User:Ganaram inukshuk/Sandbox: Difference between revisions

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| 5/1 = [[Magic]]
| 5/1 = [[Magic]]
| 6/1 = [[Würschmidt]]↓
| 6/1 = [[Würschmidt]]↓
}}
{{MOS tuning spectrum
| Scale Signature= 3L 4s<3/2>
}}
{{MOS tuning spectrum
| Scale Signature= 3L 4s<3/1>
}}
{{MOS tuning spectrum
| Scale Signature= 3L 4s<9/4>
}}
}}


Revision as of 06:37, 28 February 2025

This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.) 

{{subst:User:Ganaram inukshuk/JI ratios|Int Limit=50|Prime Limit=7|Equave=2/1}}

produces

1/1, 50/49, 49/48, 36/35, 28/27, 25/24, 21/20, 16/15, 15/14, 27/25, 49/45, 35/32, 10/9, 28/25, 9/8, 8/7, 7/6, 32/27, 25/21, 6/5, 49/40, 5/4, 32/25, 9/7, 35/27, 21/16, 4/3, 27/20, 49/36, 48/35, 25/18, 7/5, 45/32, 10/7, 36/25, 35/24, 40/27, 3/2, 32/21, 49/32, 14/9, 25/16, 8/5, 45/28, 49/30, 5/3, 42/25, 27/16, 12/7, 7/4, 16/9, 25/14, 9/5, 49/27, 50/27, 28/15, 15/8, 40/21, 48/25, 27/14, 35/18, 49/25, 2/1

MOS tuning spectrum (AKA, scale tree)

Scale tree and tuning spectrum of 3L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\7 342.857 857.143 1:1 1.000 Equalized 3L 4s
11\38 347.368 852.632 6:5 1.200 Mohaha / ptolemy↑
9\31 348.387 851.613 5:4 1.250 Mohaha / migration / mohajira
16\55 349.091 850.909 9:7 1.286
7\24 350.000 850.000 4:3 1.333 Supersoft 3L 4s
19\65 350.769 849.231 11:8 1.375 Mohaha / mohamaq
12\41 351.220 848.780 7:5 1.400 Mohaha / neutrominant
17\58 351.724 848.276 10:7 1.429 Hemif / hemififths
5\17 352.941 847.059 3:2 1.500 Soft 3L 4s
18\61 354.098 845.902 11:7 1.571 Suhajira
13\44 354.545 845.455 8:5 1.600
21\71 354.930 845.070 13:8 1.625 Golden suhajira (354.8232¢)
8\27 355.556 844.444 5:3 1.667 Semisoft 3L 4s
Suhajira / ringo
19\64 356.250 843.750 12:7 1.714 Beatles
11\37 356.757 843.243 7:4 1.750
14\47 357.447 842.553 9:5 1.800
3\10 360.000 840.000 2:1 2.000 Basic 3L 4s
Scales with tunings softer than this are proper
13\43 362.791 837.209 9:4 2.250
10\33 363.636 836.364 7:3 2.333
17\56 364.286 835.714 12:5 2.400
7\23 365.217 834.783 5:2 2.500 Semihard 3L 4s
18\59 366.102 833.898 13:5 2.600 Unnamed golden tuning (366.2564¢)
11\36 366.667 833.333 8:3 2.667
15\49 367.347 832.653 11:4 2.750
4\13 369.231 830.769 3:1 3.000 Hard 3L 4s
13\42 371.429 828.571 10:3 3.333
9\29 372.414 827.586 7:2 3.500 Sephiroth
14\45 373.333 826.667 11:3 3.667
5\16 375.000 825.000 4:1 4.000 Superhard 3L 4s
11\35 377.143 822.857 9:2 4.500 Muggles
6\19 378.947 821.053 5:1 5.000 Magic
7\22 381.818 818.182 6:1 6.000 Würschmidt↓
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 4s


Scale tree and tuning spectrum of 3L 4s⟨3/2⟩
Generator(edf) Cents Step ratio Comments
Bright Dark L:s Hardness
2\7 200.559 501.396 1:1 1.000 Equalized 3L 4s⟨3/2⟩
11\38 203.198 498.758 6:5 1.200
9\31 203.793 498.162 5:4 1.250
16\55 204.205 497.750 9:7 1.286
7\24 204.737 497.218 4:3 1.333 Supersoft 3L 4s⟨3/2⟩
19\65 205.187 496.768 11:8 1.375
12\41 205.450 496.505 7:5 1.400
17\58 205.745 496.210 10:7 1.429
5\17 206.457 495.498 3:2 1.500 Soft 3L 4s⟨3/2⟩
18\61 207.134 494.821 11:7 1.571
13\44 207.396 494.559 8:5 1.600
21\71 207.620 494.335 13:8 1.625
8\27 207.987 493.968 5:3 1.667 Semisoft 3L 4s⟨3/2⟩
19\64 208.393 493.562 12:7 1.714
11\37 208.689 493.266 7:4 1.750
14\47 209.093 492.862 9:5 1.800
3\10 210.587 491.369 2:1 2.000 Basic 3L 4s⟨3/2⟩
Scales with tunings softer than this are proper
13\43 212.219 489.736 9:4 2.250
10\33 212.714 489.241 7:3 2.333
17\56 213.093 488.862 12:5 2.400
7\23 213.638 488.317 5:2 2.500 Semihard 3L 4s⟨3/2⟩
18\59 214.156 487.799 13:5 2.600
11\36 214.486 487.469 8:3 2.667
15\49 214.884 487.071 11:4 2.750
4\13 215.986 485.969 3:1 3.000 Hard 3L 4s⟨3/2⟩
13\42 217.272 484.683 10:3 3.333
9\29 217.848 484.107 7:2 3.500
14\45 218.386 483.569 11:3 3.667
5\16 219.361 482.594 4:1 4.000 Superhard 3L 4s⟨3/2⟩
11\35 220.614 481.341 9:2 4.500
6\19 221.670 480.285 5:1 5.000
7\22 223.349 478.606 6:1 6.000
1\3 233.985 467.970 1:0 → ∞ Collapsed 3L 4s⟨3/2⟩


