Note Ratio

Name: Note Ratio
Author: Jürgen Kummer

Calculates the ratio of the tone pitches of two notes at an equal temperament.Then, an octave has twelve notes with equal sized half step distances from each other. The equality of the steps refers to the ratio, not to absolute values. The pitch ratio of two neighboring tones ist the twelfth root of two. Between any two tones, the ratio is ¹²√ 2ⁿ , this is twelfth root of two to the power of the distance of the notes, where n is the interval size.
The frequency of a tone can be taken from the tuning calculator. Please enter an interval and select, if the calculation should be done upwards or downwards. Optionally, enter a frequency. The ratio will be calculated and, if a frequency is given, the new frequency. The original note is denoted by x, and the resulting note by y. While x and y are rather uncommon in music, they are common in mathematics and therefore used here. These were chosen to better distinguish between the two relationships x to y (x/y) and y to x (y/x).

Interval:
Direction:	upwards downwards
Frequency x:
New frequency y:
Ratio x/y:
Ratio y/x:

For example, if the A4 has a frequency of 440 hertz, then the A#4 with an interval of one second upwards has a frequency of 466.1638 hertz. The ratio between these two notes is 0.9439 to 1, or 1 to 1.0595. Both mean the same thing, they are just calculated the other way around.

For an octave, the ratio is 2 to 1, or 1 to 0.5. This means that double the frequency produces the same note an octave higher, and half the frequency produces the same note an octave lower. Thus, A4 has a frequency ratio of 2 to 1 to A3, and to A5 a frequency ratio of 1 to 2. A difference of two octaves (interval 24) then corresponds to a quadrupling or quartering of the frequency, three octaves (interval 36) to an eightfold or eighthing, and so on.