Frequency ratio: Difference between revisions

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A '''frequency ratio''' (often shortened to '''ratio''') is the relationship between the frequencies of the [[pitch]]es of two or more notes. 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).

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

[[~~Chord~~]]s ~~with three or more notes can also be expressed as ratios~~. For example, the just intoned major triad in root position is 4:5:6. Chords can also be written as a string of intervals, such as 1/1–5/4–3/2. (4:5:6 can be viewed as a shorthand for 4/1:5/1:6/1 or 4/4:5/4:6/4).

Ratios with more than two terms (sometimes called '''extended ratios''') can be used to express [[chord]]s and [[Scale|scales]]. For example, the just intoned major triad in root position is 4:5:6. Chords can also be written as a string of intervals, such as 1/1–5/4–3/2. (4:5:6 can be viewed as a shorthand for 4/1:5/1:6/1 or 4/4:5/4:6/4).

The [[harmonic series]] can be represented as the infinite ratio 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:17…

The [[harmonic series]] can be represented as the infinite ratio 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:17… Segments of the harmonic series are commonly written in abbreviated form with a double colon. For example, 8:9:10:11:12:13:14:15:16 is commonly written as 8::16.

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 [[17edo]]", which really means "the chords in which the notes are in the approximate ratio of 4:6:7:9:11 in 17edo".

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+{{Redirect|Ratio|step ratios in scales|Step ratio}}
 A '''frequency ratio''' (often shortened to '''ratio''') is the relationship between the frequencies of the [[pitch]]es of two or more notes. 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).
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 When the larger number is written first (''note''/''base''), this usually signifies a note being played ''above'' some base tone (perhaps the starting note of a scale). When the smaller number is written first (''base''/''note''), this usually signifies the note being played ''below'' that base tone.
-[[Chord]]s with three or more notes can also be expressed as ratios. For example, the just intoned major triad in root position is 4:5:6. Chords can also be written as a string of intervals, such as 1/1–5/4–3/2. (4:5:6 can be viewed as a shorthand for 4/1:5/1:6/1 or 4/4:5/4:6/4).
+Ratios with more than two terms (sometimes called '''extended ratios''') can be used to express [[chord]]s and [[Scale|scales]]. For example, the just intoned major triad in root position is 4:5:6. Chords can also be written as a string of intervals, such as 1/1–5/4–3/2. (4:5:6 can be viewed as a shorthand for 4/1:5/1:6/1 or 4/4:5/4:6/4).
-The [[harmonic series]] can be represented as the infinite ratio 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:17…
+The [[harmonic series]] can be represented as the infinite ratio 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:17… Segments of the harmonic series are commonly written in abbreviated form with a double colon. For example, 8:9:10:11:12:13:14:15:16 is commonly written as 8::16.
 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 [[17edo]]", which really means "the chords in which the notes are in the approximate ratio of 4:6:7:9:11 in 17edo".