Major third: Difference between revisions
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The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition Tag: Undo |
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{{Infobox interval region | {{Infobox interval region | ||
|Name=Major third | | Name = Major third | ||
|Cents lower=372 | | Cents lower = 372 | ||
|Cents lower wide=343 | | Cents lower wide = 343 | ||
|Cents upper=440 | | Cents upper = 440 | ||
|Cents upper wide=480 | | Cents upper wide = 480 | ||
|MOSes=[[3L 4s]], [[7L 3s]], [[3L 7s]], [[3L 5s]], [[5L 3s]] | | MOSes = [[3L 4s]], [[7L 3s]], [[3L 7s]], [[3L 5s]], [[5L 3s]] | ||
|JI intervals=5/4,9/7 | | JI intervals = 5/4, 9/7 | ||
|Lower region=[[Neutral third]] <br> [[Minor third]] | | Lower region = [[Neutral third]] <br> [[Minor third]] | ||
|Higher region=[[Perfect fourth]] | | Higher region = [[Perfect fourth]] | ||
|Complement=[[Minor sixth]] | | Complement = [[Minor sixth]] | ||
|Subregions=[[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]] | | Subregions = [[Submajor third]] <br> [[Supermajor third]] <br> [[Ultramajor third]] | ||
}}{{Wikipedia}} | }}{{Wikipedia}} | ||
A '''major third (M3)''' is an interval that spans two scale steps in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 4 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 343 to 480{{cent}} ([[7edo|2\7]] to [[5edo|2\5]]). | |||
In [[just intonation]], an interval may be classified as a major third if it is reasonably mapped to 2\7 and [[24edo|8\24]] (precisely two steps of the diatonic scale and four steps of the chromatic scale). The use of 24edo's 8\24 as the mapping criteria here rather than [[12edo]]'s 4\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 400{{c}} in size, distinct from the [[minor third]] of roughly 300{{c}} and the [[neutral third]] of roughly 350{{c}}. A rough tuning range for the major third is about 370 to 440{{c}} according to [[Margo Schulter]]'s theory of interval regions. ''Major third'' in this sense refers both to the ~350–450{{c}} range as a whole, and to a specific subdivision within it (~370–415{{c}}) as opposed to supermajor thirds; major thirds sharp of this are often called "supermajor thirds". | |||
This article covers intervals between 360 and 460{{c}}. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily. | This article covers intervals between 360 and 460{{c}}. The outer range of this might be too extreme to call "major thirds", but this is done so that one can find what they're looking for easily. | ||
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== In | == In edos == | ||
The following table lists the best tuning of 5/4 and 9/7, as well as other major thirds if present, in various significant [[edo | The following table lists the best tuning of 5/4 and 9/7, as well as other major thirds if present, in various significant [[edo]]s. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Edo | ||
! 5/4 | ! 5/4 | ||
! 9/7 | ! 9/7 | ||
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* [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]]. | * [[Squares]], generated by flat supermajor thirds representing [[9/7]] and [[14/11]], such that a stack of four gives [[8/3]]. | ||
== In | == In mos scales == | ||
Intervals between 360 and 480 cents generate the following [[mos | Intervals between 360 and 480 cents generate the following [[mos]] scales: | ||
These tables start from the last monolarge mos generated by the interval range. | These tables start from the last monolarge mos generated by the interval range. | ||
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|- | |- | ||
! Range | ! Range | ||
! colspan="5" | | ! colspan="5" | Mos | ||
|- | |- | ||
| 360–400{{c}} | | 360–400{{c}} | ||