14L 22s (12/1-equivalent)

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It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are exceedingly large, complex, or chosen arbitrarily.

Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

Assume hemipyth[10] nominal names and intervals (and zero-indexing) unless otherwise stated. This article is meant to apply MMTM's theory on this scale, but it is attempted to be explained better here.

↖ 13L 21s⟨12/1⟩	↑ 14L 21s⟨12/1⟩	15L 21s⟨12/1⟩ ↗
← 13L 22s⟨12/1⟩	14L 22s (12/1-equivalent)	15L 22s⟨12/1⟩ →
↙ 13L 23s⟨12/1⟩	↓ 14L 23s⟨12/1⟩	15L 23s⟨12/1⟩ ↘

┌╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬┬┐
│║│║││║│║││║│║││║││║│║││║│║││║│║││║│││
││││││││││││││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LsLssLsLssLsLssLssLsLssLsLssLsLssLss
ssLssLsLssLsLssLsLssLssLsLssLsLssLsL

Equave

12/1 (4302.0 ¢)

Period

1\2 (2151.0 ¢)

Generator size^(ed12/1)

Bright

5\36 to 2\14 (597.5 ¢ to 614.6 ¢)

Dark

5\14 to 13\36 (1536.4 ¢ to 1553.5 ¢)

Related MOS scales

36L 14s⟨12/1⟩, 14L 36s⟨12/1⟩

Neutralized

28L 8s⟨12/1⟩

2-Flought

50L 22s⟨12/1⟩, 14L 58s⟨12/1⟩

Equal tunings^(ed12/1)

Equalized (L:s = 1:1)

5\36 (597.5 ¢)

Supersoft (L:s = 4:3)

17\122 (599.5 ¢)

12\86 (600.3 ¢)

19\136 (601.0 ¢)

7\50 (602.3 ¢)

16\114 (603.8 ¢)

9\64 (605.0 ¢)

Superhard (L:s = 4:1)

11\78 (606.7 ¢)

Collapsed (L:s = 1:0)

2\14 (614.6 ¢)

14L 22s <12/1>, also pochhammeroid (see below), colianexoid, greater f-enhar electric or greater f-enhar smitonic is a MOS scale. The notation "<12/1>" means the period of the MOS is 12/1, disambiguating it from octave-repeating 14L 22s. The name of the period interval of this scale is called the oktokaidekatave, and the . It is also equivalent to 7L 11s <√12>. Its basic tuning is 50ed12 or 25ed√12. However, the √12-based form will be used for most of this article as it is far more practical and is the original form of the scale when it was discovered.

The generator range is 597 to 615 cents (5\18<√12> to 2\7<√12>, or 5\36<12/1> to 1\7<12/1>) . The dark generator is its √12-complement. Because this is a perfect eighteenth-repeating scale, each tone has an √12 perfect eighteenth above it.

The period can range from 24/7 to 7/2, including the pure-hemipyth √12 and 1/QPochhammer[1/2]. It is because of the latter constant that Cole proposes naming this scale pochhammeroid.

Standing assumptions

The notation used in this article is 0 Pacific-Hemipyth = 0123456789ABCDEFGH (see the section on modes below), unless specified otherwise. (Alternatively, one can use any octodecimal or niftimal/triacontaheximal digit set as the numbers, as long as it is clear which set one is using.) Octodecimal digitsets will be used for naming notes as it more practical. We denote raising and lowering by a chroma (L − s, about √(256/243) using the hemipyth interpretation) by # and ♭.

Scale properties

Assume 36-nominal notation for this section.

