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Major second (diatonic interval category): Difference between revisions

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A '''major second''' ('''M2'''), also called a '''whole tone''' or simply '''tone''', is an interval that spans one scale step in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 2 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 171 to 240{{cent}} ([[7edo|1\7]] to [[5edo|1\5]]). It can be considered the large step of the diatonic scale.
{{Infobox
{{Infobox
| Title = Diatonic major second
| Title = Diatonic major second
Line 7: Line 6:
| Header 4 = Tuning range | Data 4 = 171–240{{c}}
| Header 4 = Tuning range | Data 4 = 171–240{{c}}
| Header 5 = Basic tuning | Data 5 = 200{{c}}
| Header 5 = Basic tuning | Data 5 = 200{{c}}
| Header 6 = Chromatically adjacent interval | Data 6 = [[Minor second (diatonic interval category)|Diatonic minor second]]
| Header 6 = Function on root | Data 6 = Supertonic
| Header 7 = Function on root | Data 7 = Supertonic
| Header 7 = Interval regions | Data 7 = [[Major second (interval region)|Major second]]
| Header 8 = Positions in major scale | Data 8 = 1, 2, 4, 5, 6
| Header 8 = Associated just intervals | Data 8 = [[10/9]], [[9/8]]
| Header 9 = Interval regions | Data 9 = [[Major second (interval region)|Major second]]
| Header 9 = Octave complement | Data 9 = [[Minor seventh (diatonic interval category)|Minor seventh]]
| Header 10 = Associated just intervals | Data 10 = [[10/9]], [[9/8]]
}}
}}In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to one step of the diatonic scale and two steps of the chromatic scale.
A '''major second''' ('''M2'''), also called a '''whole tone''' or simply '''tone''', is an interval that spans one scale step in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 2 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 171 to 240{{cent}} ([[7edo|1\7]] to [[5edo|1\5]]). It can be considered the large step of the diatonic scale. In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to one step of the diatonic scale and two steps of the chromatic scale.


Given its role as the large step, it can be used to construct other diatonic intervals, along with the [[Minor second (diatonic interval category)|minor second]]: two major seconds make a [[Major third (diatonic interval category)|major third]], a major second and a minor second make a [[Minor third (diatonic interval category)|minor third]], and three major seconds result in an [[augmented fourth]], also called a tritone for that reason.
Given its role as the large step, it can be used to construct other diatonic intervals, along with the [[Minor second (diatonic interval category)|minor second]]: two major seconds make a [[major third (diatonic interval category)|major third]], a major second and a minor second make a [[Minor third (diatonic interval category)|minor third]], and three major seconds result in an [[augmented fourth]], also called a tritone for that reason.


In [[TAMNAMS]], this interval is called the '''major 1-diastep'''.
In [[TAMNAMS]], this interval is called the '''major 1-diastep'''.


==Scale info==
== Scale info ==
The diatonic scale contains five major seconds. In the Ionian mode, major seconds are found on the 1st, 2nd, 4th, 5th, and 6th degrees of the scale; the other two degrees have minor seconds. The large number of major seconds compared to minor seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are [[Minor third|minor]].
The diatonic scale contains five major seconds. In the Ionian mode, major seconds are found on the 1st, 2nd, 4th, 5th, and 6th degrees of the scale; the other two degrees have minor seconds. The large number of major seconds compared to minor seconds ensures that thirds that include minor seconds (that is, minor thirds) are roughly evenly distributed with major thirds; in a scale with three small steps and four large steps, for example, six out of the seven thirds are [[Minor third|minor]].


==Tunings==
== Tunings ==
Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale.
Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale.


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{| class="wikitable"
{| class="wikitable"
|-
|-
!Tuning
! Tuning
!Step ratio
! Step ratio
!Edo
! Edo
!Cents
! Cents
|-
|-
|Equalized
| Equalized
|1:1
| 1:1
|7
| 7
|171c
| 171{{c}}
|-
|-
|Supersoft
| Supersoft
|4:3
| 4:3
|26
| 26
|184c
| 184{{c}}
|-
|-
|Soft
| Soft
|3:2
| 3:2
|19
| 19
|189c
| 189{{c}}
|-
|-
|Semisoft
| Semisoft
|5:3
| 5:3
|31
| 31
|194c
| 194{{c}}
|-
|-
|Basic
| Basic
|2:1
| 2:1
|12
| 12
|200c
| 200{{c}}
|-
|-
|Semihard
| Semihard
|5:2
| 5:2
|29
| 29
|207c
| 207{{c}}
|-
|-
|Hard
| Hard
|3:1
| 3:1
|17
| 17
|212c
| 212{{c}}
|-
|-
|Superhard
| Superhard
|4:1
| 4:1
|22
| 22
|218c
| 218{{c}}
|-
|-
|Collapsed
| Collapsed
|1:0
| 1:0
|5
| 5
|240c
| 240{{c}}
|}
|}
==In regular temperaments==
 
===P5 = 3/2===
== In regular temperaments ==
=== P5 = 3/2 ===
If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments:
If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments:


<nowiki>*</nowiki>686c generates 171c, which is 6 cents sharp, but this is the flattest a fifth can be and still generate a diatonic scale. Despite this, I thought 11/10 was suitable for inclusion as it is a significant submajor second.
{| class="wikitable"
{| class="wikitable"
|+
|+
!Just interval
! Just interval
!Cents
! Cents
!Temperament
! Temperament
!Tempered comma
! Tempered comma
!Generator (eigenmonzo tuning)
! Generator (eigenmonzo tuning)
|-
|-
|11/10
| 21/19
|165c
| 173{{c}}
|Temperament of 45/44 in 2.3.11/5
| [[Hendrix #Surprise|Surprise]]
|[[45/44]]
| [[57/56]]
|686c*
| 687{{c}}
|-
|-
|21/19
| 10/9
|173c
| 182{{c}}
|[[Hendrix#Surprise|Surprise]]
| [[Meantone]]
|[[57/56]]
| [[81/80]]
|687c
| 691{{c}}
|-
|-
|10/9
| 19/17
|182c
| 193{{c}}
|[[Meantone]]
| Little ganassi
|[[81/80]]
| [[153/152]]
|691c
| 696{{c}}
|-
|-
|19/17
| 9/8
|193c
| 204{{c}}
|Little ganassi
| [[Pythagorean]]
|[[153/152]]
| [[1/1]]
|696c
| 702{{c}}
|-
|-
|9/8
| 17/15
|204c
| 217{{c}}
|[[Pythagorean]]
| Fiventeen
|[[1/1]]
| [[136/135]]
|702c
| 708{{c}}
|-
|-
|17/15
| 8/7
|217c
| 231{{c}}
|Fiventeen
| [[Archy]]
|[[136/135]]
| [[64/63]]
|708c
| 716{{c}}
|-
|8/7
|231c
|[[Archy]]
|[[64/63]]
|716c
|}
|}


== See also ==
== See also ==
* [[Major second]] (disambiguation page)
* [[Major second]] (disambiguation page)


[[Category:Diatonic interval categories]]
[[Category:Diatonic interval categories]]
Retrieved from "https://en.xen.wiki/w/Major_second_(diatonic_interval_category)"