Major third: Difference between revisions

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== In just intonation ==

=== By prime limit ===

3-limit ~~intervals~~ in the range of major thirds ~~include~~ the Pythagorean major third of [[81/64]], ~~407.8~~{{c}} in size, which ~~corresponds to the mos-based interval category of the diatonic major third and~~ is generated by [[stacking]] four just perfect fifths of [[3/2]]~~, and the Pythagorean diminished fourth of [[8192/6561]], which is flat of 81/64 by one Pythagorean comma, and is about 384{{c}} in size~~.

The simplest 3-limit interval in the range of major thirds is the Pythagorean major third of [[81/64]], 408{{c}} in size, which is generated by [[stacking]] four just perfect fifths of [[3/2]].

Much [[odd limit|simpler]] major thirds exist in higher [[prime limit|limits]], however, for example:

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* The 5-limit '''classical major third''' is a ratio of [[5/4]], and is about 386{{c}}.

* The 7-limit '''(septimal) supermajor third''' is a ratio of [[9/7]], and is almost exactly 435{{c}}.

* The 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is ~~almost exactly 417.5~~{{c}}.

* The 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is about 418{{c}}.

* The 13-limit '''(tridecimal) ultramajor third''' is a ratio of [[13/10]], and is about 454{{c}}.

** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.

@@ Line 18: / Line 18: @@
 == In just intonation ==
 === By prime limit ===
--limit intervals in the range of major thirds include the Pythagorean major third of [[81/64]], 407.8{{c}} in size, which corresponds to the mos-based interval category of the diatonic major third and is generated by [[stacking]] four just perfect fifths of [[3/2]], and the Pythagorean diminished fourth of [[8192/6561]], which is flat of 81/64 by one Pythagorean comma, and is about 384{{c}} in size.
+The simplest 3-limit interval in the range of major thirds is the Pythagorean major third of [[81/64]], 408{{c}} in size, which is generated by [[stacking]] four just perfect fifths of [[3/2]].
 Much [[odd limit|simpler]] major thirds exist in higher [[prime limit|limits]], however, for example:
@@ Line 24: / Line 24: @@
 * The 5-limit '''classical major third''' is a ratio of [[5/4]], and is about 386{{c}}.
 * The 7-limit '''(septimal) supermajor third''' is a ratio of [[9/7]], and is almost exactly 435{{c}}.
-* The 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is almost exactly 417.5{{c}}.
+* The 11-limit '''neogothic major third''' is a ratio of [[14/11]], and is about 418{{c}}.
 * The 13-limit '''(tridecimal) ultramajor third''' is a ratio of [[13/10]], and is about 454{{c}}.
 ** There is also a 13-limit '''(tridecimal) submajor third''', which is a ratio of [[26/21]], and is about 370{{c}}.