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 14L 22s⟨12/1⟩
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 119.5 ¢
1-mosstep	Major 1-mosstep	M1ms	L	119.5 ¢ to 307.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 239.0 ¢
2-mosstep	Major 2-mosstep	M2ms	L + s	239.0 ¢ to 307.3 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	307.3 ¢ to 358.5 ¢
3-mosstep	Major 3-mosstep	M3ms	2L + s	358.5 ¢ to 614.6 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	307.3 ¢ to 478.0 ¢
4-mosstep	Major 4-mosstep	M4ms	2L + 2s	478.0 ¢ to 614.6 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	307.3 ¢ to 597.5 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	597.5 ¢ to 614.6 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	614.6 ¢ to 717.0 ¢
6-mosstep	Major 6-mosstep	M6ms	3L + 3s	717.0 ¢ to 921.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	614.6 ¢ to 836.5 ¢
7-mosstep	Major 7-mosstep	M7ms	3L + 4s	836.5 ¢ to 921.8 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	921.8 ¢ to 956.0 ¢
8-mosstep	Major 8-mosstep	M8ms	4L + 4s	956.0 ¢ to 1229.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	921.8 ¢ to 1075.5 ¢
9-mosstep	Major 9-mosstep	M9ms	4L + 5s	1075.5 ¢ to 1229.1 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	921.8 ¢ to 1195.0 ¢
10-mosstep	Major 10-mosstep	M10ms	4L + 6s	1195.0 ¢ to 1229.1 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	1229.1 ¢ to 1314.5 ¢
11-mosstep	Major 11-mosstep	M11ms	5L + 6s	1314.5 ¢ to 1536.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	1229.1 ¢ to 1434.0 ¢
12-mosstep	Major 12-mosstep	M12ms	5L + 7s	1434.0 ¢ to 1536.4 ¢
13-mosstep	Perfect 13-mosstep	P13ms	5L + 8s	1536.4 ¢ to 1553.5 ¢
13-mosstep	Augmented 13-mosstep	A13ms	6L + 7s	1553.5 ¢ to 1843.7 ¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	1536.4 ¢ to 1673.0 ¢
14-mosstep	Major 14-mosstep	M14ms	6L + 8s	1673.0 ¢ to 1843.7 ¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	1536.4 ¢ to 1792.5 ¢
15-mosstep	Major 15-mosstep	M15ms	6L + 9s	1792.5 ¢ to 1843.7 ¢
16-mosstep	Minor 16-mosstep	m16ms	6L + 10s	1843.7 ¢ to 1912.0 ¢
16-mosstep	Major 16-mosstep	M16ms	7L + 9s	1912.0 ¢ to 2151.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	6L + 11s	1843.7 ¢ to 2031.5 ¢
