Major second: Difference between revisions

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=== By prime limit ===

The '''Pythagorean ([[3-limit]]) major second''' is 9/8, which is 204 cents in size and corresponds to the MOS-based interval category of the diatonic major second. It is generated by [[stacking]] two just perfect fifths of [[3/2]]. There is also a '''Pythagorean diminished third''' of 65536/59049, which is about 180 cents in size. While called a "third", it is within the range of major seconds.

The '''Pythagorean ([[3-limit]]) major second''' is [[9/8]], which is 204 cents in size and corresponds to the MOS-based interval category of the diatonic major second. It is generated by [[stacking]] two just perfect fifths of [[3/2]]. There is also a '''Pythagorean diminished third''' of 65536/59049, which is about 180 cents in size. While called a "third", it is within the range of major seconds.

Other major seconds exist in higher [[Prime limit|limits]], however, for example:

* The 5-limit '''ptolemaic major second''' is a ratio of 10/9, however in 5-limit harmony it is used alongside 9/8. It is about 182 cents.

* The 5-limit '''ptolemaic major second''' is a ratio of [[10/9]], however in 5-limit harmony it is used alongside 9/8. It is about 182 cents.

* The 7-limit '''(septimal) supermajor second''' is a ratio of 8/7, and is about 231 cents.

* The 7-limit '''(septimal) supermajor second''' is a ratio of [[8/7]], and is about 231 cents.

* The 11-limit '''(undecimal) submajor second''' is a ratio of 11/10, and is about 165 cents.

* The 11-limit '''(undecimal) submajor second''' is a ratio of [[11/10]], and is about 165 cents, though it can also be analyzed as a [[neutral second]]. Despite that, it is also here for completeness.

* The 13-limit '''(tridecimal) ultramajor second''' is a ratio of 15/13, and is about 248 cents, ~~but~~ it ~~might~~ be ~~better~~ analyzed as an [[~~Minor~~ third|inframinor third]]. Despite that, it is also here for completeness.

* The 13-limit '''(tridecimal) ultramajor second''' is a ratio of [[15/13]], and is about 248 cents, though it can also be analyzed as an [[minor third|inframinor third]]. Despite that, it is also here for completeness.

=== By delta ===

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 === By prime limit ===
-The '''Pythagorean ([[3-limit]]) major second''' is 9/8, which is 204 cents in size and corresponds to the MOS-based interval category of the diatonic major second. It is generated by [[stacking]] two just perfect fifths of [[3/2]]. There is also a '''Pythagorean diminished third''' of 65536/59049, which is about 180 cents in size. While called a "third", it is within the range of major seconds.
+The '''Pythagorean ([[3-limit]]) major second''' is [[9/8]], which is 204 cents in size and corresponds to the MOS-based interval category of the diatonic major second. It is generated by [[stacking]] two just perfect fifths of [[3/2]]. There is also a '''Pythagorean diminished third''' of 65536/59049, which is about 180 cents in size. While called a "third", it is within the range of major seconds.
 Other major seconds exist in higher [[Prime limit|limits]], however, for example:
-* The 5-limit '''ptolemaic major second''' is a ratio of 10/9, however in 5-limit harmony it is used alongside 9/8. It is about 182 cents.
+* The 5-limit '''ptolemaic major second''' is a ratio of [[10/9]], however in 5-limit harmony it is used alongside 9/8. It is about 182 cents.
-* The 7-limit '''(septimal) supermajor second''' is a ratio of 8/7, and is about 231 cents.
+* The 7-limit '''(septimal) supermajor second''' is a ratio of [[8/7]], and is about 231 cents.
-* The 11-limit '''(undecimal) submajor second''' is a ratio of 11/10, and is about 165 cents.
+* The 11-limit '''(undecimal) submajor second''' is a ratio of [[11/10]], and is about 165 cents, though it can also be analyzed as a [[neutral second]]. Despite that, it is also here for completeness.
-* The 13-limit '''(tridecimal) ultramajor second''' is a ratio of 15/13, and is about 248 cents, but it might be better analyzed as an [[Minor third|inframinor third]]. Despite that, it is also here for completeness.
+* The 13-limit '''(tridecimal) ultramajor second''' is a ratio of [[15/13]], and is about 248 cents, though it can also be analyzed as an [[minor third|inframinor third]]. Despite that, it is also here for completeness.
 === By delta ===