MUIC & ACOUTIC – CALE, TUNING & TEMPERAMENT CALCULATOR
Just Intonation Ratio
A precise tool.
What is the Just Intonation Ratio & How does it work?
Just intonation is a tuning system where the ratios of frequencies between notes are simple whole numbers, reflecting the natural harmonies found in nature. This system aims to provide pure intervals that are mathematically precise.
In contrast, equal temperament divides the octave into twelve equal parts on a logarithmic scale, making each semitone equally spaced. While this allows for easier modulation between keys, it introduces small errors compared to just intonation.
text{Cents Error} = 1200 times log_2(frac{f_{text{just}}}{f_{text{equal}}})
fjust = Frequency in just intonation, fequal = Frequency in equal temperament
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Result
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Frequently Asked Questions
What is just intonation?
Just intonation is a tuning system where the ratios of frequencies between notes are simple whole numbers, aiming for pure intervals.
How does just intonation differ from equal temperament?
Just intonation uses simple whole number ratios, while equal temperament divides the octave into twelve equal parts on a logarithmic scale.
What is cents error in this context?
Cents error refers to the difference between just intonation and equal temperament, measured in cents. A cents error of 1 indicates a small discrepancy.
Can you explain the benefits of just intonation over equal temperament?
Just intonation provides pure intervals that are mathematically precise, reflecting natural harmonies, whereas equal temperament allows for easier modulation between keys but introduces slight errors.
How do I use this calculator to find just intonation ratios?
Input the desired interval or note into the calculator, and it will provide you with the corresponding just intonation ratio.
What are some common intervals used in just intonation?
Common intervals include the perfect fifth (3:2), major third (5:4), and minor third (6:5).
Is just intonation used in modern music?
Yes, just intonation is used by some musicians and composers for its pure sound, though it is less common than equal temperament.
Results are for informational purposes only and do not constitute professional advice.