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
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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&nbsp;third]] <br> [[Minor&nbsp;third]]
| Lower region = [[Neutral&nbsp;third]] <br> [[Minor&nbsp;third]]
|Higher region=[[Perfect&nbsp;fourth]]
| Higher region = [[Perfect&nbsp;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]]).


A '''major third (M3),''' as an [[interval region]], 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".  
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]].  


In the [[5L 2s|diatonic]] scale, a major third is an interval that spans 2 scale steps 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]]).  
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".  
 
In [[just intonation]], an interval may be classified as a major third if it can be reasonably mapped to two steps of the diatonic scale and four steps of the chromatic scale, or if it falls within the major third region.  


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 EDOs ==
== 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|EDO]]s.
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
! 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 MOS scales ==
== In mos scales ==
Intervals between 360 and 480 cents generate the following [[mos|MOS]] scales:
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" | MOS
! colspan="5" | Mos
|-
|-
| 360–400{{c}}
| 360–400{{c}}