Interval size measure: Difference between revisions

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: {{nowrap|''a''\''N'' − ''b''\''N'' = (''a'' − ''b'')\''N''}} expresses the same thing as {{nowrap|2''a''/''N'' / 2''b''/''N'' {{=}} 2(''a'' - ''b'')/''N''.}}

Backslash notation can be extended to support [[nonoctave]] [[equal tuning]]s by writing the tuning in full after the backslash. For example, 11\13edt means 11 steps of [[13edt]], 14\9edf means 14 steps of [[9edf]], and 7\12ed12/5 means 7 steps of [[12ed12/5]].

=== Gross ===

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Intervals are sometimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music. An early unit for measuring intervals is the "[[tone]]" which dates back to classic Greece.

In serial music, all intervals were measured by the number of 12edo [[semitone]]s. In analogy, the '''relative interval measure''' is the number of steps between two pitches of an [[equal tuning]], sometimes called "[[degree]]s". These measures can be written using [[#Backslash notation|backslash notation]], which looks like a frequency ratio but using a backslash (instead of a forward slash) to indicate a logarithmic ratio. For example, 11\15 means 11 steps of 15edo, 4\9edf means 4 steps of 9edf, and 16\21ed12/7 means 16 steps of 21ed12/7.

In serial music, all intervals were measured by the number of 12edo [[semitone]]s. In analogy, the '''relative interval measure''' is the number of steps between two pitches of an [[equal tuning]], sometimes called "[[degree]]s". These measures can be written using [[#Backslash notation|backslash notation]] if the degree itself isn't sufficiently clear in context.

=== Fine ===

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 : {{nowrap|''a''\''N'' &minus; ''b''\''N'' = (''a'' &minus; ''b'')\''N''}} expresses the same thing as {{nowrap|2<sup>''a''/''N''</sup> / 2<sup>''b''/''N''</sup> {{=}} 2<sup>(''a'' - ''b'')/''N''</sup>.}}
+Backslash notation can be extended to support [[nonoctave]] [[equal tuning]]s by writing the tuning in full after the backslash. For example, 11\13edt means 11 steps of [[13edt]], 14\9edf means 14 steps of [[9edf]], and 7\12ed12/5 means 7 steps of [[12ed12/5]].
 === Gross ===
@@ Line 21: / Line 23: @@
 Intervals are sometimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music. An early unit for measuring intervals is the "[[tone]]" which dates back to classic Greece.
-In serial music, all intervals were measured by the number of 12edo [[semitone]]s. In analogy, the '''relative interval measure''' is the number of steps between two pitches of an [[equal tuning]], sometimes called "[[degree]]s". These measures can be written using [[#Backslash notation|backslash notation]], which looks like a frequency ratio but using a backslash (instead of a forward slash) to indicate a logarithmic ratio. For example, 11\15 means 11 steps of 15edo, 4\9edf means 4 steps of 9edf, and 16\21ed12/7 means 16 steps of 21ed12/7.
+In serial music, all intervals were measured by the number of 12edo [[semitone]]s. In analogy, the '''relative interval measure''' is the number of steps between two pitches of an [[equal tuning]], sometimes called "[[degree]]s". These measures can be written using [[#Backslash notation|backslash notation]] if the degree itself isn't sufficiently clear in context.
 === Fine ===