Minor sixth

A minor sixth (m6) is the smaller of the two sixths – intervals spanning 6 degrees or 5 scale steps in the diatonic scale. It is found between the 1st and 6th notes of the minor scale, hence its name. Another diatonic interval around the same size is the augmented fifth (A5). More generally, an interval close to 800 cents in size can be called a minor sixth.

As an interval region

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Minor sixth

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Name	Minor sixth
Lower bound	740¢ – 760¢
Upper bound	830¢ – 840¢
Example JI intervals
Intervals	8/5 (813.7¢) 128/81 (792.2¢)
Related regions

The minor sixth, as a concrete interval region, is typically near 800 ¢ in size, distinct from the major sixth of roughly 900 ¢ and the neutral sixth of roughly 850 ¢. A rough tuning range for the minor sixth is about 760 to 828 ¢ according to Margo Schulter's theory of interval regions. Minor sixth in this sense refers both to the ~740–840 ¢ range as a whole, and to a specific subdivision within it (~785–840 ¢) as opposed to subminor sixths; minor sixths flat of this are often called "subminor sixths".

In mos scales

Intervals between 720 and 840 cents 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
800–840 ¢	1L 2s	3L 1s	3L 4s	3L 7s
764–800 ¢	1L 1s	2L 1s	3L 2s	3L 5s	3L 8s
750–764 ¢					8L 3s
720–750 ¢				5L 3s

As a diatonic interval category

Diatonic minor sixth

MOS	5L 2s
Other names	Minor 5-diastep
Generator span	-4 generators
Tuning range	720–857 ¢
Basic tuning	800 ¢
Function on root	Submediant
Interval regions	Minor sixth, neutral sixth
Associated just intervals	8/5, 128/81
Octave complement	Major third

As a diatonic interval category, a minor sixth is an interval that spans five scale steps in the diatonic scale with the minor (narrower) quality. It is generated by stacking 4 fourths octave reduced, and depending on the specific tuning, it ranges from 720 to 857 ¢ (3\5 to 5\7).

In just intonation, an interval may be classified as a minor sixth if it is reasonably mapped to five steps of the diatonic scale and eight steps of the chromatic scale.

The minor sixth is often the bounding interval of a tertian triad chord in inversion, and as such is often involved in chord structures in diatonic harmony.

In TAMNAMS, this interval is called the minor 5-diastep.

The augmented fifth is enharmonic with the minor sixth, ranging from 686 to 960 ¢ (4\7 to 4\5). It is arguably the most common of the enharmonic intervals besides the chromatic semitone itself, appearing in the augmented triad. It is generated by stacking 8 fifths octave reduced, and is as such not found in the diatonic scale. Regardless, in TAMNAMS, it may be called the augmented 4-diastep.

In just intonation, an interval may be classified as an augmented fifth if it is reasonably mapped to four steps of the diatonic scale and eight steps of the chromatic scale.

Scale info

The diatonic scale contains three minor sixths. In the Ionian mode, minor sixths are found on the third, sixth, and seventh degrees of the scale; the other four degrees have major sixths. This roughly equal distribution is analogous to that of the thirds.

Tunings

Being an abstract mos degree, and not a specific interval, the diatonic minor sixth 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. This is similar for the augmented fifth.

The tuning range of the diatonic minor sixth ranges from 720 to 857.2 ¢. The generator for a given tuning in cents, n, for the diatonic minor sixth can be found by (3600 - n)/4. For example, the sixth 816 ¢ gives us (3600 - 816)/4 = 2784/4 = 696 ¢, corresponding to 50edo.

The tuning range of the diatonic augmented fifth ranges from 686 to 960 ¢. The generator for a given tuning in cents, n, for the augmented fifth can be found by (4800 - n)/8. For example, the augmented fifth 816 ¢ gives us (4800 - 816)/8 = 3984/8 = 498 ¢, corresponding to 200edo.

In just intonation

By prime limit

The simplest 3-limit minor sixth is the Pythagorean minor sixth of 128/81, 792 ¢ in size, which is generated by stacking four just perfect fourths of 4/3. There is also a Pythagorean augmented fifth of about 816 ¢.

Much simpler minor sixths and augmented fifths exist in higher limits, however, for example:

• The 5-limit classical minor sixth is a ratio of 8/5 and is about 814 ¢.
• The 7-limit (septimal) subminor sixth is a ratio of 14/9 and is almost exactly 765 ¢.
• The 11-limit neogothic minor sixth is a ratio of 11/7, and is about 782 ¢. (Note that this is often considered an imperfect or augmented fifth.)
• The 13-limit (tridecimal) inframinor sixth is a ratio of 20/13, and is about 746 ¢.
  • There is also a 13-limit (tridecimal) supraminor sixth, which is a ratio of 21/13, and is about 830 ¢.
• The 17-limit (septendecimal) supraminor sixth is a ratio of 34/21, and is about 834 ¢.

Note that the ratios of higher-limit supraminor sixths approximate the golden ratio – the golden ratio itself as a musical interval is a supraminor sixth of about 833 cents.

In regular temperaments

See Major third #In regular temperaments