7L 2s
| ↖ 6L 1s | ↑ 7L 1s | 8L 1s ↗ |
| ← 6L 2s | 7L 2s | 8L 2s → |
| ↙ 6L 3s | ↓ 7L 3s | 8L 3s ↘ |
┌╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLLLsLLLL
7L 2s, named armotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 666.7 ¢ to 685.7 ¢, or from 514.3 ¢ to 533.3 ¢. Scales of this form are strongly associated with Armodue theory, as applied to septimal mavila and Hornbostel temperaments.
Name
The TAMNAMS name for this pattern is armotonic, in reference to Armodue theory. Superdiatonic is also in use.
Scale properties
- 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 diatonic interval categories.
{{subst:MOS data temporary}}
Proposed mode names
The Ad- mode names proposed by groundfault have the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc.
| UDP | Cyclic order |
Step pattern |
Super- Mode Names | Ad- Mode Names (ground) |
|---|---|---|---|---|
| 8|0 | 1 | LLLLsLLLs | Superlydian | TBD |
| 7|1 | 6 | LLLsLLLLs | Superionian | Adlocrian |
| 6|2 | 2 | LLLsLLLsL | Supermixolydian | Adphrygian |
| 5|3 | 7 | LLsLLLLsL | Supercorinthian | Adaeolian |
| 4|4 | 3 | LLsLLLsLL | Superolympian | Addorian |
| 3|5 | 8 | LsLLLLsLL | Superdorian | Admixolydian |
| 2|6 | 4 | LsLLLsLLL | Superaeolian | Adionian |
| 1|7 | 9 | sLLLLsLLL | Superphrygian | Adlydian |
| 0|8 | 5 | sLLLsLLLL | Superlocrian | TBD |
Note names
7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.
Theory
Temperament interpretations
Mavila is an important harmonic entropy minimum here, insofar as 678 ¢ can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 5\9 | 666.667 | 533.333 | 1:1 | 1.000 | Equalized 7L 2s Near exact-7/6 Armodue | |||||
| 29\52 | 669.231 | 530.769 | 6:5 | 1.200 | ||||||
| 24\43 | 669.767 | 530.233 | 5:4 | 1.250 | ||||||
| 43\77 | 670.130 | 529.870 | 9:7 | 1.286 | ||||||
| 19\34 | 670.588 | 529.412 | 4:3 | 1.333 | Supersoft 7L 2s Near exact-20/17 Pentagoth | |||||
| 52\93 | 670.968 | 529.032 | 11:8 | 1.375 | ||||||
| 33\59 | 671.186 | 528.814 | 7:5 | 1.400 | Near exact-5/4 Mavila | |||||
| 47\84 | 671.429 | 528.571 | 10:7 | 1.429 | ||||||
| 14\25 | 672.000 | 528.000 | 3:2 | 1.500 | Soft 7L 2s Near exact-13/11 Pentagoth | |||||
| 51\91 | 672.527 | 527.473 | 11:7 | 1.571 | ||||||
| 37\66 | 672.727 | 527.273 | 8:5 | 1.600 | ||||||
| 60\107 | 672.897 | 527.103 | 13:8 | 1.625 | ||||||
| 23\41 | 673.171 | 526.829 | 5:3 | 1.667 | Semisoft 7L 2s | |||||
| 55\98 | 673.469 | 526.531 | 12:7 | 1.714 | ||||||
| 32\57 | 673.684 | 526.316 | 7:4 | 1.750 | Near exact-7/4 Armodue | |||||
| 41\73 | 673.973 | 526.027 | 9:5 | 1.800 | ||||||
| 9\16 | 675.000 | 525.000 | 2:1 | 2.000 | Basic 7L 2s Scales with tunings softer than this are proper | |||||
| 40\71 | 676.056 | 523.944 | 9:4 | 2.250 | ||||||
| 31\55 | 676.364 | 523.636 | 7:3 | 2.333 | ||||||
| 53\94 | 676.596 | 523.404 | 12:5 | 2.400 | ||||||
| 22\39 | 676.923 | 523.077 | 5:2 | 2.500 | Semihard 7L 2s | |||||
| 57\101 | 677.228 | 522.772 | 13:5 | 2.600 | ||||||
| 35\62 | 677.419 | 522.581 | 8:3 | 2.667 | ||||||
| 48\85 | 677.647 | 522.353 | 11:4 | 2.750 | ||||||
| 13\23 | 678.261 | 521.739 | 3:1 | 3.000 | Hard 7L 2s | |||||
| 43\76 | 678.947 | 521.053 | 10:3 | 3.333 | Near exact-6/5 Mavila | |||||
| 30\53 | 679.245 | 520.755 | 7:2 | 3.500 | ||||||
| 47\83 | 679.518 | 520.482 | 11:3 | 3.667 | ||||||
| 17\30 | 680.000 | 520.000 | 4:1 | 4.000 | Superhard 7L 2s | |||||
| 38\67 | 680.597 | 519.403 | 9:2 | 4.500 | ||||||
| 21\37 | 681.081 | 518.919 | 5:1 | 5.000 | ||||||
| 25\44 | 681.818 | 518.182 | 6:1 | 6.000 | ||||||
| 4\7 | 685.714 | 514.286 | 1:0 | → ∞ | Collapsed 7L 2s | |||||