Neutral third: Difference between revisions

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A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.

Diatonically, neutral thirds appear as part of the variant of diatonic with generators halved, where the neutral third is the generator and the 600-cent [[tritone]] is the period.

The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.

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== In just intonation ==

=== By prime limit ===

The [[3-limit]] and 5-limit do not have simple neutral thirds, so we start with the 7-limit:

The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit:

* The 7-limit '''artoneutral''' and '''tendoneutral thirds''' are the ratios of [[60/49]] and [[49/40]] respectively, and they are slightly flat of and slightly sharp of 351{{c}} respectively.

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 {{Wikipedia}}
 A '''neutral third''' ('''n3'''), as a concrete [[interval region]], is typically near 350 [[cents]] in size, distinct from the [[minor third]] of roughly 300 [[cent]]s and the [[major third]] of roughly 400{{c}}. A rough tuning range for the neutral third is 330 to 370{{c}} according to [[Margo Schulter]]'s theory of interval regions.
+Diatonically, neutral thirds appear as part of the variant of diatonic with generators halved, where the neutral third is the generator and the 600-cent [[tritone]] is the period.
 The neutral third range is generally divided at roughly 350{{c}} into '''artoneutral''' (flatter) and '''tendoneutral''' (sharper) thirds. As such, neutral thirds tend to exist in pairs.
@@ Line 18: / Line 20: @@
 == In just intonation ==
 === By prime limit ===
-The [[3-limit]] and 5-limit do not have simple neutral thirds, so we start with the 7-limit:
+The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit:
 * The 7-limit '''artoneutral''' and '''tendoneutral thirds''' are the ratios of [[60/49]] and [[49/40]] respectively, and they are slightly flat of and slightly sharp of 351{{c}} respectively.