5L 5s
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.
| ↖ 4L 4s | ↑ 5L 4s | 6L 4s ↗ |
| ← 4L 5s | 5L 5s | 6L 5s → |
| ↙ 4L 6s | ↓ 5L 6s | 6L 6s ↘ |
sLsLsLsLsL
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 | ||||||