Major second (diatonic interval category)

A major second (M2), also called a whole tone or simply tone, is an interval that spans one scale step in the diatonic scale with the major (wider) quality. It is generated by stacking 2 fifths octave reduced, and depending on the specific tuning, it ranges from 171 to 240 ¢ (1\7 to 1\5). It can be considered the large step of the diatonic scale.

Diatonic major second

MOS	5L 2s
Other names	Major 1-diastep
Generator span	+2 generators
Tuning range	171–240 ¢
Basic tuning	200 ¢
Chromatically adjacent interval	Diatonic minor second
Function on root	Supertonic
Positions in major scale	1, 2, 4, 5, 6
Interval regions	Major second
Associated just intervals	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.

Given its role as the large step, it can be used to construct other diatonic intervals, along with the minor second: two major seconds make a major third, a major second and a minor second make a 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.

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.

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 ¢. The generator for a given tuning in cents, n, for the diatonic major second can be found by ⁠n + 1200/2⁠. For example, the third 192 ¢ gives us ⁠192 + 1200/2⁠ = ⁠1392/2⁠ = 696 ¢, corresponding to 50edo.

Several example tunings are provided below:

Tuning	Step ratio	Edo	Cents
Equalized	1:1	7	171c
Supersoft	4:3	26	184c
Soft	3:2	19	189c
Semisoft	5:3	31	194c
Basic	2:1	12	200c
Semihard	5:2	29	207c
Hard	3:1	17	212c
Superhard	4:1	22	218c
Collapsed	1:0	5	240c

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:

*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.

Just interval	Cents	Temperament	Tempered comma	Generator (eigenmonzo tuning)
11/10	165c	Temperament of 45/44 in 2.3.11/5	45/44	686c*
21/19	173c	Surprise	57/56	687c
10/9	182c	Meantone	81/80	691c
19/17	193c	Little ganassi	153/152	696c
9/8	204c	Pythagorean	1/1	702c
17/15	217c	Fiventeen	136/135	708c
8/7	231c	Archy	64/63	716c

See also

• Major second (disambiguation page)