14L 22s (12/1-equivalent)
Assume hemipyth[10] nominal names and intervals unless otherwise stated.
The 7L 11s (√12-equivalent) scale, also greater pochhammeroid (see below), greater 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. Its basic tuning is 25ed√12 or 50ed12.
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 greater 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) by # and f "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 two pentachords in its first dekatave. The others are named after a certain 'core' or first-wave member of the Colian Nexus.
| 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-Pochhammer | The canonically second 'core' of the Colian Nexus, 2-analogue-related functions. |
| 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). |
Scale tree
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Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}
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| Generator(ed12/1) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 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 | ||||||
| 12\86 | 600.273 | 1550.705 | 3:2 | 1.500 | Soft 14L 22s⟨12/1⟩ | |||||
| 43\308 | 600.598 | 1550.380 | 11:7 | 1.571 | ||||||
| 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⟩ | |||||