Minor seventh: Difference between revisions

(5 intermediate revisions by 2 users not shown)

Line 1:

A '''minor seventh (m7)''' is an interval that spans six scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 2 fourths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 960 to 1029{{cent}} ([[5edo|4\5]] to [[7edo|6\7]]).

In [[just intonation]], an interval may be classified as a minor seventh if it is reasonably mapped to 6\7 and [[24edo|20\24]] (precisely six steps of the diatonic scale and ten steps of the chromatic scale). The use of 24edo's 20\24 as the mapping criteria here rather than [[12edo]]'s 10\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. While the 24edo patent val does not map 7/4 to 20\24, the 24d val does, and that can still be considered a reasonable mapping.

As a concrete [[interval region]], it is typically near 1000{{c}} in size, distinct from the [[major seventh]] of roughly 1100{{c}} and the [[neutral seventh]] of roughly 1050{{c}}. A rough tuning range for the minor seventh is about 960 to 1025{{c}} according to [[Margo Schulter]]'s theory of interval regions.

This article covers intervals between 940 and 1040 cents. The outer range of this might be too extreme to call "minor sevenths", but this is done so that one can find what they're looking for easily.

== In just intonation ==

=== By prime limit ===

The Pythagorean ([[3-limit]]) minor seventh is [[16/9]], which is 996{{c}} in size and corresponds to the mos-based interval category of the diatonic minor seventh. It is generated by [[stacking]] two just perfect fourths of [[4/3]].

Other ~~major seconds~~ exist in higher [[prime limit|limits]]:

Other minor sevenths exist in higher [[prime limit|limits]]:

* The 5-limit '''ptolemaic minor seventh''' is a ratio of [[9/5]], however in 5-limit harmony it is used alongside 16/9. It is about 1018{{c}}.

* The 7-limit '''(septimal) subminor seventh''', '''harmonic seventh''', or '''overtone seventh''' is a ratio of [[7/4]], and is about 969{{c}}.

The mean of 16/9, 9/5 and 7/4 is [[959/540]].

@@ Line 1: / Line 1: @@
+A '''minor seventh (m7)''' is an interval that spans six scale steps in the [[5L 2s|diatonic]] scale with the minor (narrower) quality. It is generated by stacking 2 fourths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 960 to 1029{{cent}} ([[5edo|4\5]] to [[7edo|6\7]]).
+In [[just intonation]], an interval may be classified as a minor seventh if it is reasonably mapped to 6\7 and [[24edo|20\24]] (precisely six steps of the diatonic scale and ten steps of the chromatic scale). The use of 24edo's 20\24 as the mapping criteria here rather than [[12edo]]'s 10\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. While the 24edo patent val does not map 7/4 to 20\24, the 24d val does, and that can still be considered a reasonable mapping.
+As a concrete [[interval region]], it is typically near 1000{{c}} in size, distinct from the [[major seventh]] of roughly 1100{{c}} and the [[neutral seventh]] of roughly 1050{{c}}. A rough tuning range for the minor seventh is about 960 to 1025{{c}} according to [[Margo Schulter]]'s theory of interval regions.
+This article covers intervals between 940 and 1040 cents. The outer range of this might be too extreme to call "minor sevenths", but this is done so that one can find what they're looking for easily.
 == In just intonation ==
 === By prime limit ===
 The Pythagorean ([[3-limit]]) minor seventh is [[16/9]], which is 996{{c}} in size and corresponds to the mos-based interval category of the diatonic minor seventh. It is generated by [[stacking]] two just perfect fourths of [[4/3]].
-Other major seconds exist in higher [[prime limit|limits]]:
+Other minor sevenths exist in higher [[prime limit|limits]]:
 * The 5-limit '''ptolemaic minor seventh''' is a ratio of [[9/5]], however in 5-limit harmony it is used alongside 16/9. It is about 1018{{c}}.
 * The 7-limit '''(septimal) subminor seventh''', '''harmonic seventh''', or '''overtone seventh''' is a ratio of [[7/4]], and is about 969{{c}}.
+The mean of 16/9, 9/5 and 7/4 is [[959/540]].
 {{Navbox intervals}}