Minor third (interval region)

← Major second

Interval region

Neutral third →

Name	Minor third
Lower bound	240¢ – 260¢
Upper bound	330¢ – 340¢
Generated MOSes	5L 4s, 4L 5s, 4L 3s
Example JI intervals
Intervals	6/5 (315.6¢) 7/6 (266.9¢)
Related regions
Complement	Major sixth

A minor third (m3) is the smaller of the two "thirds" - intervals spanning 3 degrees or 2 scale steps in the diatonic scale. It is found between the 1st and 3rd notes of the minor scale, hence its name. Another diatonic interval around the same size is the augmented second. More generally, an interval close to 300 cents in size can be called a minor third.

As an interval region

The minor third (m3), as a concrete interval region, is typically near 300 ¢ in size, distinct from the major third of roughly 400 ¢ and the neutral third of roughly 350 ¢. A rough tuning range for the minor third is about 260 to 330 ¢ according to Margo Schulter's theory of interval regions. Minor third in this sense refers both to the ~240–340 ¢ range as a whole, and to a specific subdivision within it (~285–340 ¢) as opposed to subminor thirds; minor thirds flat of this are often called "subminor thirds".

This section covers intervals between 240 and 340 ¢. The outer range of this might be too extreme to call "minor thirds", but this is done so that one can find what they're looking for easily.

In mos scales

Intervals between 267 and 343 ¢ generate the following mos scales:

These tables start from the last monolarge mos generated by the interval range.

Scales with more than 12 notes are not included.

Range	Mos
240–267 ¢	1L 3s	4L 1s	5L 4s
267–300 ¢			4L 5s
300–327 ¢	1L 2s	3L 1s	4L 3s	4L 7s
327–343 ¢				7L 4s

As a diatonic interval category

Diatonic minor third

MOS	5L 2s
Other names	Minor 2-diastep
Generator span	-3 generators
Tuning range	240–343 ¢
Basic tuning	300 ¢
Function on root	Mediant
Interval regions	Semifourth, minor third, neutral third
Associated just intervals	6/5, 32/27
Octave complement	Major sixth

As a diatonic interval category, a minor third is an interval that spans two scale steps in the diatonic scale with the minor (narrower) quality. It is generated by stacking 3 fourths octave reduced, and depending on the specific tuning, it ranges from 240 to 343 ¢ (1\5 to 2\7).

In just intonation, an interval may be classified as a minor third if it is reasonably mapped to two steps of the diatonic scale and three steps of the chromatic scale, or formally 2\7 and 6\24. The use of 24edo's 6\24 as the mapping criteria here rather than 12edo's 3\12 better captures the characteristics of many intervals in the 11- and 13-limit.

The major third can be stacked with a minor third to form a perfect fifth, and as such is often involved in chord structures in diatonic harmony.

In TAMNAMS, this interval is called the minor 2-diastep.

The augmented second is enharmonic with the minor third, ranging from 171 to 480 ¢ (1\7 to 2\5). It is generated by stacking 9 fifths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the augmented 1-diastep.

In just intonation, an interval may be classified as an augmented second if it is reasonably mapped to one steps of the diatonic scale and three steps of the chromatic scale, or formally 1\7 and 6\24.

Scale info

The diatonic scale contains four minor thirds. In the Ionian mode, minor thirds are found on the second, third, sixth, and seventh degrees of the scale; the other three degrees have major thirds. This roughly equal distribution leads to diatonic tonality being largely based on the distinction between major and minor thirds and triads.

In just intonation

By prime limit

3-limit intervals in the range of minor thirds include the Pythagorean minor third of 32/27, 294.1 ¢ in size, which corresponds to the mos-based interval category of the diatonic minor third and is generated by stacking three just perfect fourths of 4/3, and the Pythagorean augmented second of 19683/16384, which is sharp of 32/27 by one Pythagorean comma, and is about 318 ¢ in size.

Much simpler minor thirds exist in higher limits, however, for example:

• The 5-limit classical minor third is a ratio of 6/5, and is about 316 ¢.
• The 7-limit (septimal) subminor third is a ratio of 7/6, and is about 267 ¢.
• The 13-limit neogothic minor third is a ratio of 13/11, and is about 290 ¢.
  • Note that this is not the fifth complement to the neogothic major third, which is actually a ratio of 33/28, and is about 284 ¢.
• The 13-limit (tridecimal) inframinor third is a ratio of 15/13, and is about 248 ¢.
  • There is also a 13-limit (tridecimal) supraminor third, which is a ratio of 63/52, and is about 332 ¢.
• The 17-limit (septendecimal) supraminor third is a ratio of 17/14, and is about 336 ¢.

By delta

See Delta-N ratio.

Delta-1		Delta-2		Delta-3		Delta-4
6/5	316 ¢	13/11	290 ¢	17/14	336 ¢	23/19	331 ¢
7/6	267 ¢	15/13	248 ¢	19/16	298 ¢	25/21	302 ¢
				20/17	281 ¢	27/23	278 ¢
				22/19	254 ¢	29/25	257 ¢
				23/20	242 ¢

In edos

The following table lists the best tuning of 7/6 and 6/5, as well as other minor thirds if present, in various significant edos.

Edo	7/6	6/5	Other minor thirds
12	300 ¢
15	240 ¢	320 ¢
16	300 ¢
17	282 ¢
19	253 ¢	316 ¢
22	273 ¢	327 ¢
24	250 ¢	300 ¢
25	288 ¢	336 ¢	240 ¢ ≈ 15/13
26	277 ¢	323 ¢
27	267 ¢	311 ¢
29	248 ¢	331 ¢	290 ¢ ≈ 32/27, 13/11
31	271 ¢	310 ¢
34	282 ¢	318 ¢	247 ¢ ≈ 15/13
41	263 ¢	322 ¢	293 ¢ ≈ 32/27
53	272 ¢	317 ¢	340 ¢ ≈ 17/14, 294 ¢ ≈ 32/27, 249 ¢ ≈ 15/13

In regular temperaments

The two simplest minor third ratios are 7/6 and 6/5. The following notable temperaments are generated by them:

• Kleismic, which stacks six 6/5s (octave reduced) to reach 3/2

Todo: complete list