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More generally, an interval close to 200 cents can be called a major second.
More generally, an interval close to 200 cents can be called a major second.
The major second is also called the '''tone''', or '''whole tone''' for clarity (as distinct from the [[Semitone (interval region)|semitone]]).


== As an interval region ==
== As an interval region ==
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== As a diatonic interval category ==
== As a diatonic interval category ==
As a diatonic interval category, a major second 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]]).
{{Infobox|Title=Diatonic major second|Header 1=MOS|Data 1=[[5L 2s]]|Header 2=Other names|Data 2=Major 1-diastep|Header 3=Generator span|Data 3=+2 generators|Header 4=Tuning range|Data 4=171–240{{c}}|Header 5=Basic tuning|Data 5=200{{c}}|Header 6=Function on root|Data 6=Supertonic|Header 7=Interval regions|Data 7=[[Major second (interval region)|Major second]]|Header 8=Associated just intervals|Data 8=[[10/9]], [[9/8]]|Header 9=Octave complement|Data 9=[[Minor seventh (diatonic interval category)|Minor seventh]]}}As a diatonic interval category, a major second 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 2 steps of the chromatic scale - formally, this is 4\24, which is used as opposed to [[12edo]]'s 2\12 to better capture the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]] - and 1 step of the diatonic scale. Diminished thirds are mapped to 2 steps of the chromatic scale and 2 steps of the diatonic scale.
In [[just intonation]], an interval may be classified as a major second if it is reasonably mapped to 2 steps of the chromatic scale - formally, this is 4\24, which is used as opposed to [[12edo]]'s 2\12 to better capture the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]] - and 1 step of the diatonic scale. Diminished thirds are mapped to 2 steps of the chromatic scale and 2 steps of the diatonic scale.


In TAMNAMS, the major second is called the '''major 1-diastep'''.
In TAMNAMS, the major second is called the '''major 1-diastep'''.
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 [[Tritone|augmented fourth]], also called a tritone for that reason.


=== Scale info ===
=== Scale info ===
In the Ionian (major) mode of the diatonic scale, the five major seconds can be found on the 1st, 2nd, 4th, 5th, and 6th degrees.  
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 ===
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.
 
The tuning range of the diatonic major second ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n''<nowiki>, for the diatonic major second can be found by {{nowrap| (</nowiki>''n'' + 1200)/2. For example, the third 192{{c}} gives us {{nowrap|(192 + 1200)/2 {{=}} 1392/2 {{=}} 696{{c}}}}, corresponding to 50edo.
 
Several example tunings are provided below:
{| class="wikitable center-all left-1"
!Tuning
!Step ratio
!Edo
!Cents
|-
|Equalized
|1:1
|7
|171{{c}}
|-
|Supersoft
|4:3
|26
|184{{c}}
|-
|Soft
|3:2
|19
|189{{c}}
|-
|Semisoft
|5:3
|31
|194{{c}}
|-
|Basic
|2:1
|12
|200{{c}}
|-
|Semihard
|5:2
|29
|207{{c}}
|-
|Hard
|3:1
|17
|212{{c}}
|-
|Superhard
|4:1
|22
|218{{c}}
|-
|Collapsed
|1:0
|5
|240{{c}}
|}


== In just intonation ==
== In just intonation ==
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{{Todo|complete list|inline=1}}
{{Todo|complete list|inline=1}}


Due to the [[9/8]] major second being closely related to the perfect fifth, it is often useful to detune the fifth to approach other intervals with the diatonic major second. If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments:
{| class="wikitable center-2 center-5"
|+
!Just
interval
!Cents
!Temperament
!Vanishing
comma
!Generator
(eigenmonzo tuning)
|-
|21/19
|173{{c}}
|[[Hendrix#Surprise|Surprise]]
|[[57/56]]
|687{{c}}
|-
|10/9
|182{{c}}
|[[Meantone]]
|[[81/80]]
|691{{c}}
|-
|19/17
|193{{c}}
|Little ganassi
|[[153/152]]
|696{{c}}
|-
|9/8
|204{{c}}
|[[Pythagorean]]
|[[1/1]]
|702{{c}}
|-
|17/15
|217{{c}}
|Fiventeen
|[[136/135]]
|708{{c}}
|-
|8/7
|231{{c}}
|[[Archy]]
|[[64/63]]
|716{{c}}
|}
{{Navbox intervals}}
{{Navbox intervals}}
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