Ratios

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A frequency ratio is the relationship between the frequencies of two sound waves. For example, a piano string vibrating at 110 Hz (110 times per second) and a piano string vibrating at 220 Hz are in a 2:1 ratio (since 220/110 reduces to 2/1).

Ratios of frequencies may be written several ways:

2/1

2:1

1/2

1:2

When the larger number is written first, this usually signifies a second note being played above some base tone (perhaps the starting note of a scale). When the smaller number is written first, this usually signifies the second note being played below that base tone.

The harmonic series can be represented as a ratio - 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:17... etc.

Chords can also be expressed as ratios. For example, the just intoned major chord in root position is 4:5:6. (When chords are expressed as ratios, the above rule about the notes being above or below a base tone doesn't usually apply). Chords can also be written as a string of intervals, such as the major chord 1/1–5/4–3/2

In the context of just intonation, ratios are almost always used to label and identify intervals and chords. However, the use of ratios to identify intervals and chords in tempered scales is also common - in these cases, it is implied that the notes are in the approximate ratio indicated. For example, a common shorthand expression might be "4:6:7:9:11 chords in 17-EDO" - which really means "The chords in which the notes are in the approximate ratio of 4:6:7:9:11 in 17-EDO".