Concept

Blend — where it appears

How far two instruments playing the same note are heard as one sound rather than as two. It is decided by how far apart their spectra sit at that pitch, by whether their notes begin together, and by the room, which holds one instrument's upper partials longer than the other's.

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

A room pulls the compass apart rather than evening it out. How long a pizzicato entering 6 decibels above a held note keeps the composite spectrum, at eight pitches across two and a half octaves, heard 15 metres from the stage. no room: 0.07, 0.05, 0.06, 0.06, 0.02, 0.05, 0.05, 0.04 seconds; a concert hall: 0.61, 0.27, 0.50, 0.38, 0.01, 0.25, 0.27, 0.19 seconds; a large stone church: 1.03, 0.39, 0.79, 0.56, never, 0.33, 0.35, 0.23 seconds. Dry the figures barely move — a spread of 3.0 across the whole compass — because a room is the thing that varies with frequency and there is none. In a hall the spread is 44. The room does not scale the dry answer by a constant: it multiplies it by between four and nine times depending on the note, and at C6 it makes the pluck's position worse rather than better, because the two instruments' spectra nearly coincide there and the pluck starts only 4.0 decibels ahead instead of twelve.

One note in the compass loses its pizzicato

Dry, how long a pluck keeps the composite spectrum barely depends on which note it plays: three-hundredths of a second at the worst pitch and seven at the best, a spread of three. In a concert hall the same eight notes spread by a factor of forty-three, and in a stone church one of them never gets the note at all. The room does not scale the dry answer by a constant — it multiplies it by between four and nine times depending on the pitch, and at the one note where the two instruments' spectra nearly coincide it makes the pluck's position worse instead of better.

timbre · Spectrum

Every pair has a worst note, and for most of them it is at one end of the compass. The margin at the strike — how much nearer the composite spectrum sits to the decaying instrument's own spectrum than to the held instrument's, in decibels of log-spectral distance — for every ordered pair of six radiators at every semitone from C3 to C7, with the decaying instrument entering 6 dB above. violin over voice: worst −34.9 dB at E♭3, best 14.9 dB at C♯6, behind at 35 of 49 pitches; violin over clarinet: worst −2.2 dB at B♭4, best 19.6 dB at F♯6, behind at 3 of 49 pitches; violin over oboe: worst −0.3 dB at B♭4, best 11.4 dB at E3, behind at 1 of 49 pitches; violin over flue pipe: worst 2.7 dB at C7, best 16.9 dB at E3; violin over trumpet: worst −13.8 dB at B♭4, best −3.4 dB at D3, behind at 49 of 49 pitches; voice over violin: worst −9.2 dB at C♯6, best 41.8 dB at E3, behind at 8 of 49 pitches; voice over clarinet: worst 1.4 dB at C♯6, best 43.1 dB at E3; voice over oboe: worst −8.2 dB at C♯6, best 44.5 dB at E3, behind at 6 of 49 pitches; voice over flue pipe: worst −14.7 dB at C7, best 47.5 dB at E♭3, behind at 8 of 49 pitches; voice over trumpet: worst −24.2 dB at C7, best 39.5 dB at E3, behind at 20 of 49 pitches; clarinet over violin: worst −14.0 dB at F♯6, best 7.0 dB at B♭4, behind at 26 of 49 pitches; clarinet over voice: worst −36.6 dB at E3, best 3.5 dB at C♯6, behind at 46 of 49 pitches; clarinet over oboe: worst −14.2 dB at F♯6, best 5.5 dB at C3, behind at 27 of 49 pitches; clarinet over flue pipe: worst −14.5 dB at G6, best 13.3 dB at C3, behind at 18 of 49 pitches; clarinet over trumpet: worst −25.5 dB at F♯6, best −6.5 dB at C3, behind at 49 of 49 pitches; oboe over violin: worst −7.5 dB at E3, best 5.8 dB at B♭4, behind at 43 of 49 pitches; oboe over voice: worst −37.7 dB at E3, best 13.8 dB at C♯6, behind at 37 of 49 pitches; oboe over clarinet: worst −0.8 dB at C3, best 19.2 dB at F♯6, behind at 10 of 49 pitches; oboe over flue pipe: worst 2.4 dB at C7, best 14.3 dB at C3; oboe over trumpet: worst −14.2 dB at F4, best −12.8 dB at F♯6, behind at 49 of 49 pitches; flue pipe over violin: worst −12.7 dB at D3, best 3.0 dB at C7, behind at 43 of 49 pitches; flue pipe over voice: worst −40.4 dB at E♭3, best 19.4 dB at C7, behind at 34 of 49 pitches; flue pipe over clarinet: worst −7.7 dB at C3, best 18.9 dB at G6, behind at 24 of 49 pitches; flue pipe over oboe: worst −10.4 dB at C3, best 2.1 dB at C7, behind at 45 of 49 pitches; flue pipe over trumpet: worst −21.0 dB at C4, best −16.3 dB at C7, behind at 49 of 49 pitches; trumpet over violin: worst 8.7 dB at C3, best 17.3 dB at B♭4; trumpet over voice: worst −29.3 dB at E3, best 29.9 dB at C7, behind at 26 of 49 pitches; trumpet over clarinet: worst 10.7 dB at C3, best 30.6 dB at F♯6; trumpet over oboe: worst 16.9 dB at D5, best 18.8 dB at C7; trumpet over flue pipe: worst 21.2 dB at C7, best 24.7 dB at B♭3. A pale cell is a pitch at which the two spectra nearly coincide and the room has almost nothing to multiply; an unfilled cell is one at which the decaying instrument never leads at all.

