Enter any 3 values (starting frequency, final frequency, time, and octave rate) into the calculator to determine the missing variable. This calculator helps in understanding the rate of frequency change over time (in octaves per unit time).

Octaves per Minute Calculator

Enter any 3 values to calculate the missing variable

Octaves Per Minute Formula

The following formula is used to calculate the octave rate (octaves per minute) from a starting frequency and a final frequency over a given time.

O = \frac{\log_2\left(\frac{F_2}{F_1}\right)}{T}

Variables:

  • O is the octave rate (octaves per minute)
  • F1 is the starting frequency (Hz)
  • F2 is the final frequency (Hz)
  • T is the time (minutes)

To calculate octaves per minute, divide the logarithm base 2 of the frequency ratio (final frequency divided by starting frequency) by the time in minutes.

What is Octaves Per Minute?

Octaves per minute is a measure of how quickly a frequency doubles (or halves) over time. In music, an octave is the interval between one musical pitch and another with double its frequency. To compute an octave rate from measurements, you need a starting frequency, an ending frequency, and the elapsed time.

How to Calculate Octaves Per Minute?

The following steps outline how to calculate the Octaves Per Minute.

  1. First, determine the starting frequency (F1) in Hertz (Hz).
  2. Next, determine the final frequency (F2) in Hertz (Hz) and the time (T) in minutes.
  3. Next, gather the formula from above: O = log2(F2/F1) / T.
  4. Finally, calculate the Octaves Per Minute (O).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Starting frequency (F1) = 440 Hz (A4 note); Final frequency (F2) = 880 Hz (A5 note)

Time (T) = 2 minutes