17-mosstep	Major 17-mosstep	M17ms	7L + 10s	2031.5 ¢ to 2151.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	7L + 11s	2151.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	7L + 12s	2151.0 ¢ to 2270.5 ¢
19-mosstep	Major 19-mosstep	M19ms	8L + 11s	2270.5 ¢ to 2458.3 ¢
20-mosstep	Minor 20-mosstep	m20ms	7L + 13s	2151.0 ¢ to 2390.0 ¢
20-mosstep	Major 20-mosstep	M20ms	8L + 12s	2390.0 ¢ to 2458.3 ¢
21-mosstep	Minor 21-mosstep	m21ms	8L + 13s	2458.3 ¢ to 2509.5 ¢
21-mosstep	Major 21-mosstep	M21ms	9L + 12s	2509.5 ¢ to 2765.5 ¢
22-mosstep	Minor 22-mosstep	m22ms	8L + 14s	2458.3 ¢ to 2629.0 ¢
22-mosstep	Major 22-mosstep	M22ms	9L + 13s	2629.0 ¢ to 2765.5 ¢
23-mosstep	Diminished 23-mosstep	d23ms	8L + 15s	2458.3 ¢ to 2748.5 ¢
23-mosstep	Perfect 23-mosstep	P23ms	9L + 14s	2748.5 ¢ to 2765.5 ¢
24-mosstep	Minor 24-mosstep	m24ms	9L + 15s	2765.5 ¢ to 2868.0 ¢
24-mosstep	Major 24-mosstep	M24ms	10L + 14s	2868.0 ¢ to 3072.8 ¢
25-mosstep	Minor 25-mosstep	m25ms	9L + 16s	2765.5 ¢ to 2987.5 ¢
25-mosstep	Major 25-mosstep	M25ms	10L + 15s	2987.5 ¢ to 3072.8 ¢
26-mosstep	Minor 26-mosstep	m26ms	10L + 16s	3072.8 ¢ to 3107.0 ¢
26-mosstep	Major 26-mosstep	M26ms	11L + 15s	3107.0 ¢ to 3380.1 ¢
27-mosstep	Minor 27-mosstep	m27ms	10L + 17s	3072.8 ¢ to 3226.5 ¢
27-mosstep	Major 27-mosstep	M27ms	11L + 16s	3226.5 ¢ to 3380.1 ¢
28-mosstep	Minor 28-mosstep	m28ms	10L + 18s	3072.8 ¢ to 3346.0 ¢
28-mosstep	Major 28-mosstep	M28ms	11L + 17s	3346.0 ¢ to 3380.1 ¢
29-mosstep	Minor 29-mosstep	m29ms	11L + 18s	3380.1 ¢ to 3465.5 ¢
29-mosstep	Major 29-mosstep	M29ms	12L + 17s	3465.5 ¢ to 3687.4 ¢
30-mosstep	Minor 30-mosstep	m30ms	11L + 19s	3380.1 ¢ to 3585.0 ¢
30-mosstep	Major 30-mosstep	M30ms	12L + 18s	3585.0 ¢ to 3687.4 ¢
31-mosstep	Perfect 31-mosstep	P31ms	12L + 19s	3687.4 ¢ to 3704.5 ¢
31-mosstep	Augmented 31-mosstep	A31ms	13L + 18s	3704.5 ¢ to 3994.7 ¢
32-mosstep	Minor 32-mosstep	m32ms	12L + 20s	3687.4 ¢ to 3824.0 ¢
32-mosstep	Major 32-mosstep	M32ms	13L + 19s	3824.0 ¢ to 3994.7 ¢
33-mosstep	Minor 33-mosstep	m33ms	12L + 21s	3687.4 ¢ to 3943.5 ¢
33-mosstep	Major 33-mosstep	M33ms	13L + 20s	3943.5 ¢ to 3994.7 ¢
34-mosstep	Minor 34-mosstep	m34ms	13L + 21s	3994.7 ¢ to 4063.0 ¢
34-mosstep	Major 34-mosstep	M34ms	14L + 20s	4063.0 ¢ to 4302.0 ¢
35-mosstep	Minor 35-mosstep	m35ms	13L + 22s	3994.7 ¢ to 4182.5 ¢
35-mosstep	Major 35-mosstep	M35ms	14L + 21s	4182.5 ¢ to 4302.0 ¢
36-mosstep	Perfect 36-mosstep	P36ms	14L + 22s	4302.0 ¢

