Minor third

A minor third (m3) in the diatonic scale is an interval that spans two scale steps 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 2\7 and 6\24 (precisely two steps of the diatonic scale and four steps of the chromatic scale). 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.

As a concrete interval region, it 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 article 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 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 11-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) submajor 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:

Todo: complete list