Major second: Difference between revisions
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In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to 1\7 and [[24edo|4\24]] (precisely one step of the diatonic scale and two steps of the chromatic scale). The use of 24edo's 4\24 as the mapping criteria here rather than [[12edo]]'s 2\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to 1\7 and [[24edo|4\24]] (precisely one step of the diatonic scale and two steps of the chromatic scale). The use of 24edo's 4\24 as the mapping criteria here rather than [[12edo]]'s 2\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. | ||
As a concrete [[interval region]], it is typically near | As a concrete [[interval region]], it is typically near 200{{c}} in size, distinct from the [[Semitone (interval region)|semitone]] of roughly 100 ¢ and the [[neutral second]] of roughly 150{{c}}. A rough tuning range for the major second is about 180 to 240{{c}} according to [[Margo Schulter]]'s theory of interval regions. | ||
This article covers intervals between 160 and | This article covers intervals between 160 and 260{{c}}. The outer range of this might be too extreme to call "major seconds", but this is done so that one can find what they're looking for easily. | ||
== In just intonation == | == In just intonation == | ||
=== By prime limit === | === By prime limit === | ||
The Pythagorean ([[3-limit]]) major second is [[9/8]], which is 204 | The Pythagorean ([[3-limit]]) major second is [[9/8]], which is 204{{c}} 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: | 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 | * 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{{c}}. | ||
* The 7-limit '''(septimal) supermajor second''' is a ratio of [[8/7]], and is about 231 | * The 7-limit '''(septimal) supermajor second''' is a ratio of [[8/7]], and is about 231{{c}}. | ||
* The 11-limit '''(undecimal) submajor second''' is a ratio of [[11/10]], and is about 165 | * The 11-limit '''(undecimal) submajor second''' is a ratio of [[11/10]], and is about 165{{c}}, 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 | * The 13-limit '''(tridecimal) ultramajor second''' is a ratio of [[15/13]], and is about 248{{c}}, though it can also be analyzed as an [[minor third|inframinor third]]. Despite that, it is also here for completeness. | ||
=== By delta === | === By delta === | ||
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| 15 | | 15 | ||
| 160{{c}} | | 160{{c}} | ||
| colspan="2" |240{{c}} | | colspan="2" | 240{{c}} | ||
| | | | ||
|- | |- | ||
| Line 178: | Line 178: | ||
| 204{{c}} | | 204{{c}} | ||
| 226{{c}} | | 226{{c}} | ||
| 249{{c}} ≈ 15/13 | | {{nowrap|249{{c}} ≈ 15/13}} | ||
|} | |} | ||