Generator chain

Generator chain of 14L 22s⟨12/1⟩
Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
24	Augmented 12-mosdegree	A12md	Augmented 30-mosdegree	A30md
23	Augmented 7-mosdegree	A7md	Augmented 25-mosdegree	A25md
22	Augmented 2-mosdegree	A2md	Augmented 20-mosdegree	A20md
21	Augmented 15-mosdegree	A15md	Augmented 33-mosdegree	A33md
20	Augmented 10-mosdegree	A10md	Augmented 28-mosdegree	A28md
19	Augmented 5-mosdegree	A5md	Augmented 23-mosdegree	A23md
18	Augmented 0-mosdegree	A0md	Augmented 18-mosdegree	A18md
17	Augmented 13-mosdegree	A13md	Augmented 31-mosdegree	A31md
16	Major 8-mosdegree	M8md	Major 26-mosdegree	M26md
15	Major 3-mosdegree	M3md	Major 21-mosdegree	M21md
14	Major 16-mosdegree	M16md	Major 34-mosdegree	M34md
13	Major 11-mosdegree	M11md	Major 29-mosdegree	M29md
12	Major 6-mosdegree	M6md	Major 24-mosdegree	M24md
11	Major 1-mosdegree	M1md	Major 19-mosdegree	M19md
10	Major 14-mosdegree	M14md	Major 32-mosdegree	M32md
9	Major 9-mosdegree	M9md	Major 27-mosdegree	M27md
8	Major 4-mosdegree	M4md	Major 22-mosdegree	M22md
7	Major 17-mosdegree	M17md	Major 35-mosdegree	M35md
6	Major 12-mosdegree	M12md	Major 30-mosdegree	M30md
5	Major 7-mosdegree	M7md	Major 25-mosdegree	M25md
4	Major 2-mosdegree	M2md	Major 20-mosdegree	M20md
3	Major 15-mosdegree	M15md	Major 33-mosdegree	M33md
2	Major 10-mosdegree	M10md	Major 28-mosdegree	M28md
1	Perfect 5-mosdegree	P5md	Perfect 23-mosdegree	P23md
0	Perfect 0-mosdegree Perfect 18-mosdegree	P0md P18md	Perfect 18-mosdegree Perfect 36-mosdegree	P18md P36md
−1	Perfect 13-mosdegree	P13md	Perfect 31-mosdegree	P31md
−2	Minor 8-mosdegree	m8md	Minor 26-mosdegree	m26md
−3	Minor 3-mosdegree	m3md	Minor 21-mosdegree	m21md
−4	Minor 16-mosdegree	m16md	Minor 34-mosdegree	m34md
−5	Minor 11-mosdegree	m11md	Minor 29-mosdegree	m29md
−6	Minor 6-mosdegree	m6md	Minor 24-mosdegree	m24md
−7	Minor 1-mosdegree	m1md	Minor 19-mosdegree	m19md
−8	Minor 14-mosdegree	m14md	Minor 32-mosdegree	m32md
−9	Minor 9-mosdegree	m9md	Minor 27-mosdegree	m27md
−10	Minor 4-mosdegree	m4md	Minor 22-mosdegree	m22md
−11	Minor 17-mosdegree	m17md	Minor 35-mosdegree	m35md
−12	Minor 12-mosdegree	m12md	Minor 30-mosdegree	m30md
−13	Minor 7-mosdegree	m7md	Minor 25-mosdegree	m25md
−14	Minor 2-mosdegree	m2md	Minor 20-mosdegree	m20md
−15	Minor 15-mosdegree	m15md	Minor 33-mosdegree	m33md
−16	Minor 10-mosdegree	m10md	Minor 28-mosdegree	m28md
−17	Diminished 5-mosdegree	d5md	Diminished 23-mosdegree	d23md
−18	Diminished 18-mosdegree	d18md	Diminished 36-mosdegree	d36md
−19	Diminished 13-mosdegree	d13md	Diminished 31-mosdegree	d31md
−20	Diminished 8-mosdegree	d8md	Diminished 26-mosdegree	d26md
−21	Diminished 3-mosdegree	d3md	Diminished 21-mosdegree	d21md
−22	Diminished 16-mosdegree	d16md	Diminished 34-mosdegree	d34md
−23	Diminished 11-mosdegree	d11md	Diminished 29-mosdegree	d29md
−24	Diminished 6-mosdegree	d6md	Diminished 24-mosdegree	d24md

Modes

Scale degrees of the modes of 14L 22s⟨12/1⟩
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
34\|0(2)	1	LsLssLsLssLsLssLssLsLssLsLssLsLssLss	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.
32\|2(2)	6	LsLssLsLssLssLsLssLsLssLsLssLssLsLss	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
30\|4(2)	11	LsLssLssLsLssLsLssLsLssLssLsLssLsLss	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
28\|6(2)	16	LssLsLssLsLssLsLssLssLsLssLsLssLsLss	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
26\|8(2)	3	LssLsLssLsLssLssLsLssLsLssLsLssLssLs	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.
24\|10(2)	8	LssLsLssLssLsLssLsLssLsLssLssLsLssLs	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.
22\|12(2)	13	LssLssLsLssLsLssLsLssLssLsLssLsLssLs	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.
20\|14(2)	18	sLsLssLsLssLsLssLssLsLssLsLssLsLssLs	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Perf.
18\|16(2)	5	sLsLssLsLssLssLsLssLsLssLsLssLssLsLs	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.
16\|18(2)	10	sLsLssLssLsLssLsLssLsLssLssLsLssLsLs	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.
14\|20(2)	15	sLssLsLssLsLssLsLssLssLsLssLsLssLsLs	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Perf.
12\|22(2)	2	sLssLsLssLsLssLssLsLssLsLssLsLssLssL	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Perf.
10\|24(2)	7	sLssLsLssLssLsLssLsLssLsLssLssLsLssL	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.
8\|26(2)	12	sLssLssLsLssLsLssLsLssLssLsLssLsLssL	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.
6\|28(2)	17	ssLsLssLsLssLsLssLssLsLssLsLssLsLssL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Perf.
4\|30(2)	4	ssLsLssLsLssLssLsLssLsLssLsLssLssLsL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
2\|32(2)	9	ssLsLssLssLsLssLsLssLsLssLssLsLssLsL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0\|34(2)	14	ssLssLsLssLsLssLsLssLssLsLssLsLssLsL	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.

