Tuning and temperament

Every note name in PedalScope — the drive note of a transfer curve, the pitch axis under a chart, the two notes of a Chord IMD probe, the rows of a waveform matrix — is resolved through one tuning system for one instrument, and until now the app named neither. This page states what is assumed, so that a number on screen can be read for what it is.

The reference

A4 = 440 Hz and twelve-tone equal temperament: every semitone is the same ratio, the twelfth root of two, so A2 is 110.00 Hz, E3 is 164.81 Hz, and E6 is 1318.51 Hz. Wherever a frequency falls between names the label carries its deviation in cents (a cent is a hundredth of a semitone), as in “C♯4 −20¢”. Neither the reference nor the temperament is adjustable.

Note names are nominal

The app’s E3 is 164.81 Hz. No particular guitar’s third fret produces exactly that. A fretted note is routinely 5 to 20 cents off its nominal pitch — the string stretches under the finger, an uncompensated nut pulls the low positions sharp (the whole premise of compensated-nut systems), and bridge intonation is a setup, not a constant. So when a chart says “at E3”, read “at the nominal E3”: the stimulus is a reference tone at the named pitch, not a claim about what comes out of an instrument. The measurement is about what the circuit does to a tone at that frequency; how far your own E3 sits from it is a fact about your guitar.

One exception: E2 is 82.4 Hz

The standard drive note is E2, and the app plays it at 82.4 Hz rather than the 12-TET 82.407 Hz. The reason is continuity, not tuning: 82.4 Hz is the value every early record was measured at, kept verbatim so that the default stimulus stays bit-identical and an explicit E2 pick produces the identical stimulus to the default, comparable with every record before it. Every other note name is exact 12-TET. The difference is 0.15 cents — far inside what any instrument holds — and the waveform matrix’s default low note and its note anchor are the same 82.4 Hz.

What the interval tile’s cents offsets mean

A Chord IMD record’s interval tile reads something like “A2 −4¢ + E3 −7¢”. Those offsets are deliberate. The two-tone probe is snapped to the analysis lattice — both notes moved to exact analysis-bin centres, and the bins chosen so that every intermodulation product lands well clear of every other and of both notes (the reasoning is on How Chord IMD is analyzed). The offsets are the price of separable products, and the app caps them at ±15 cents on each note, so the interval you asked for is still unambiguously the interval that is played.

The tile shows the offsets for the capture in front of you, and they depend on the sample rate, because the bin grid does. One worked example, at 96 kHz (48 kHz is identical): A2 is played at 109.77 Hz, 3.6 cents flat, and E3 at 164.15 Hz, 6.9 cents flat. The delivered interval is 696.65 cents on every rate — 3.35 cents narrower than an equal-tempered fifth, 5.3 cents narrower than a just 3 : 2 — because the ratio of the two bin numbers, 109 : 163, is fixed once and only its common factor changes with the grid; at 88.2 and 44.1 kHz the same ratio lands A2 0.3 cents sharp and E3 3.0 cents flat. All of these are smaller than what a player’s own instrument does to the same interval, so a visible cents offset on the tile is a small, disclosed accommodation and not a detuned instrument.

The note spans assume a six-string guitar in standard tuning

The Guitar axis range is 70 Hz to 8 kHz — the low E with a little drop-tuning headroom, up to where guitar-speaker cabinets have rolled off. The transfer curve’s probe notes run E2 · A2 · E3 · A3 · E4 · A4 · E5 · A5 · A6 · C7, the waveform matrix’s default note span is E2 to E6, and the default Chord IMD interval is A2 + E3, a power chord’s fifth on the fifth and fourth strings. All of it is the standard-tuned six-string guitar. A seven-string, a baritone, or a bass in standard tuning has notes below E2 that these spans do not reach; instrument presets that move the spans are planned as future work, and a stated assumption is what will make them legible when they arrive.