Standard pitch

One note as an anchor

On the page Scales it says how all the other notes arise from this one note: the international tuning standard is A4 equal to 440 Hz, agreed internationally in 1939 and codified by the ISO in 1955 (ISO 16). From this anchor every further note is calculated with twelve-tone equal temperament. Each semitone is the twelfth root of two, about 1.0594631, times the frequency of the preceding one. That is why C4 sounds at 261.63 Hz and E4 at 329.63 Hz.

The page Tools adds the prehistory: after centuries of regional disagreement the orchestral A lay somewhere between about 415 Hz in the Baroque and in places up to about 450 Hz in the 19th century. Today some ensembles still tune to 442 or 443 Hz for a brighter sound.

Why the number stays changeable

The page Tuning & Cents stresses: the number is a convention. What matters for playing together is not the absolute value but that everyone uses the same one. If you play with an orchestra that tunes to 442 Hz, or in historical performance practice at 415 Hz, has to reset the tuner accordingly. The Tools page says that 415 Hz lies almost exactly a semitone below 440 Hz.

The tuner on Maikstrings and in the app Music Tools Duo works with A4 equal to 440 Hz as the default setting; the standard pitch can be changed freely.

The standard pitch on the guitar

On the guitar there are several ways to the standard pitch. On the page Intervals it says: if you fret the high E string at the 5th fret, A sounds at 440 Hz, the standard tuning note. On the page Notes on the Fretboard you find the note A on the A string at the twelfth fret, on the D string at the seventh, on the G string at the second and on the B string at the tenth. Only the last sounds at 440 Hz; the other three sound an octave lower, at 220 Hz.

Beats as a listening aid

How to adjust a note by ear is described by the page Tuning & Cents: the beat frequency corresponds to the difference of the two frequencies. If 440 and 442 hertz sound together, the sound pulses twice per second. Piano tuners work with exactly this: they count beats per second.

Common mistakes

• Taking the standard pitch for a given of nature: 440 Hz is an agreement. Baroque ensembles tune lower, many orchestras higher.
• Not setting the tuner to match the ensemble: If the orchestra plays at 442 Hz, the reference value has to be adjusted, otherwise you sound out of tune despite a green display.
• Confusing A4 and A3: A4 at 440 Hz is the A above middle C (written a′ in German Helmholtz notation). An octave lower lies A3 with 220 Hz.