Modes

Cole proposes naming the modes this way: Each period is split up into three pentachords and a trichord. There are three modes which defy the classification of three 2L 3s pentachords and a 1L 2s trichord, having pentachords with one large step and four small steps. However, they are still included for completeness. An ambiguous mode is named after the first two pentachords. Pacific-Hemipyth is regarded as mode 0 or 18.

Mode	UDP	Cyclic order	Name	Name origin
LsLss LsLss LsLss Lss LsLss LsLss LsLss Lss	34\|0(2)	1	Atlantic-QFind	The canonically first 'core' of the Colian Nexus, qfind.
LsLss LsLss LssLs Lss LsLss LsLss LssLs Lss	32\|2(2)	6	Atlantic-Planet	Named after PlanetN9ne.
LsLss LssLs LssLs Lss LsLss LssLs LssLs Lss	30\|4(2)	11	Atlantic-Lumian	This mode's first dekatave has an Atlantic pentachord and a Lumian pentachord.
LssLs LssLs LssLs Lss LssLs LssLs LssLs Lss	28\|6(2)	16	Lumian-Q-Series	The canonically second 'core' of the Colian Nexus, 2-analogue-related functions. Named after the Q-series.
LssLs LssLs LssLs sLs LssLs LssLs LssLs sLs	26\|8(2)	3	Lumian-Moosey	Named after Moosey.
LssLs LssLs sLsLs sLs LssLs LssLs sLsLs sLs	24\|10(2)	8	Lumian-Drone	Named after DroneBetter.
LssLs sLsLs sLsLs sLs LssLs sLsLs sLsLs sLs	22\|12(2)	13	Lumian-Pacific	This mode's first dekatave has a Lumian pentachord and a Pacific pentachord.
sLsLs sLsLs sLsLs sLs sLsLs sLsLs sLsLs sLs	20\|14(2)	18 or 0	Pacific-Hemipyth	The canonically third 'core' of the Colian Nexus, hemipyth.
sLsLs sLsLs sLssL sLs sLsLs sLsLs sLssL sLs	18\|16(2)	5	Pacific-NimbleRogue	Named after NimbleRogue.
sLsLs sLssL sLssL sLs sLsLs sLssL sLssL sLs	16\|18(2)	10	Pacific-Taliesin	This mode's first dekatave has a Pacific pentachord and a Taliesin pentachord.
sLssL sLssL sLssL sLs sLssL sLssL sLssL sLs	14\|20(2)	15	Taliesin-Riemannic	The canonically fourth 'core' of the Colian Nexus, Riemannic, a conlang created by Cole.
sLssL sLssL sLssL ssL sLssL sLssL sLssL ssL	12\|22(2)	2	Taliesin-Wwei	Named after wwei47.
sLssL sLssL ssLsL ssL sLssL sLssL ssLsL ssL	10\|24(2)	7	Taliesin-LaundryPizza	Named after LaundryPizza03.
sLssL ssLsL ssLsL ssL sLssL ssLsL ssLsL ssL	8\|26(2)	12	Taliesin-Dresden	This mode's first dekatave has a Taliesin pentachord and a Dresden pentachord.
ssLsL ssLsL ssLsL ssL ssLsL ssLsL ssLsL ssL	6\|28(2)	17	Dresden-Heav	Named after Heav.
ssLsL ssLsL ssLss LsL ssLsL ssLsL ssLss LsL	4\|30(2)	4	Subdresden-Nimrgod	Named after the canonically first of three tuppers created by User:2^67-1, Nimrgod.
ssLsL ssLss LsLss LsL ssLsL ssLss LsLss LsL	2\|32(2)	9	Subdresden-Boris	Named after the canonically second of three tuppers created by User:2^67-1, Boris Grothendieck.
ssLss LsLss LsLss LsL ssLss LsLss LsLss LsL	0\|34(2)	14	Subdresden-Pergele	Named after the canonically third of three tuppers created by User:2^67-1, Pergele (originator of this idea is Frostburn in a meme post).

