User:MisterShafXen/5L 5s

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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 ↘
Scale structure
Step pattern LsLsLsLsLs
sLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\5 (240.0 ¢)
Generator size
Bright 1\10 to 1\5 (120.0 ¢ to 240.0 ¢)
Dark 0\5 to 1\10 (0.0 ¢ to 120.0 ¢)
TAMNAMS information
Name pentawood
Prefix pentawd-
Abbrev. pw
Related MOS scales
Parent none
Sister 5L 5s (self)
Daughters 10L 5s, 5L 10s
Neutralized 10edo
2-Flought 15L 5s, 5L 15s
Equal tunings
Equalized (L:s = 1:1) 1\10 (120.0 ¢)
Supersoft (L:s = 4:3) 4\35 (137.1 ¢)
Soft (L:s = 3:2) 3\25 (144.0 ¢)
Semisoft (L:s = 5:3) 5\40 (150.0 ¢)
Basic (L:s = 2:1) 2\15 (160.0 ¢)
Semihard (L:s = 5:2) 5\35 (171.4 ¢)
Hard (L:s = 3:1) 3\20 (180.0 ¢)
Superhard (L:s = 4:1) 4\25 (192.0 ¢)
Collapsed (L:s = 1:0) 1\5 (240.0 ¢)
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Scale properties

