5L 5s
| ↖ 4L 4s | ↑ 5L 4s | 6L 4s ↗ |
| ← 4L 5s | 5L 5s | 6L 5s → |
| ↙ 4L 6s | ↓ 5L 6s | 6L 6s ↘ |
┌╥┬╥┬╥┬╥┬╥┬┐ │║│║│║│║│║││ ││││││││││││ └┴┴┴┴┴┴┴┴┴┴┘
sLsLsLsLsL
5L 5s, named pentawood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 5 small steps, with a period of 1 large step and 1 small step that repeats every 240.0¢, or 5 times every octave. Generators that produce this scale range from 120¢ to 240¢, or from 0¢ to 120¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
There is only one significant harmonic entropy minimum with this MOS pattern: blackwood, in which intervals of the prime numbers 3 and 7 are all represented using steps of 5edo, and the generator reaches intervals of 5 like 6/5, 5/4, or 7/5.
In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-pentawdstep | Perfect 0-pentawdstep | P0pws | 0 | 0.0¢ |
| 1-pentawdstep | Minor 1-pentawdstep | m1pws | s | 0.0¢ to 120.0¢ |
| Major 1-pentawdstep | M1pws | L | 120.0¢ to 240.0¢ | |
| 2-pentawdstep | Perfect 2-pentawdstep | P2pws | L + s | 240.0¢ |
| 3-pentawdstep | Minor 3-pentawdstep | m3pws | L + 2s | 240.0¢ to 360.0¢ |
| Major 3-pentawdstep | M3pws | 2L + s | 360.0¢ to 480.0¢ | |
| 4-pentawdstep | Perfect 4-pentawdstep | P4pws | 2L + 2s | 480.0¢ |
| 5-pentawdstep | Minor 5-pentawdstep | m5pws | 2L + 3s | 480.0¢ to 600.0¢ |
| Major 5-pentawdstep | M5pws | 3L + 2s | 600.0¢ to 720.0¢ | |
| 6-pentawdstep | Perfect 6-pentawdstep | P6pws | 3L + 3s | 720.0¢ |
| 7-pentawdstep | Minor 7-pentawdstep | m7pws | 3L + 4s | 720.0¢ to 840.0¢ |
| Major 7-pentawdstep | M7pws | 4L + 3s | 840.0¢ to 960.0¢ | |
| 8-pentawdstep | Perfect 8-pentawdstep | P8pws | 4L + 4s | 960.0¢ |
| 9-pentawdstep | Minor 9-pentawdstep | m9pws | 4L + 5s | 960.0¢ to 1080.0¢ |
| Major 9-pentawdstep | M9pws | 5L + 4s | 1080.0¢ to 1200.0¢ | |
| 10-pentawdstep | Perfect 10-pentawdstep | P10pws | 5L + 5s | 1200.0¢ |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (pentawddegree) | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||
| 5|0(5) | 1 | LsLsLsLsLs | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. | Maj. | Perf. |
| 0|5(5) | 2 | sLsLsLsLsL | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. | Min. | Perf. |
Scale tree
| Generator | Cents | L | s | L/s | Comments | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Chroma-positive | Chroma-negative | ||||||||||
| 1\10 | 120.000 | 120.000 | 1 | 1 | 1.000 | ||||||
| 6\55 | 130.909 | 109.091 | 6 | 5 | 1.200 | Qintosec↑ | |||||
| 5\45 | 133.333 | 106.667 | 5 | 4 | 1.250 | ||||||
| 9\80 | 135.000 | 105.000 | 9 | 7 | 1.286 | ||||||
| 4\35 | 137.143 | 102.857 | 4 | 3 | 1.333 | ||||||
| 11\95 | 138.947 | 101.053 | 11 | 8 | 1.375 | ||||||
| 7\60 | 140.000 | 100.000 | 7 | 5 | 1.400 | Warlock | |||||
| 10\85 | 141.176 | 98.824 | 10 | 7 | 1.428 | ||||||
| 3\25 | 144.000 | 96.000 | 3 | 2 | 1.500 | L/s = 3/2 | |||||
| 11\90 | 146.667 | 93.333 | 11 | 7 | 1.571 | ||||||
| 8\65 | 147.692 | 92.308 | 8 | 5 | 1.600 | ||||||
| 13\105 | 148.571 | 91.429 | 13 | 8 | 1.625 | Unnamed golden tuning | |||||
| 5\40 | 150.000 | 90.000 | 5 | 3 | 1.667 | ||||||
| 12\95 | 151.579 | 88.421 | 12 | 7 | 1.714 | ||||||
| 7\55 | 152.727 | 87.273 | 7 | 4 | 1.750 | Quinkee | |||||
| 9\70 | 154.286 | 85.714 | 9 | 5 | 1.800 | ||||||
| 2\15 | 160.000 | 80.000 | 2 | 1 | 2.000 | Basic pentawood Blacksmith is optimal around here | |||||
| 9\65 | 166.154 | 73.846 | 9 | 4 | 2.250 | Trisedodge | |||||
| 7\50 | 168.000 | 72.000 | 7 | 3 | 2.333 | ||||||
| 12\85 | 169.412 | 70.588 | 12 | 5 | 2.400 | ||||||
| 5\35 | 171.429 | 68.571 | 5 | 2 | 2.500 | ||||||
| 13\90 | 173.333 | 66.667 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 8\55 | 174.545 | 65.455 | 8 | 3 | 2.667 | ||||||
| 11\75 | 176.000 | 64.000 | 11 | 4 | 2.750 | ||||||
| 3\20 | 180.000 | 60.000 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
| 10\65 | 184.615 | 55.385 | 10 | 3 | 3.333 | ||||||
| 7\45 | 186.667 | 53.333 | 7 | 2 | 3.500 | ||||||
| 11\70 | 188.571 | 51.429 | 11 | 3 | 3.667 | ||||||
| 4\25 | 192.000 | 48.000 | 4 | 1 | 4.000 | ||||||
| 9\55 | 196.364 | 43.636 | 9 | 2 | 4.500 | ||||||
| 5\30 | 200.000 | 40.000 | 5 | 1 | 5.000 | ||||||
| 6\35 | 205.714 | 34.286 | 6 | 1 | 6.000 | Cloudtone↓ | |||||
| 1\5 | 240.000 | 0.000 | 1 | 0 | → inf | ||||||