14L 22s (12/1-equivalent): Difference between revisions
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==Mode | ==Mode name origins== | ||
For clarity, 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. | For clarity, 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. | ||
Revision as of 08:47, 3 March 2025
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. 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⟩ ↘ |
┌╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬┬┐ │║│║││║│║││║│║││║││║│║││║│║││║│║││║│││ ││││││││││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLssLsLssLsLssLsLssLssLsLssLsLssLsL
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 TAMNAMS system is used in this article to name 14L 22s <12/1> intervals, step size ratios and step ratio ranges. However, the equave is taken to be the period of the scale, √12, as it is more practical.
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.
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MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
Modes
Cole proposes naming the modes this way:
| UDP | Cyclic order |
Step pattern |
Mode names |
|---|---|---|---|
| 34|0(2) | 1 | LsLssLsLssLsLssLssLsLssLsLssLsLssLss | Atlantic-QFind |
| 32|2(2) | 6 | LsLssLsLssLssLsLssLsLssLsLssLssLsLss | Atlantic-Planet |
| 30|4(2) | 11 | LsLssLssLsLssLsLssLsLssLssLsLssLsLss | Atlantic-Lumian |
| 28|6(2) | 16 | LssLsLssLsLssLsLssLssLsLssLsLssLsLss | Lumian-Q-Series |
| 26|8(2) | 3 | LssLsLssLsLssLssLsLssLsLssLsLssLssLs | Lumian-Moosey |
| 24|10(2) | 8 | LssLsLssLssLsLssLsLssLsLssLssLsLssLs | Lumian-Drone |
| 22|12(2) | 13 | LssLssLsLssLsLssLsLssLssLsLssLsLssLs | Lumian-Pacific |
| 20|14(2) | 18 | sLsLssLsLssLsLssLssLsLssLsLssLsLssLs | Pacific-Hemipyth |
| 18|16(2) | 5 | sLsLssLsLssLssLsLssLsLssLsLssLssLsLs | Pacific-NimbleRogue |
| 16|18(2) | 10 | sLsLssLssLsLssLsLssLsLssLssLsLssLsLs | Pacific-Taliesin |
| 14|20(2) | 15 | sLssLsLssLsLssLsLssLssLsLssLsLssLsLs | Taliesin-Riemannic |
| 12|22(2) | 2 | sLssLsLssLsLssLssLsLssLsLssLsLssLssL | Taliesin-Wwei |
| 10|24(2) | 7 | sLssLsLssLssLsLssLsLssLsLssLssLsLssL | Taliesin-LaundryPizza |
| 8|26(2) | 12 | sLssLssLsLssLsLssLsLssLssLsLssLsLssL | Taliesin-Dresden |
| 6|28(2) | 17 | ssLsLssLsLssLsLssLssLsLssLsLssLsLssL | Dresden-Heav |
| 4|30(2) | 4 | ssLsLssLsLssLssLsLssLsLssLsLssLssLsL | Subdresden-Nimrgod |
| 2|32(2) | 9 | ssLsLssLssLsLssLsLssLsLssLssLsLssLsL | Subdresden-Boris |
| 0|34(2) | 14 | ssLssLsLssLsLssLsLssLssLsLssLsLssLsL | Subdresden-Pergele |
Mode name origins
For clarity, 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.
| Mode | UDP | Name | Name origin |
| LsLss LsLss LsLss Lss LsLss LsLss LsLss Lss | 34|0(2) | Atlantic-QFind | The canonically first 'core' of the Colian Nexus, qfind. |
| LsLss LsLss LssLs Lss LsLss LsLss LssLs Lss | 32|2(2) | Atlantic-Planet | Named after PlanetN9ne. |
| LsLss LssLs LssLs Lss LsLss LssLs LssLs Lss | 30|4(2) | 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) | 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) | Lumian-Moosey | Named after Moosey. |
| LssLs LssLs sLsLs sLs LssLs LssLs sLsLs sLs | 24|10(2) | Lumian-Drone | Named after DroneBetter. |
| LssLs sLsLs sLsLs sLs LssLs sLsLs sLsLs sLs | 22|12(2) | 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) | Pacific-Hemipyth | The canonically third 'core' of the Colian Nexus, hemipyth. |
| sLsLs sLsLs sLssL sLs sLsLs sLsLs sLssL sLs | 18|16(2) | Pacific-NimbleRogue | Named after NimbleRogue. |
| sLsLs sLssL sLssL sLs sLsLs sLssL sLssL sLs | 16|18(2) | 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) | 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) | Taliesin-Wwei | Named after wwei47. |
| sLssL sLssL ssLsL ssL sLssL sLssL ssLsL ssL | 10|24(2) | Taliesin-LaundryPizza | Named after LaundryPizza03. |
| sLssL ssLsL ssLsL ssL sLssL ssLsL ssLsL ssL | 8|26(2) | 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) | Dresden-Heav | Named after Heav. |
| ssLsL ssLsL ssLss LsL ssLsL ssLsL ssLss LsL | 4|30(2) | 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) | 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) | 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 | ||||||||||||
Scale tree
| 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 | 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⟩ | |||||