Minor sixth: Difference between revisions

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| Header 9 = Octave complement | Data 9 = [[Major third]]

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As a diatonic interval category, a minor sixth is an interval that spans five scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 4 fourths [[~~Octave~~ reduction|octave reduced]], and depending on the specific tuning, it ranges from 720 to 857{{cent}} ([[5edo|3\5]] to [[7edo|5\7]]).

As a diatonic interval category, a minor sixth is an interval that spans five scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 4 fourths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 720 to 857{{cent}} ([[5edo|3\5]] to [[7edo|5\7]]).

In [[just intonation]], an interval may be classified as a minor sixth if it is reasonably mapped to five steps of the diatonic scale and eight steps of the chromatic scale.

The minor sixth is often the bounding interval of a [[~~Triad~~|tertian triad]] chord in inversion, and as such is often involved in chord structures in diatonic harmony.

The minor sixth is often the bounding interval of a [[triad|tertian triad]] chord in inversion, and as such is often involved in chord structures in diatonic harmony.

In [[TAMNAMS]], this interval is called the '''minor 5-diastep'''.

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The tuning range of the diatonic minor sixth ranges from 720 to 857.2{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic minor sixth can be found by {{nowrap| (3600 - ''n'')/4 }}. For example, the sixth 816{{c}} gives us {{nowrap| (3600 - 816)/4 {{=}} 2784/4 {{=}} 696{{c}} }}, corresponding to 50edo.

The tuning range of the diatonic augmented fifth ranges from 686 to 960{{c}}. The generator for a given tuning in cents, n, for the augmented fifth can be found by (4800-n)/8. For example, the augmented fifth 816{{c}} gives us {{nowrap| (4800 - 816)/8 {{=}} 3984/8 {{=}} 498{{c}} }}, corresponding to 200edo.

The tuning range of the diatonic augmented fifth ranges from 686 to 960{{c}}. The generator for a given tuning in cents, n, for the augmented fifth can be found by {{nowrap| (4800 - ''n'')/8 }}. For example, the augmented fifth 816{{c}} gives us {{nowrap| (4800 - 816)/8 {{=}} 3984/8 {{=}} 498{{c}} }}, corresponding to 200edo.

== In just intonation ==

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* The 17-limit '''(septendecimal) supraminor sixth''' is a ratio of [[34/21]], and is about 834{{c}}.

Note that the ratios of higher-limit supraminor sixths approximate the golden ratio - the [[golden ratio]] itself as a musical interval is a supraminor sixth of about 833 cents.

Note that the ratios of higher-limit supraminor sixths approximate the golden ratio – the [[golden ratio]] itself as a musical interval is a supraminor sixth of about 833 cents.

== In regular temperaments ==

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 | Header 9 = Octave complement | Data 9 = [[Major third]]
 }}
-As a diatonic interval category, a minor sixth is an interval that spans five scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 4 fourths [[Octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 720 to 857{{cent}} ([[5edo|3\5]] to [[7edo|5\7]]).
+As a diatonic interval category, a minor sixth is an interval that spans five scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 4 fourths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 720 to 857{{cent}} ([[5edo|3\5]] to [[7edo|5\7]]).
 In [[just intonation]], an interval may be classified as a minor sixth if it is reasonably mapped to five steps of the diatonic scale and eight steps of the chromatic scale.
-The minor sixth is often the bounding interval of a [[Triad|tertian triad]] chord in inversion, and as such is often involved in chord structures in diatonic harmony.
+The minor sixth is often the bounding interval of a [[triad|tertian triad]] chord in inversion, and as such is often involved in chord structures in diatonic harmony.
 In [[TAMNAMS]], this interval is called the '''minor 5-diastep'''.
@@ Line 74: / Line 74: @@
 The tuning range of the diatonic minor sixth ranges from 720 to 857.2{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic minor sixth can be found by {{nowrap| (3600 - ''n'')/4 }}. For example, the sixth 816{{c}} gives us {{nowrap| (3600 - 816)/4 {{=}} 2784/4 {{=}} 696{{c}} }}, corresponding to 50edo.
-The tuning range of the diatonic augmented fifth ranges from 686 to 960{{c}}. The generator for a given tuning in cents, n, for the augmented fifth can be found by (4800-n)/8. For example, the augmented fifth 816{{c}} gives us {{nowrap| (4800 - 816)/8 {{=}} 3984/8 {{=}} 498{{c}} }}, corresponding to 200edo.
+The tuning range of the diatonic augmented fifth ranges from 686 to 960{{c}}. The generator for a given tuning in cents, n, for the augmented fifth can be found by {{nowrap| (4800 - ''n'')/8 }}. For example, the augmented fifth 816{{c}} gives us {{nowrap| (4800 - 816)/8 {{=}} 3984/8 {{=}} 498{{c}} }}, corresponding to 200edo.
 == In just intonation ==
@@ Line 88: / Line 88: @@
 * The 17-limit '''(septendecimal) supraminor sixth''' is a ratio of [[34/21]], and is about 834{{c}}.
-Note that the ratios of higher-limit supraminor sixths approximate the golden ratio - the [[golden ratio]] itself as a musical interval is a supraminor sixth of about 833 cents.
+Note that the ratios of higher-limit supraminor sixths approximate the golden ratio – the [[golden ratio]] itself as a musical interval is a supraminor sixth of about 833 cents.
 == In regular temperaments ==