Intervals on 0

Here are some intervals on the note 0.

								5♭♭	A♭♭	F♭♭	2♭♭	7♭♭	C♭♭	H♭♭	4♭♭	9♭♭	E♭♭	→
								dd5	d10	d15	d2	d7	d12	d17	d4	d9	d14
1♭	6♭	B♭	G♭	3♭	8♭	D♭	0♭	5♭	A♭	F♭	2♭	7♭	C♭	H♭	4♭	9♭	E♭	→
d1	d6	d11	d16	d3	d8	d13	d0	d5	m10	m15	m2	m7	m12	m17	m4	m9	m14
1	6	B	G	3	8	D	0	5	A	F	2	7	C	H	4	9	E	→
m1	m6	m11	m16	m3	m8	P13	P0	P5	M10	M15	M2	M7	M12	M17	M4	M9	M14
1#	6#	B#	G#	3#	8#	D#	0#	5#	A#	F#	2#	7#	C#	H#	4#	9#	E#	→
M1	M6	M11	M16	M3	M8	A13	A0	A5	A10	A15	A2	A7	A12	A17	A4	A9	A14
1##	6##	B##	G##	3##	8##	D##	→
A1	A6	A11	A16	A3	A8	AA13

Simple tunings

Simple Tunings of 14L 22s⟨12/1⟩
Scale degree	Abbrev.	Basic (2:1) 50ed12		Hard (3:1) 64ed12		Soft (3:2) 86ed12
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\50	0.0	0\64	0.0	0\86	0.0
Minor 1-mosdegree	m1md	1\50	86.0	1\64	67.2	2\86	100.0
Major 1-mosdegree	M1md	2\50	172.1	3\64	201.7	3\86	150.1
Minor 2-mosdegree	m2md	2\50	172.1	2\64	134.4	4\86	200.1
Major 2-mosdegree	M2md	3\50	258.1	4\64	268.9	5\86	250.1
Minor 3-mosdegree	m3md	4\50	344.2	5\64	336.1	7\86	350.2
Major 3-mosdegree	M3md	5\50	430.2	7\64	470.5	8\86	400.2
Minor 4-mosdegree	m4md	5\50	430.2	6\64	403.3	9\86	450.2
Major 4-mosdegree	M4md	6\50	516.2	8\64	537.7	10\86	500.2
Diminished 5-mosdegree	d5md	6\50	516.2	7\64	470.5	11\86	550.3
Perfect 5-mosdegree	P5md	7\50	602.3	9\64	605.0	12\86	600.3
Minor 6-mosdegree	m6md	8\50	688.3	10\64	672.2	14\86	700.3
Major 6-mosdegree	M6md	9\50	774.4	12\64	806.6	15\86	750.3
Minor 7-mosdegree	m7md	9\50	774.4	11\64	739.4	16\86	800.4
Major 7-mosdegree	M7md	10\50	860.4	13\64	873.8	17\86	850.4
Minor 8-mosdegree	m8md	11\50	946.4	14\64	941.1	19\86	950.4
Major 8-mosdegree	M8md	12\50	1032.5	16\64	1075.5	20\86	1000.5
Minor 9-mosdegree	m9md	12\50	1032.5	15\64	1008.3	21\86	1050.5
Major 9-mosdegree	M9md	13\50	1118.5	17\64	1142.7	22\86	1100.5
Minor 10-mosdegree	m10md	13\50	1118.5	16\64	1075.5	23\86	1150.5
Major 10-mosdegree	M10md	14\50	1204.5	18\64	1209.9	24\86	1200.5
Minor 11-mosdegree	m11md	15\50	1290.6	19\64	1277.1	26\86	1300.6
Major 11-mosdegree	M11md	16\50	1376.6	21\64	1411.6	27\86	1350.6
Minor 12-mosdegree	m12md	16\50	1376.6	20\64	1344.4	28\86	1400.6
Major 12-mosdegree	M12md	17\50	1462.7	22\64	1478.8	29\86	1450.7
Perfect 13-mosdegree	P13md	18\50	1548.7	23\64	1546.0	31\86	1550.7
Augmented 13-mosdegree	A13md	19\50	1634.7	25\64	1680.5	32\86	1600.7
Minor 14-mosdegree	m14md	19\50	1634.7	24\64	1613.2	33\86	1650.8
Major 14-mosdegree	M14md	20\50	1720.8	26\64	1747.7	34\86	1700.8
Minor 15-mosdegree	m15md	20\50	1720.8	25\64	1680.5	35\86	1750.8
Major 15-mosdegree	M15md	21\50	1806.8	27\64	1814.9	36\86	1800.8
