How to Use JI Calc to Build Perfect-Tuned Scales

Create Custom Just-Intonation Intervals with JI Calc

JI Calc is a tool for designing and examining just‑intonation (JI) intervals—pure, ratio‑based tunings built from small whole‑number frequency ratios. Use JI Calc to convert ratios to cents, combine prime factors, and produce playable tunings.

What you can do

• Enter or build intervals using prime‑limit factorization (2, 3, 5, 7, 11, …).
• Convert a ratio (e.g., ⁄₄) to cents and frequency multipliers.
• Create chains of intervals (stack ratios) and see resulting ratios and cents.
• Normalize intervals into a single octave (divide or multiply by powers of 2).
• Export or copy tuning data for use in synths, samplers, or tuning software.

Quick workflow

1. Pick a target pitch reference (A = 440 Hz by default).
2. Specify an interval as a ratio or by prime exponents (e.g., 3^1·5^-1 for ⁄₅).
3. JI Calc shows the decimal multiplier, cents value, and octave‑normalized form.
4. Chain or combine intervals to build scales; adjust to minimize large prime deviations.
5. Export intervals as frequency values or cent offsets for your instrument.

Practical tips

• Use small primes (3, 5, 7, 11) for musically consonant intervals.
• Keep numerator and denominator small to avoid impractical tuning ratios.
• Compare intervals in cents to equal temperament equivalents to hear differences.
• When building scales, decide whether to prioritize purity of specific intervals (e.g., pure fifths) or evenness across the scale.

If you want, I can generate a sample 7‑note JI scale (with ratios, cents, and frequencies for A=440 Hz).