A doubling's worst note belongs to one instrument, not to the pair

The essay before this one found one pitch at which a violin and a flue pipe nearly share a spectrum and asked which pitch that is for every pair. Run over six radiators, thirty ordered pairs and forty-nine semitones, the answer is that seventeen pairs choose a worst note and thirteen simply run out of compass — and that the seventeen do not choose thirty different notes. They cluster in fours and threes, and each cluster is one instrument's own filter: the violin's worst note is B flat 4, its strongest body resonance; the clarinet's is F sharp 6, its cutoff; the voice's is C sharp 6, where its second partial meets its second formant. A doubling fails at a note that belongs to one of its players.

timbre · Spectrum

Inside the compasses the instruments have, 8 of the map's seventeen worst notes cannot be played by both. The margin at the strike for every ordered pair of six radiators from C3 upward, with every note outside the pair's shared compass greyed: the violin from G3 to E7, a soprano from C4 to C6, a B♭ clarinet sounding D3 to B♭6, the oboe B♭3 to A6, a B♭ trumpet sounding E3 to B♭5, a flue pipe throughout. violin over voice: shared C4 to C6, worst inside it −30.6 dB at C4; violin over clarinet: shared G3 to B♭6, worst inside it −2.2 dB at B♭4; violin over oboe: shared B♭3 to A6, worst inside it −0.3 dB at B♭4; violin over flue pipe: shared G3 to C7, worst inside it 2.7 dB at C7; violin over trumpet: shared G3 to B♭5, worst inside it −13.8 dB at B♭4; voice over violin: shared C4 to C6, worst inside it −5.9 dB at C6; the full map's worst, C♯6, is outside; voice over clarinet: shared C4 to C6, worst inside it 6.9 dB at F♯5; the full map's worst, C♯6, is outside; voice over oboe: shared C4 to C6, worst inside it −3.4 dB at C6; the full map's worst, C♯6, is outside; voice over flue pipe: shared C4 to C6, worst inside it −2.5 dB at C6; voice over trumpet: shared C4 to B♭5, worst inside it −12.6 dB at F♯5; clarinet over violin: shared G3 to B♭6, worst inside it −14.0 dB at F♯6; clarinet over voice: shared C4 to C6, worst inside it −31.3 dB at C4; the full map's worst, E3, is outside; clarinet over oboe: shared B♭3 to A6, worst inside it −14.2 dB at F♯6; clarinet over flue pipe: shared D3 to B♭6, worst inside it −14.5 dB at G6; clarinet over trumpet: shared E3 to B♭5, worst inside it −22.7 dB at A♭5; the full map's worst, F♯6, is outside; oboe over violin: shared B♭3 to A6, worst inside it −6.0 dB at E4; the full map's worst, E3, is outside; oboe over voice: shared C4 to C6, worst inside it −33.0 dB at C4; the full map's worst, E3, is outside; oboe over clarinet: shared B♭3 to A6, worst inside it 0.2 dB at B♭3; oboe over flue pipe: shared B♭3 to A6, worst inside it 4.2 dB at A6; oboe over trumpet: shared B♭3 to B♭5, worst inside it −14.2 dB at F4; flue pipe over violin: shared G3 to C7, worst inside it −11.3 dB at G3; flue pipe over voice: shared C4 to C6, worst inside it −34.8 dB at C4; flue pipe over clarinet: shared D3 to B♭6, worst inside it −7.7 dB at D3; flue pipe over oboe: shared B♭3 to A6, worst inside it −10.4 dB at B♭3; flue pipe over trumpet: shared E3 to B♭5, worst inside it −21.0 dB at C4; trumpet over violin: shared G3 to B♭5, worst inside it 9.1 dB at F4; trumpet over voice: shared C4 to B♭5, worst inside it −22.4 dB at C4; the full map's worst, E3, is outside; trumpet over clarinet: shared E3 to B♭5, worst inside it 11.0 dB at E3; trumpet over oboe: shared B♭3 to B♭5, worst inside it 16.9 dB at D5; trumpet over flue pipe: shared E3 to B♭5, worst inside it 22.7 dB at B♭5. Of the seventeen worst notes the full map chose, 8 lie outside a compass and 9 inside.

Half the worst notes of a doubling are notes nobody can play

A map of where two instruments' spectra come closest found seventeen pairs with a worst note of their own, gathered into four clusters, each belonging to one instrument's filter. It drew every instrument over the same five octaves. Read inside the compass each pair can actually play, eight of the seventeen worst notes are out of reach — the voice's C♯6 lies a semitone above a soprano's top C, and its E3 below her lowest note — and two pairs that seemed only to run downhill turn out to have a worst note after all. Of the four clusters, only the violin's B♭4 is advice every pair in it can use.

timbre · Spectrum

Named alongside it

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

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