MUIC & ACOUTIC – CALE, TUNING & TEMPERAMENT CALCULATOR
Meantone Temperament
A precise tool.
What is the Meantone Temperament & How does it work?
Meantone temperament is a system of musical tuning in which the perfect fifth (the interval between one pitch and another that is half an octave higher) is tuned to a slightly smaller size than the just intonation ratio of 3:2. This results in a more uniform distribution of intervals across the scale, making it easier to modulate between keys.
f_{text{meantone}} = f_0 times (sqrt[12]{2})^{n}
f_{text{meantone}} = frequency of the note in meantone temperament
f_0 = reference frequency (e.g., A4 at 440 Hz)
n = number of half steps from the reference pitch
f_0 = reference frequency (e.g., A4 at 440 Hz)
n = number of half steps from the reference pitch
In quarter-comma meantone temperament, the perfect fifth is tuned to a ratio of 256:243, which introduces a small comma (the difference between the Pythagorean and just intonation fifths) that is divided into four equal parts. This system allows for more consonant major thirds but can make some intervals less pure.
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Frequently Asked Questions
What is meantone temperament?
Meantone temperament is a musical tuning system where the perfect fifth is slightly smaller than the just intonation ratio, resulting in more uniform intervals across the scale.
How do I use this calculator for meantone temperament?
Enter your reference frequency (e.g., A4 at 440 Hz) and the note number to calculate its frequency in meantone temperament.
What is the formula used in this calculator?
The formula used is f_{text{meantone}} = f_0 times (sqrt[12]{2})^{n}, where f_0 is the reference frequency and n is the note number.
Why use meantone temperament over other tunings?
Meantone temperament allows for easier modulation between keys due to its more uniform distribution of intervals, making it popular in Western music.
Can this calculator be used for any instrument?
Yes, this calculator can be used for any instrument that uses the standard chromatic scale and requires tuning in meantone temperament.
What is the difference between just intonation and meantone temperament?
Just intonation uses exact mathematical ratios for intervals, while meantone temperament slightly adjusts these ratios to create a more uniform scale across keys.
How does meantone temperament affect music composition?
Meantone temperament allows composers to modulate between keys more easily, which can add complexity and variety to compositions.
Results are for informational purposes only and do not constitute professional advice.