Neutral third scales

Neutral third scales are characterized by the division of the 3/2 "perfect fifth" into two equal "neutral thirds". It usually refers to a MOS or MODMOS generated by a neutral third (usually from 342.9c in 7edo to 360c in 10edo).

One possible temperament interpretation is that the neutral third generator can be taken to represent either 11/9 or 27/22. This means the comma 243/242 is tempered out, resulting in the neutral temperament and its extensions (described below).

If the fifth harmonic is used at all, it makes sense to map it to 8 generators by tempering out 81/80, making it a meantone system, sometimes called mohaha. If 7 is also mapped a particular way it is called mohajira. Alternatively, 64/63 could be tempered out, leading to a 2.3.7.11 version of neutrominant temperament. But neither of these adjustments to the farther-out intervals affects its basic nature as a "neutral thirds" scale, which equally subdivides the 3/2 into two equal parts.

Any temperament tempering out 243/242 lends itself to neutral thirds; this becomes more significant when fifths are of low complexity, such as hemififths or the rank three temperament jove, but also includes miracle, harry and so forth. Nor does a scale need to be a MOS to qualify as a neutral thirds scale; that name could reasonably be given to Oktone, for example.

Interval chains

Basic 2.3.11 neutral thirds scale

296.85	647.37	997.90	148.42	498.95	849.47	0.	350.53	701.05	1051.58	202.10	552.63	903.15
32/27	16/11	16/9	12/11	4/3	18/11	1/1	11/9	3/2	11/6	9/8	11/8	27/16

2.3.5.11 mohaha

815.25	1163.34	311.44	659.53	1007.63	155.72	503.81	851.91	0.	348.09	696.19	1044.28	192.37	540.47	888.56	36.66	384.75
8/5		6/5	16/11	16/9~9/5	12/11~11/10	4/3	18/11	1/1	11/9	3/2	11/6	10/9~9/8	11/8	5/3		5/4

2.3.7.11 suhajira

414.38	768.34	1122.29	276.25	630.21	984.17	138.13	492.08	846.04	0.	353.96	707.92	1061.87	215.83	569.79	923.75	77.71	431.66	785.62
14/11	14/9		7/6	16/11	7/4~16/9	12/11	4/3	18/11	1/1	11/9	3/2	11/6	9/8~8/7	11/8	12/7		9/7	11/7

MOSes

Neutral third scales are associated with the MOS patterns: 3L 4s and 7L 3s.

In the 3L4s MOS, the large step is a 9/8 and the small step is a 12/11 neutral second. In the 7L3s MOS, the 12/11 is now the large step and the small step is a 33/32 quarter tone.

Munits

Though they differ in the specifics of their temperaments, all neutral third scales have certain munits in common.

• 4/3 Lss, 4/3 sLs: Rather than being divided into two large steps and one small step as in the diatonic scale, 4/3 can always be divided into one large step and two small steps. The large step is 9/8, and the two small steps are "neutral seconds" representing the sub-munit "32/27 ss".
• 11/8 LsL: In contrast, two large steps and a small step make a much less consonant and more colorful interval, 11/8.

Lumatone mapping

See: Lumatone mapping for neutral thirds scales.

Neutral thirds scales by EDO

Not an exhaustive list.

7edo

1 1 1 1 1 1 1

7edo

10edo

2 1 2 1 2 1 1

Neutral Hypolydian

2 1 2 1 1 2 1

Neutral Hypodorian

2 1 1 2 1 2 1

Neutral Lydian

1 2 1 2 1 2 1

Neutral Dorian

1 2 1 2 1 1 2

Neutral Hypophrygian

Any other scales which contain the 3rd (360c) and 6th (720c) degrees of 10edo are also considered neutral thirds scales.

17edo

See also: 17edo neutral scale

3 2 3 2 3 2 2

Neutral Hypolydian

3 2 3 2 2 3 2

Neutral Hypodorian

3 2 2 3 2 3 2

Neutral Lydian

2 3 2 3 2 3 2

Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi

2 3 2 3 2 2 3

Neutral Hypophrygian

Any other scales which contain the 5th (~353c) and 10th (~706c) degrees of 10edo are also considered neutral thirds scales.

24edo

See also: 24edo scales

4 3 4 3 4 3 3

Neutral Hypolydian

4 3 4 3 3 4 3

Neutral Hypodorian

4 3 3 4 3 4 3

Neutral Lydian

3 4 3 4 3 4 3

Neutral Dorian, Misaelides 2nd Byzantine mode, Maqam Sikah Baladi

3 4 3 4 3 3 4

Neutral Hypophrygian

Any other scales which contain the 7th (350c) and 14th (700c) degrees of 10edo are also considered neutral thirds scales.