Semitone Calculator

Welcome to Omni's semitone calculator, a tool that will help you calculate the distance between two known frequencies or the frequency of a note given the number of semitones between them. This calculator also expresses your results in cents or semitones 🎵

Keep reading to learn about:

• What is a semitone and how to go from semitones to Hz;
• What is a cent in music and how to go from cents to semitones;
• How to calculate the distance between two notes in semitones and cents; and
• How many cents are from 432 Hz to 440 Hz frequencies.

With the semitone calculator, you can get the distance between two frequencies in terms of semitones or cents. To use the semitone calculator:

1. On the first field, Frequency 1 (ƒ₁), input the value of one of your frequencies in hertz (Hz).

2. On the second field, Frequency 2 (ƒ₂), enter the number corresponding to the other frequency.

3. In the rows below, the calculator will show you the distance in number of semitones and cents between the inputted frequencies

For example, if you'd like to know how many cents are from 432 Hz to 440 Hz:

1. Input 432 Hz on the Frequency 1 (ƒ₁) field.

2. After you input this value, a new row will appear, indicating the closest musical note to this frequency you entered and by how much it's on pitch or not. For our example, this frequency corresponds to A4 with a deviation of -31.767 cents.

3. Next, proceed to enter the 440 Hz on the Frequency 2 (ƒ₂) row.

4. Similarly, the calculator will indicate the closest musical note to this value. This frequency corresponds exactly to A4.

5. Finally, the semitone calculator will give you the results for the Semitones between frequencies (n) and Cents between frequencies. For this particular example, these correspond to:

   • Semitones between frequencies (n) = 0.31767 st
   • Cents between frequencies = 31.767 cent

A semitone, also known as a half step or a half tone, is the smallest musical interval used in Western music. It represents the distance between two consecutive notes. For example, two consecutive frets on a guitar or keys on a piano or keyboard:

• From C (white key) to C♯ (black key), there's a semitone.

• From E (white key) to F (white key), there's a semitone.

• From F (white key) to G (white key), there're two semitones.

Or we could also see this on any musical scale. For example, a major scale that always follows the formula of whole, whole, half, whole, whole, whole, half:

• From C to D, there's a whole tone (two semitones).

• From D to E, there's a whole tone (two semitones).

• From F to F, there's a half (one semitone).

• From F to G, there's a whole tone (two semitones).

• From G to A, there's a whole tone (two semitones).

• From B to C, there's a whole tone (two semitones).

• From C to B, there's a half (one semitone).

In terms of frequencies, a semitone is equal to a frequency ratio of 2^1/12 (approximately 1.0595) for equal-tempered tuning.

To measure the distance between two notes' frequencies f₁ and f₂, one of the units of measure used is the cent. This unit was created by Alexander Ellis (1885), who took a musical octave and divided it into 1200 cents.

For a 12 tone equal temperament, each of the 12 semitones are equally separated by 100 cents. Thus, one cent is equal to a 1/100 semitone or a 1/1200 of an octave.

To express the exact semitone in other octaves, the difference between these two notes will be different in hertz but always the same in cents (100 cents). The primary use of cents notation is that it allows expressing the same frequency ratio as a constant value, independent of the octave. It's also used to compare similar intervals in different tuning systems.

The formula to calculate the number of cents between given frequencies f₁ and f₂:

cent = 1200 × log₂(f₂ / f₁)

To convert two frequencies in hertz (Hz) to semitones (st), use the formula:

n = 12 × log₂(f₂ / f₁)

where:

• n – Number of semitones [st]; and
• f₁ and f₂ are frequencies in hertz [Hz].

For example, if f₁ = 36.71 Hz and f₂ = 698.46 Hz, then:

1. n = 12 × log₂(698.46 Hz / 36.71 Hz)
2. n = 12 × log₂(19.026)
3. n = 51 st

It's not hard to go from semitones to cents! Simply multiply the number of semitones by 100 cent/st et voilà! For example, to convert 51 st to cents, you calculate as follows:

cents = 51 st × (100 cent/st) = 5100 cent.

100 cents. Every half step or semitone corresponds to 100 cents. The twelve-tone equal temperament musical system divides an octave into 12 semitones equally distanced by 100 cents. A half step is also known as a semitone.

1200 cents. There're 12 semitones or half steps in one octave, and since every semitone is equal to 100 cents, the total of cents in an octave is 1200.

-31.767 cents. To get this value:

1. Use the formula:

   n = 1200 × log₂(f₂/f₁).

2. Substitute the values of frequencies in hertz:

   f₁ = 440 Hz and f₂ = 432 Hz
   n = 1200 × log₂(432Hz / 440 Hz)

3. Perform the corresponding calculation to get the value:

   n = -31.767 cent