# 24 Helmholtz temperament

For a general introduction to European historical tunings and these presets, please visit Introduction to European historical tunings and temperaments.

## About this tuning

Each fifthPitches a fifth apart have a 2:3 frequency ratio (in just intonation) or a difference of 700 cents (in 12 tone equal temperament).Visit the link to learn more is narrowed by 1/8 of a schisma (about 0.25 cents) so that 8 fifths produce a 4:5 quintalIn Just/Rational Intonation tunings, ratios are often categorized by the prime numbers that constitute them. The Latin-derived terms "tertial" and "quintal," initiated by composer Catherine Lamb, are used to semantically describe the color and function qualities of the specific primes referenced (3 and 5), as well as the chordal and scale structures these primes generate. Higher primes have traditionally been named in similar manner, i.e. "septimal" (7), "undecimal" (11), "tridecimal" (13), etc.Visit the link to learn more major third. Quintal and tertialIn Just/Rational Intonation tunings, ratios are often categorized by the prime numbers that constitute them. The Latin-derived terms "tertial" and "quintal," initiated by composer Catherine Lamb, are used to semantically describe the color and function qualities of the specific primes referenced (3 and 5), as well as the chordal and scale structures these primes generate. Higher primes have traditionally been named in similar manner, i.e. "septimal" (7), "undecimal" (11), "tridecimal" (13), etc.Visit the link to learn more commasA comma is a small difference in pitch between the same interval in different tuning systems.Visit the link to learn more are both reduced to ca. 20.5 cents, so flats are enharmonic with comma-lowered sharp equivalents, and sharps are enharmonic with comma-raised equivalents.

## Learning more

- Klaus Lang:
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