Minor 16-mosdegree	m16md	22\50	1892.9	28\64	1882.1	38\86	1900.9
Major 16-mosdegree	M16md	23\50	1978.9	30\64	2016.5	39\86	1950.9
Minor 17-mosdegree	m17md	23\50	1978.9	29\64	1949.3	40\86	2000.9
Major 17-mosdegree	M17md	24\50	2064.9	31\64	2083.8	41\86	2050.9
Perfect 18-mosdegree	P18md	25\50	2151.0	32\64	2151.0	43\86	2151.0
Minor 19-mosdegree	m19md	26\50	2237.0	33\64	2218.2	45\86	2251.0
Major 19-mosdegree	M19md	27\50	2323.1	35\64	2352.6	46\86	2301.0
Minor 20-mosdegree	m20md	27\50	2323.1	34\64	2285.4	47\86	2351.1
Major 20-mosdegree	M20md	28\50	2409.1	36\64	2419.8	48\86	2401.1
Minor 21-mosdegree	m21md	29\50	2495.1	37\64	2487.1	50\86	2501.1
Major 21-mosdegree	M21md	30\50	2581.2	39\64	2621.5	51\86	2551.2
Minor 22-mosdegree	m22md	30\50	2581.2	38\64	2554.3	52\86	2601.2
Major 22-mosdegree	M22md	31\50	2667.2	40\64	2688.7	53\86	2651.2
Diminished 23-mosdegree	d23md	31\50	2667.2	39\64	2621.5	54\86	2701.2
Perfect 23-mosdegree	P23md	32\50	2753.3	41\64	2755.9	55\86	2751.3
Minor 24-mosdegree	m24md	33\50	2839.3	42\64	2823.2	57\86	2851.3
Major 24-mosdegree	M24md	34\50	2925.3	44\64	2957.6	58\86	2901.3
Minor 25-mosdegree	m25md	34\50	2925.3	43\64	2890.4	59\86	2951.3
Major 25-mosdegree	M25md	35\50	3011.4	45\64	3024.8	60\86	3001.4
Minor 26-mosdegree	m26md	36\50	3097.4	46\64	3092.0	62\86	3101.4
Major 26-mosdegree	M26md	37\50	3183.4	48\64	3226.5	63\86	3151.4
Minor 27-mosdegree	m27md	37\50	3183.4	47\64	3159.2	64\86	3201.5
Major 27-mosdegree	M27md	38\50	3269.5	49\64	3293.7	65\86	3251.5
Minor 28-mosdegree	m28md	38\50	3269.5	48\64	3226.5	66\86	3301.5
Major 28-mosdegree	M28md	39\50	3355.5	50\64	3360.9	67\86	3351.5
Minor 29-mosdegree	m29md	40\50	3441.6	51\64	3428.1	69\86	3451.6
Major 29-mosdegree	M29md	41\50	3527.6	53\64	3562.6	70\86	3501.6
Minor 30-mosdegree	m30md	41\50	3527.6	52\64	3495.3	71\86	3551.6
Major 30-mosdegree	M30md	42\50	3613.6	54\64	3629.8	72\86	3601.6
Perfect 31-mosdegree	P31md	43\50	3699.7	55\64	3697.0	74\86	3701.7
Augmented 31-mosdegree	A31md	44\50	3785.7	57\64	3831.4	75\86	3751.7
Minor 32-mosdegree	m32md	44\50	3785.7	56\64	3764.2	76\86	3801.7
Major 32-mosdegree	M32md	45\50	3871.8	58\64	3898.6	77\86	3851.8
Minor 33-mosdegree	m33md	45\50	3871.8	57\64	3831.4	78\86	3901.8
Major 33-mosdegree	M33md	46\50	3957.8	59\64	3965.9	79\86	3951.8
Minor 34-mosdegree	m34md	47\50	4043.8	60\64	4033.1	81\86	4051.8
Major 34-mosdegree	M34md	48\50	4129.9	62\64	4167.5	82\86	4101.9
Minor 35-mosdegree	m35md	48\50	4129.9	61\64	4100.3	83\86	4151.9
Major 35-mosdegree	M35md	49\50	4215.9	63\64	4234.7	84\86	4201.9
Perfect 36-mosdegree	P36md	50\50	4302.0	64\64	4302.0	86\86	4302.0

