Ratio Calculator
Multiply, divide, and stack just-intonation ratios into one reduced result.
What the calculator does
Build a stack of frequency ratios and the module multiplies them into a single combined ratio, shown in lowest terms. Each term is a numerator over a denominator with an optional exponent, so you can raise a ratio to a power or, with a negative exponent, invert it to divide. Stack 3/2 and 5/4, for example, and the result is 15/8. It is built for just intonation: exact integer ratios, never rounded to the nearest cent.
Stacking ratios
Start from the base ratio and add as many terms as you need. Every term carries a numerator, a denominator, and a signed exponent: a positive exponent multiplies the ratio by itself, and a negative exponent inverts it, so 3/2 with an exponent of -1 divides by a fifth rather than multiplying by one. The running product is reduced to lowest terms as you type, so the headline ratio is always coprime. Every term stays an exact integer ratio, so stacks that trip up general-purpose fraction tools work here: twelve fifths reduce to the Pythagorean comma, 531441/524288.
Octave reduction, decimal, and cents
The result headlines the octave-reduced ratio, folded into a single octave (the 1 to 2 range), alongside its decimal value and its size in cents. When the raw stacked ratio spans more than an octave, the full-register ratio is shown next to the reduced form so you can see both the pitch class and the absolute interval at once.
Auditioning the result
Audition the interval against a 1/1 base tone at a configurable fundamental frequency. The octave-reduced interval always plays; the full-register interval plays when its pitch stays inside the audible range. The tone glides in real time as you edit a term, so A/B comparisons between two stacks stay live.
Who this is for
Useful whenever intervals are built from prime ratios rather than equal-tempered steps. Just-intonation and xenharmonic composers can combine commas and prime intervals and read the reduced result; theorists can show how stacked ratios multiply into a single fraction; anyone can move between ratio, decimal, and cents without leaving the app. To convert a single interval between ratios and cents or find a constrained approximation of a cent value, use Interval & Tuning.