Intervals of 5L 5s
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 ¢
Harmonic entropy info for 5L 5s
Interval Range in cents Average of HE
(from HE Calc)		 Min of HE
Perfect 0-pentawdstep 0.0 ¢ ~2.4654 nats ~2.4654 nats
Minor 1-pentawdstep 0.0 ¢ to 120.0 ¢ ~4.7311 nats ~4.6719 nats
Major 1-pentawdstep 120.0 ¢ to 240.0 ¢ ~4.6129 nats ~4.5888 nats
Perfect 2-pentawdstep 240.0 ¢ ~4.5865 nats ~4.5865 nats
Minor 3-pentawdstep 240.0 ¢ to 360.0 ¢ ~4.5726 nats ~4.5422 nats
Major 3-pentawdstep 360.0 ¢ to 480.0 ¢ ~4.5439 nats ~4.4864 nats
Perfect 4-pentawdstep 480.0 ¢ ~4.5131 nats ~4.5131 nats
Minor 5-pentawdstep 480.0 ¢ to 600.0 ¢ ~4.5966 nats ~4.5599 nats
Major 5-pentawdstep 600.0 ¢ to 720.0 ¢ ~4.6185 nats ~4.5985 nats
Perfect 6-pentawdstep 720.0 ¢ ~4.3710 nats ~4.3710 nats
Minor 7-pentawdstep 720.0 ¢ to 840.0 ¢ ~4.5901 nats ~4.5712 nats
Major 7-pentawdstep 840.0 ¢ to 960.0 ¢ ~4.5152 nats ~4.4330 nats
Perfect 8-pentawdstep 960.0 ¢ ~4.5498 nats ~4.5498 nats
Minor 9-pentawdstep 960.0 ¢ to 1080.0 ¢ ~4.5963 nats ~4.5786 nats
Major 9-pentawdstep 1080.0 ¢ to 1200.0 ¢ ~4.6583 nats ~4.6158 nats
Perfect 10-pentawdstep 1200.0 ¢ ~3.3273 nats ~3.3273 nats
Simple Tunings of 5L 5s
Scale degree Abbrev. Basic (2:1)
15edo 		Hard (3:1)
20edo 		Soft (3:2)
25edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-pentawddegree P0pwd 0\15 0.0 0\20 0.0 0\25 0.0
Minor 1-pentawddegree m1pwd 1\15 80.0 1\20 60.0 2\25 96.0
Major 1-pentawddegree M1pwd 2\15 160.0 3\20 180.0 3\25 144.0
Perfect 2-pentawddegree P2pwd 3\15 240.0 4\20 240.0 5\25 240.0
Minor 3-pentawddegree m3pwd 4\15 320.0 5\20 300.0 7\25 336.0
Major 3-pentawddegree M3pwd 5\15 400.0 7\20 420.0 8\25 384.0
Perfect 4-pentawddegree P4pwd 6\15 480.0 8\20 480.0 10\25 480.0
Minor 5-pentawddegree m5pwd 7\15 560.0 9\20 540.0 12\25 576.0
Major 5-pentawddegree M5pwd 8\15 640.0 11\20 660.0 13\25 624.0
Perfect 6-pentawddegree P6pwd 9\15 720.0 12\20 720.0 15\25 720.0
Minor 7-pentawddegree m7pwd 10\15 800.0 13\20 780.0 17\25 816.0
Major 7-pentawddegree M7pwd 11\15 880.0 15\20 900.0 18\25 864.0
Perfect 8-pentawddegree P8pwd 12\15 960.0 16\20 960.0 20\25 960.0
Minor 9-pentawddegree m9pwd 13\15 1040.0 17\20 1020.0 22\25 1056.0
Major 9-pentawddegree M9pwd 14\15 1120.0 19\20 1140.0 23\25 1104.0
Perfect 10-pentawddegree P10pwd 15\15 1200.0 20\20 1200.0 25\25 1200.0
Generator chain of 5L 5s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
2 Augmented 0-pentawddegree A0pwd Augmented 2-pentawddegree A2pwd Augmented 4-pentawddegree A4pwd Augmented 6-pentawddegree A6pwd Augmented 8-pentawddegree A8pwd
1 Major 1-pentawddegree M1pwd Major 3-pentawddegree M3pwd Major 5-pentawddegree M5pwd Major 7-pentawddegree M7pwd Major 9-pentawddegree M9pwd
0 Perfect 0-pentawddegree
Perfect 2-pentawddegree		 P0pwd
P2pwd		 Perfect 2-pentawddegree
Perfect 4-pentawddegree		 P2pwd
P4pwd		 Perfect 4-pentawddegree
Perfect 6-pentawddegree		 P4pwd
P6pwd		 Perfect 6-pentawddegree
Perfect 8-pentawddegree		 P6pwd
P8pwd		 Perfect 8-pentawddegree
Perfect 10-pentawddegree		 P8pwd
P10pwd
−1 Minor 1-pentawddegree m1pwd Minor 3-pentawddegree m3pwd Minor 5-pentawddegree m5pwd Minor 7-pentawddegree m7pwd Minor 9-pentawddegree m9pwd
−2 Diminished 2-pentawddegree d2pwd Diminished 4-pentawddegree d4pwd Diminished 6-pentawddegree d6pwd Diminished 8-pentawddegree d8pwd Diminished 10-pentawddegree d10pwd
Modes of 5L 5s
UDP Cyclic
order		 Step
pattern
5|0(5) 1 LsLsLsLsLs
0|5(5) 2 sLsLsLsLsL

Scale tree

Scale tree and tuning spectrum of 5L 5s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\10 120.000 120.000 1:1 1.000 Equalized 5L 5s
6\55 130.909 109.091 6:5 1.200
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 Supersoft 5L 5s
11\95 138.947 101.053 11:8 1.375
7\60 140.000 100.000 7:5 1.400
10\85 141.176 98.824 10:7 1.429
3\25 144.000 96.000 3:2 1.500 Soft 5L 5s
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
5\40 150.000 90.000 5:3 1.667 Semisoft 5L 5s
12\95 151.579 88.421 12:7 1.714
7\55 152.727 87.273 7:4 1.750
9\70 154.286 85.714 9:5 1.800
2\15 160.000 80.000 2:1 2.000 Basic 5L 5s
9\65 166.154 73.846 9:4 2.250
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 Semihard 5L 5s
13\90 173.333 66.667 13:5 2.600
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 Hard 5L 5s
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 Superhard 5L 5s
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
1\5 240.000 0.000 1:0 → ∞ Collapsed 5L 5s
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