Generator

The flow through the larynx, over two periods of a 110 Hz note

Volume flow against time, in Rosenberg's two-half-cosine model of the glottal pulse — a slow opening, a faster closing, and a closed phase during which no air passes at all. M1 — chest is open for 50 per cent of each period and opens 2.4 times as slowly as it closes. Nothing here is a displacement: the folds are a valve on a steady stream of air, and the flat stretches are the moments they are shut. At 110 Hz each period lasts 9.1 milliseconds, of which 4.5 is silence.

Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.

It makes a noise. 17 of its 17 placements carry sound, built from the same numbers as the drawing, offering these buttons: 1600 Pa — 87 dB, 220 Hz in chest, 2400 Pa — 93 dB, 500 Pa — 63 dB, 800 Pa — 75 dB, M1 — chest — the bare source at 110 Hz, M1 — chest — the bare source at 220 Hz, M1 — chest, no tract — 110 Hz and 8 more.

Called by 5 essays

the blast radius of changing it

The other instrument with a reed

The folds do not vibrate the way a string does. They open and shut across a steady stream of air, once per period, and what leaves the larynx is a train of flow pulses with a closed phase in it. Everything said about the voice's tone is a statement about the shape of that pulse — and the shape has two numbers in it.

instruments · The voice

Two mechanisms, the notes both of them make, and the seam. The frequency range of each laryngeal mechanism for an adult male voice, on a logarithmic axis, with the band both can produce shaded. M1 — chest runs 82–349 Hz and M2 — falsetto runs 220–698 Hz, so 799 cents of the range — 8.0 semitones — can be sung either way. The two dots inside that band are the measured signature that this is a bifurcation rather than a threshold: the change upward happens at 330 Hz and the change downward at 294 Hz, 200 cents lower. A threshold is crossed at the same place in both directions and this is not.

Two mechanisms, and the seam between them

Every singer has a place in the range where the voice changes character, and eight semitones of it can be produced either way. The measurement that settles what kind of a place it is takes ten seconds: the change upward happens two hundred cents higher than the change downward, and a threshold cannot do that.

instruments · The voice

A reed that shuts at 5000 pascals, and the air it lets through. Volume flow through the reed channel against the pressure across it, in the quasi-static model: Bernoulli flow through an opening that closes linearly with pressure. The flow peaks at 1667 pascals — exactly a third of the closing pressure, for any reed, because that is where the two effects balance — and it is 0.18 litres a second there. Everything to the right of that peak is the argument: the flow falls as the player blows harder, from 0.18 to 0.05 litres a second by 4500 pascals, and a resistance that behaves that way supplies energy instead of taking it. There is no reed inertia in this model, so it cannot squeak.

The reed is a valve, not a vibrator

Three essays here have said that a clarinet's reed does not choose the note, and none of them said what it does instead. It chops a steady stream of air, and past a third of the pressure that closes it the flow falls as the player blows harder — a resistance with the wrong sign, which is the only thing in the instrument capable of putting energy into an oscillation that is otherwise losing it.

instruments · Air column

The note that moved by a minor third

A has been anywhere between 392 and 465 hertz in the surviving record, which is 296 cents — a minor third short of six. The usual conclusion is that absolute pitch level is a convention and nothing musical depends on it. That is true of everything written on paper and false of everything that happens in a throat or a body: a singer's register break sits at a fixed frequency, so across the historical range it lands three semitones further down the written page. Transposing a piece is not a uniform operation, because the performer does not transpose.

tuning · Pitch standard

Where the register break falls on a tenor's page. The two measured laryngeal crossings — 330 hertz going up and 294 coming down — read as WRITTEN notes, against the pitch standard the part is performed at. The crossings are frequencies and do not move; the notation does, so the seam slides down the stave by exactly the interval the standard rises. At A392 the upward crossing is written F♯4, at A415 it is F4, at A440 E4 and at A465 E♭4 — a minor third of movement across four centuries, on a part nobody rewrote. Across the range drawn the seam passes 4 written semitones. The shaded horizontal band is the tenor's written compass, C3 to A4; the seam is inside it at 7 of the 7 documented standards drawn.

A standard moves the page, and not the seam

Every earlier essay has priced a pitch standard against something with a fixed length in it. A voice has none, so nothing about it changes at all — what changes is where the written note falls against a break in the larynx that is a frequency and stays put. At A415 that break is written F4, at A440 it is E4 and at Chorton it is E♭4: a minor third of movement across four centuries, on a part nobody rewrote.

tuning · Pitch standard

All figures · What can be heard