Tuning Reference (String Frequencies & Temperaments)

What it is for

Most tuners only show "in tune" or "flat". Sometimes you need the numbers: the exact frequency of every string when your orchestra tunes to A = 442 Hz, what a baroque ensemble at A = 415 Hz means for your violin's G string, or how many cents each note of a historical temperament sits away from the piano you know.

The Tuning Reference lists the strings of an instrument tuning (guitar, 7-string, bass, ukulele, violin, viola, cello, double bass, mandolin or banjo) and a whole octave of notes, each with its frequency in hertz and its deviation from equal temperament in cents. Six temperaments are available: equal temperament, 5-limit just intonation, Pythagorean, quarter-comma meantone, Werckmeister III and Vallotti. The tuner and drones in Tonegrid's Practice view use exactly the same tables.

It does not model piano stretch tuning or the inharmonicity of real strings.

Worked example

With the default guitar in standard tuning at A4 = 440 Hz in equal temperament, the strings come out as E2 82.407 Hz, A2 110.000 Hz, D3 146.832 Hz, G3 195.998 Hz, B3 246.942 Hz and E4 329.628 Hz, every one 0.00 cents from equal temperament.

Now a cellist who plays continuo in a group using Vallotti at A = 442 Hz: choose Cello: C G D A, enter 442, pick Vallotti with tonic C and octave 2. The strings are C2 65.927 Hz (+5.87 cents), G2 98.667 Hz (+3.91), D3 147.666 Hz (+1.96) and A3 221.000 Hz (0.00). Each fifth below A is a sixth of a Pythagorean comma narrower than pure, so the lower strings sit a little sharp of equal temperament. In the octave table, E2 is −1.96 cents and B2 −3.91 cents: Vallotti's thirds in C are purer than on a piano.

The third example sets just intonation on D at A4 = 442 Hz for a D drone: F♯3 is 15.64 cents flat of equal temperament, which is exactly the pure major third 5/4 above D.

How to read the result

• The strings table appears when you choose an instrument; string 1 is the first note in the tuning name.
• The octave table has the note, MIDI number, frequency, Cents from equal (positive = sharper than a piano tuned to the same A) and Cents above tonic (the size of each step in the temperament).
• The note below the tables describes the chosen temperament in one sentence.

Tips and common mistakes

• A4 always stays at the reference pitch, so in every temperament A shows 0.00 cents. Some tuners anchor the tonic instead; then all values shift by the same amount.
• The Tonic matters for every temperament except equal temperament: just intonation and meantone sound best in their own key and worse further away.
• One cent is a hundredth of a semitone. Differences below about 5 cents are hard to hear on single notes but clear in chords and against a drone.
• For bowed strings tuned in pure fifths, choose Pythagorean: its fifths are exactly 3/2.

FAQ

Which reference pitch should I use?

440 Hz is the international standard. Many orchestras tune to 442 or 443 Hz, and baroque ensembles often use 415 Hz, a semitone below 440.

What is the difference between Werckmeister III and Vallotti?

Both are well temperaments in which every key is usable. Werckmeister III tempers four fifths by a quarter of the Pythagorean comma; Vallotti tempers six fifths by a sixth, which makes the change from key to key smoother.

Can I tune with this page?

Use the tuner in Tonegrid's Practice view for that: it listens with your microphone and compares against these same frequencies.