14L 22s (12/1-equivalent)

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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
Parent	14L 8s⟨12/1⟩
Sister	22L 14s⟨12/1⟩
Daughters	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 ¢)
Soft (L:s = 3:2)	12\86 (600.3 ¢)
Semisoft (L:s = 5:3)	19\136 (601.0 ¢)
Basic (L:s = 2:1)	7\50 (602.3 ¢)
Semihard (L:s = 5:2)	16\114 (603.8 ¢)
Hard (L:s = 3:1)	9\64 (605.0 ¢)
Superhard (L:s = 4:1)	11\78 (606.7 ¢)
Collapsed (L:s = 1:0)	2\14 (614.6 ¢)

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

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

The equave 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 TAMNAMS system is used in this article to name 7L 11s <√12> intervals and step size ratios and step ratio ranges.

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 digit set as the numbers, as long as it is clear which set one is using.) We denote raising and lowering by a chroma (L − s, about √(256/243) using the hemipyth interpretation) by # and ♭ "flat (F molle)".

Modes

For clarity, each mode is split up into three pentachords and a trichord. There are three modes which defy this classification, 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.

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

Genchain

The genchain for this scale is as follows:

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