Scale tree

Scale tree and tuning spectrum of 14L 22s⟨12/1⟩
Generator^(ed12/1)						Cents		Step ratio		Comments
Generator^(ed12/1)						Bright	Dark	L:s	Hardness	Comments
5\36						597.494	1553.484	1:1	1.000	Equalized 14L 22s⟨12/1⟩
					27\194	598.726	1552.252	6:5	1.200
				22\158		599.006	1551.971	5:4	1.250
					39\280	599.201	1551.777	9:7	1.286
			17\122			599.453	1551.525	4:3	1.333	Supersoft 14L 22s⟨12/1⟩
					46\330	599.666	1551.311	11:8	1.375
				29\208		599.792	1551.186	7:5	1.400
					41\294	599.933	1551.045	10:7	1.429	Hemipyth tuning for this scale is around here;
		12\86				600.273	1550.705	3:2	1.500	Soft 14L 22s⟨12/1⟩ Approximately the step ratio for the scale with 1/QPochhammer[1/2] as period.
					43\308	600.598	1550.380	11:7	1.571	The sum of the sizes of all the small steps is equal to the sum of the sizes of all the large steps.
				31\222		600.723	1550.254	8:5	1.600
					50\358	600.832	1550.146	13:8	1.625
			19\136			601.008	1549.969	5:3	1.667	Semisoft 14L 22s⟨12/1⟩
					45\322	601.205	1549.773	12:7	1.714
				26\186		601.349	1549.629	7:4	1.750
					33\236	601.545	1549.433	9:5	1.800
	7\50					602.274	1548.704	2:1	2.000	Basic 14L 22s⟨12/1⟩ Scales with tunings softer than this are proper
					30\214	603.078	1547.900	9:4	2.250
				23\164		603.323	1547.655	7:3	2.333
					39\278	603.512	1547.466	12:5	2.400
			16\114			603.783	1547.194	5:2	2.500	Semihard 14L 22s⟨12/1⟩
					41\292	604.042	1546.936	13:5	2.600
				25\178		604.207	1546.770	8:3	2.667
					34\242	604.407	1546.571	11:4	2.750
		9\64				604.962	1546.015	3:1	3.000	Hard 14L 22s⟨12/1⟩
					29\206	605.615	1545.362	10:3	3.333
				20\142		605.909	1545.068	7:2	3.500
					31\220	606.185	1544.793	11:3	3.667
			11\78			606.686	1544.292	4:1	4.000	Superhard 14L 22s⟨12/1⟩
					24\170	607.335	1543.643	9:2	4.500
				13\92		607.885	1543.093	5:1	5.000
					15\106	608.767	1542.210	6:1	6.000
2\14						614.565	1536.413	1:0	→ ∞	Collapsed 14L 22s⟨12/1⟩

14L 22s (12/1-equivalent)

Contents

Standing assumptions

Scale properties

Intervals

Generator chain

Modes

Modes

Intervals on 0

Simple tunings

Scale tree

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