundary is where the neighbourhood changes
  3. 3 How much of this is new
  4. 4 How long until it comes back
  5. 5 The form a first hearing cannot have
  6. +4 more
9 essays · form 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 Three metres as trees. Three metres — 4/4, 2 + 2 + 2 + 2; 6/8, 3 + 3; 5/8, 3 + 2 — each drawn as the bar dividing into beats and the beats dividing again. Simple and compound metres have the same number of beats and differ in the second division; an additive metre has beats of unequal length, which no single division produces.

Additive metre

  1. 1 Beats of unequal length
  2. 2 How unequal a beat is allowed to be
  3. 3 How long a limping bar can be
  4. 4 A twenty-five is a nine until its last unit
  5. 5 The accent buys two units, however loud it is
  6. +3 more
8 essays · rhythm A 7-semitone sequence at 120 ms a tone. Tones drawn as pitch against time, one bar per tone. The events are the same in both readings of this pattern; what changes is whether a listener assigns them to one line that leaps back and forth or to two lines that each stay put. Nothing in the drawing decides which, and nothing in the sound does either.

Auditory scene

  1. 1 The ear builds objects, and sometimes offers a choice
  2. 2 What makes two partials one note
  3. 3 The spectrum that will not fuse
  4. 4 The partials that do not die together
  5. 5 The exchange rate nobody has
  6. +3 more
8 essays · perception A tempered interval moves its difference tone several times further than itself. For every interval inside the octave tuned to twelve equal steps, how far the difference tone f₂ − f₁ lands from where the just interval would put it, in cents, with the interval's own departure from just drawn as the thin bar beside it. minor second −198.0 (the interval −11.7); major second −35.5 (the interval −3.9); minor third −96.0 (the interval −15.6); major third +67.4 (the interval +13.7); fourth +7.8 (the interval +2.0); fifth −5.9 (the interval −2.0); minor sixth −36.7 (the interval −13.7); major sixth +38.8 (the interval +15.6); minor seventh −39.8 (the interval −17.6); major seventh +25.0 (the interval +11.7). The major third's product is +67.4 cents out and the minor third's −96.0, and the largest error is the minor second's, at −198: a product moves p/(p − q) times as far as the interval p:q that made it.

Combination tone

  1. 1 The third sound magnifies cents, not hertz
  2. 2 The tone on the root changes hands at the fifth
  3. 3 A major triad's combination tones are its own notes
  4. 4 The bass line under a passage in thirds
  5. 5 A combination-tone bass needs a forte
  6. +3 more
8 essays · intervals Six rhythms, all from the same construction. Euclidean rhythms generated by Bjorklund's algorithm, which spreads a number of onsets as evenly as a number of steps allows. The patterns were not transcribed from recordings; they are what the algorithm produces, and the names beside them are where each one is already in use.

Euclidean rhythm

  1. 1 As evenly as possible, which turns out to be a famous rhythm
  2. 2 The rotation the necklace cannot see
  3. 3 What the clave buys with its unevenness
  4. 4 The frontier and the ruler
  5. 5 The longest silence is not a third axis
  6. +3 more
8 essays · rhythm Every point on one curve sounds equally loud. The equal-loudness contours of ISO 226:2003, evaluated from the standard's own parameters. The lowest curve is the threshold of hearing. Because the curves are not parallel — they crowd together in the bass and spread apart in the middle — the same change in decibels is a different change in loudness at every frequency, and a spectrum that was balanced at one level is not balanced at another.

Loudness

  1. 1 The quietest thing audible, and why the volume knob is a tone control
  2. 2 A chord is not as loud as its notes
  3. 3 Loud is relative, and it comes down slowly
  4. 4 The dynamics are in the score already
  5. 5 A page has two decibels
  6. +3 more
8 essays · perception What one tone hides, and in which direction. The masked threshold beside a tone masker: any probe below one of these curves is inaudible while the masker sounds. The frequency axis is in Bark, the scale on which the ear's filters are evenly spaced, so the pattern is a pair of straight lines. The upper slope is much shallower than the lower one and gets shallower still as the masker gets louder — masking spreads upward, not downward.

Masking

  1. 1 One sound hides another, and it hides upward
  2. 2 A sound hides what came before it
  3. 3 A loud chord is a smaller chord
  4. 4 An equal note cannot be masked
  5. 5 The listener is given the top voice, and the bass as a sine
  6. +3 more
8 essays · perception

All essays