# Semitone Calculator

## Semitone Calculator

How to find the interval between two frequencies in semitones? Our Semitone Calculator can help you do just that. Enter the **first frequency** and **second frequency** into the calculator to find the interval between them in semitones.

### How to Use the Calculator

Here’s how you can use the Semitone Calculator:

**Enter the First Frequency**into the input field.- Example: Enter
`440`

.

- Example: Enter
**Select the Unit**for the first frequency (Hz or kHz).- Example: Select
`Hz`

.

- Example: Select
**Enter the Second Frequency**into the input field.- Example: Enter
`880`

.

- Example: Enter
**Select the Unit**for the second frequency (Hz or kHz).- Example: Select
`Hz`

.

- Example: Select
- Click the “Calculate” button to see the result.

The calculator will show the interval between the two frequencies in semitones and cents.

## What is a Semitone?

A semitone, also known as a half step or half tone, is the smallest musical interval commonly used in Western music. It is the interval between two adjacent keys on a piano keyboard, whether white or black.

### Formula

The formula to calculate the interval between two frequencies in semitones is:

$\text{Semitones}=12\times {\mathrm{log}}_{2}\left(\frac{\text{Frequency2}}{\text{Frequency1}}\right)$

$\text{Cents}=1200\times {\mathrm{log}}_{2}\left(\frac{\text{Frequency2}}{\text{Frequency1}}\right)$

**Variables**

Variable | Description |
---|---|

Frequency 1 | The first frequency (Hz or kHz) |

Frequency 2 | The second frequency (Hz or kHz) |

Semitones | Interval in semitones |

Cents | Interval in cents |

## Calculation Examples

### Example 1

**Frequency 1**:`440 Hz`

**Frequency 2**:`880 Hz`

**Step-by-Step Calculation**:

**Enter the First Frequency**:`440`

**Select the Unit**:`Hz`

**Enter the Second Frequency**:`880`

**Select the Unit**:`Hz`

**Apply the Formula**

$\text{Semitones}=12\times {\mathrm{log}}_{2}\left(\frac{880}{440}\right)\approx 12$

$\text{Cents}=1200\times {\mathrm{log}}_{2}\left(\frac{880}{440}\right)\approx 1200$

Result:

- The interval between
`440 Hz`

and`880 Hz`

is approximately`12 semitones`

or`1200 cents`

.

### Example 2

**Frequency 1**:`500 Hz`

**Frequency 2**:`1000 Hz`

**Step-by-Step Calculation**:

**Enter the First Frequency**:`500`

**Select the Unit**:`Hz`

**Enter the Second Frequency**:`1000`

**Select the Unit**:`Hz`

**Apply the Formula**:

$\text{Semitones}=12\times {\mathrm{log}}_{2}\left(\frac{1000}{500}\right)\approx 12$

$\text{Cents}=1200\times {\mathrm{log}}_{2}\left(\frac{1000}{500}\right)\approx 1200$

Result:

- The interval between
`500 Hz`

and`1000 Hz`

is approximately`12 semitones`

or`1200 cents`

.

I hope you liked the tool, In case you are facing any error or issue while using the semitone calculator, please report us at report an error page.