Translating scale intervals from and to ratios, Hertz, decimals and cents
Throughout history, the intervals of musical scales have been described in several different units of measure: lengths, mathematical ratios, frequency in cycles per second or Hertz (Hz), decimals and cents.
Cents are a logarithmic unit, 100 cents per semitone, starting from A440 Hertz.
Scales are often published in cents, for example, and you may want to translate the intervals to ratios. On the other hand, you might want to translate ratios to cents to easily compare their relative sizes.
The Pitch Palette Calculator converts any one of these units into the other three.
The Calculator has three rows: Units, Output and Input.
Select the units you want to convert from by clicking your mouse on one of
the four option buttons on the top row of the calculator. An input box will
appear on the input row (the bottom row) underneath the type of unit you selected.
Type the units in the input box and press Enter. The results will appear on
the output row (middle row) underneath each of the types of units.
On the left hand side of the Calculator, there is a box labeled Base Pitch.
The default value in this box is 440 Hertz, which is a common default value
for the A above Middle C. This value is used in converting units from one type
to another. This value can be changed by clicking your mouse on that box and
changing the Base Pitch to another number.
Sometimes you may convert from cents, frequency or decimal to ratio and get a high number ratio like 44567:36775. You may wonder if there isn't a simpler ratio that would do. In fact, there likely is. The problem is that logarithmic cents are not precise; that is, they are rounded off. You might want to simply check the Table of Intervals in the appendix to find a small number ratio that is close to the cents figure you are trying to convert. Historical and international scales described in cents are often approximate, so be careful.