What are other intonations that exist in music?

Question

I was wondering about the different intonations that have been used in the history of music. I have heard about Pythagorean Intonation, but are there any other types that exist ?

Answer 1

There are a few other types of intonation:

1. Ptolemaic sequence - a tuning for the diatonic scale proposed by Ptolemy

   It is produced through a tetrachord consisting of a greater tone (9:8), lesser tone (10:9), and just diatonic semitone (16:15).

C - 1:1 (0 cents)

D - 9:8 (204 cents)

E - 5:4 (386 cents)

F - 4:3 (498 cents)

G - 3:2 (702 cents)

A - 5:3 (884 cents)

B - 15:8 (1088 cents)

C - 2:1 (1200 cents)

Pythagorean diatonic scale on C:

More information availale here.

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2. Just Intonation - is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Just Notation is frequently found in string and a cappella vocal music, as individual pitches are tweaked up or down to provide rational intervals.

The two notes in any just interval are members of the same harmonic series. Justly tuned intervals can be written as either ratios, with a colon (for example, 3:2), or as fractions, with a solidus (3/2). For example, two tones, one at 300 hertz (cycles per second) and the other at 200 hertz, are both multiples of 100 Hz and as such members of the harmonic series built on 100 Hz. Thus 3:2, known as a perfect fifth, may be defined as the musical interval (the ratio) between the second and third harmonics of any fundamental pitch.

Example of a Harmonic Series with Just Intonation:

More information available here.

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3. Equal Temperament - The most commonly used system of tuning.

It is the basis of the 12-tone chromatic scale. The octave is divided into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the 12th root of 2 (12√2 ≈ 1.05946). The 12TET is usually tunes to A = 440hz. (This is the current standard pitch, but the standard pitch has been increasing due to these reasons. Each part is called a semitone. This (as mentioned above) is the widest used system of tuning.

12 Note Chromatic Scale:

More information available here.

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All information for this answer has been taken from Wikipedia.org.

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Here's a partial list of alternate tunings available in Logic Pro X:

• 1/2 comma mean tone
• Two kinds of 1/4 comma mean tone
• Two kinds of 1/6 comma mean tone
• Two Pythagorean tunings
• Three different seven limit tunings
• Eight different tunings developed by Andreas Werckmeister
• Three different Silberman tunings
• Six Mersenne tunings
• Four Neidhart tunings
• Three Kepler tunings
• Four Kirnberger tunings
• A plethora of Asian tunings like Balinese gamelan, six different Indian tunings, Tibetan, Siamese, and several others
• Many more

There are theoretically an infinite number of possible tunings, and there seems to be hundreds of tunings that have actually been used historically across various cultures.