113 Hz in Music Theory: Note, Cents and Harmonics

Where 113 Hz Falls on the Keyboard

A tuner will usually show 113 Hz as A, needle almost half a semitone sharp. If you tune to A4 = 432 Hz instead, A2 is 108 Hz and A♯2 is 114.42 Hz, so 113 Hz reads as an A♯2 about 22 cents flat.

The calculation

The distance between two frequencies in cents is 1200 × log₂(f₂ ÷ f₁). For 113 Hz against A2: 1200 × log₂(113 ÷ 110) = 1200 × log₂(1.02727) ≈ 46.6 cents. A semitone is 100 cents, so 113 Hz is just under halfway to the next note.

Octaves and Harmonics of 113 Hz

Because 113 Hz is about 47 cents sharp of A, its octaves are too. Its upper harmonics land between notes as well:

Played against a standard-tuned A2 (110 Hz), a 113 Hz tone creates 3 beats per second: the difference between the two frequencies. That slow wobble is exactly what you hear when tuning a string that is close but not yet in tune.

Physical Properties of a 113 Hz Tone

• Period: 1 ÷ 113 ≈ 8.85 milliseconds per cycle.
• Wavelength in air: 343 m/s ÷ 113 Hz ≈ 3.04 m (about 10 ft) at 20 °C.
• Room acoustics: a room dimension of about 1.52 m (half that wavelength) has its first axial resonance near 113 Hz, so low-frequency build-up around this pitch is common in small rooms.
• Hearing: 113 Hz is well within human hearing (roughly 20 Hz–20 kHz), but the ear is less sensitive here than in the 1–5 kHz range, so it needs more sound pressure to seem equally loud.

Testing a 113 Hz tone with a tone generator or headphones? Keep the volume moderate. See how loud 113 decibels is for safe listening levels.

Instruments and Voices That Can Play 113 Hz

• Bass guitar and double bass: the open A string is A1 (55 Hz) and 113 Hz sits just above the A2 an octave higher. Fretless instruments can hit it exactly; on a fretted bass it needs a slight bend.
• Cello: the lowest string is C2 (about 65.4 Hz), so 113 Hz is comfortably in range and reachable by finger position.
• Trombone, tuba and bassoon: 113 Hz is in their low-to-middle register; players can adjust pitch with slide or embouchure.
• Male voices: 113 Hz is in the normal range of bass and baritone singers and close to typical adult male speaking pitch.
• Synthesizers and software: any oscillator can be set to exactly 113 Hz, or to A2 with a +47 cent fine-tune.
• Piano and fixed-pitch instruments: cannot play 113 Hz unless retuned.

113 Hz vs 113 BPM

They are easy to confuse but measure different things. 113 Hz is 113 cycles per second and you hear it as pitch. 113 BPM is 113 beats per minute, only about 1.88 events per second, and you hear it as tempo. For tempo, delay times and a metronome, see 113 BPM; for playlist ideas, see 113 BPM songs.

Is 113 Hz Special?

Musically, no: 113 Hz is not a standard pitch in any common tuning system, and we are not aware of well-known compositions built around it. You may see 113 Hz listed in "healing frequency" or meditation playlists, but there is no good scientific evidence that it, or any single frequency, has special effects on the body. Its interest is mathematical: 113 is a prime number, so the frequency shares no simple whole-number ratio with standard concert pitches.

Frequently Asked Questions