Scale tree and tuning spectrum of 3L 4s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
2\7 543.416 1358.539 1:1 1.000 Equalized 3L 4s⟨3/1⟩
11\38 550.566 1351.389 6:5 1.200
9\31 552.180 1349.775 5:4 1.250
16\55 553.296 1348.659 9:7 1.286
7\24 554.737 1347.218 4:3 1.333 Supersoft 3L 4s⟨3/1⟩
19\65 555.956 1345.999 11:8 1.375
12\41 556.670 1345.285 7:5 1.400
17\58 557.470 1344.485 10:7 1.429
5\17 559.399 1342.556 3:2 1.500 Soft 3L 4s⟨3/1⟩
18\61 561.233 1340.722 11:7 1.571
13\44 561.941 1340.014 8:5 1.600
21\71 562.550 1339.405 13:8 1.625
8\27 563.542 1338.413 5:3 1.667 Semisoft 3L 4s⟨3/1⟩
19\64 564.643 1337.312 12:7 1.714
11\37 565.446 1336.509 7:4 1.750
14\47 566.540 1335.415 9:5 1.800
3\10 570.587 1331.369 2:1 2.000 Basic 3L 4s⟨3/1⟩
Scales with tunings softer than this are proper
13\43 575.010 1326.945 9:4 2.250
10\33 576.350 1325.605 7:3 2.333
17\56 577.379 1324.576 12:5 2.400
7\23 578.856 1323.099 5:2 2.500 Semihard 3L 4s⟨3/1⟩
18\59 580.257 1321.698 13:5 2.600
11\36 581.153 1320.802 8:3 2.667
15\49 582.231 1319.724 11:4 2.750
4\13 585.217 1316.738 3:1 3.000 Hard 3L 4s⟨3/1⟩
13\42 588.700 1313.255 10:3 3.333
9\29 590.262 1311.693 7:2 3.500
14\45 591.719 1310.236 11:3 3.667
5\16 594.361 1307.594 4:1 4.000 Superhard 3L 4s⟨3/1⟩
11\35 597.757 1304.198 9:2 4.500
6\19 600.617 1301.338 5:1 5.000
7\22 605.168 1296.788 6:1 6.000
1\3 633.985 1267.970 1:0 → ∞ Collapsed 3L 4s⟨3/1⟩


Scale tree and tuning spectrum of 3L 4s⟨9/4⟩
Generator(ed9/4) Cents Step ratio Comments
Bright Dark L:s Hardness
2\7 401.117 1002.793 1:1 1.000 Equalized 3L 4s⟨9/4⟩
11\38 406.395 997.515 6:5 1.200
9\31 407.587 996.323 5:4 1.250
16\55 408.410 995.500 9:7 1.286
7\24 409.474 994.436 4:3 1.333 Supersoft 3L 4s⟨9/4⟩
19\65 410.374 993.536 11:8 1.375
12\41 410.900 993.010 7:5 1.400
17\58 411.491 992.419 10:7 1.429
5\17 412.915 990.995 3:2 1.500 Soft 3L 4s⟨9/4⟩
18\61 414.269 989.641 11:7 1.571
13\44 414.792 989.118 8:5 1.600
21\71 415.241 988.669 13:8 1.625
8\27 415.973 987.937 5:3 1.667 Semisoft 3L 4s⟨9/4⟩
19\64 416.786 987.124 12:7 1.714
11\37 417.379 986.531 7:4 1.750
14\47 418.186 985.724 9:5 1.800
3\10 421.173 982.737 2:1 2.000 Basic 3L 4s⟨9/4⟩
Scales with tunings softer than this are proper
13\43 424.438 979.472 9:4 2.250
10\33 425.427 978.483 7:3 2.333
17\56 426.187 977.723 12:5 2.400
7\23 427.277 976.633 5:2 2.500 Semihard 3L 4s⟨9/4⟩
18\59 428.312 975.598 13:5 2.600
11\36 428.973 974.938 8:3 2.667
15\49 429.768 974.142 11:4 2.750
4\13 431.972 971.938 3:1 3.000 Hard 3L 4s⟨9/4⟩
13\42 434.544 969.366 10:3 3.333
9\29 435.696 968.214 7:2 3.500
14\45 436.772 967.138 11:3 3.667
5\16 438.722 965.188 4:1 4.000 Superhard 3L 4s⟨9/4⟩
11\35 441.229 962.681 9:2 4.500
6\19 443.340 960.570 5:1 5.000
7\22 446.699 957.211 6:1 6.000
1\3 467.970 935.940 1:0 → ∞ Collapsed 3L 4s⟨9/4⟩

MOS intro

First sentence:

  • Single-period 2/1-equivalent: xL ys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into x large and y small steps.
  • Multi-period 2/1-equivalent: nxL nys (TAMNAMS name tamnams-name), also called other-name, is an octave-repeating moment of symmetry scale that divides the octave (2/1) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
  • Single-period 3/1-equivalent: 3/1-equivalent xL ys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, c cents) into x large and y small steps.
  • Multi-period 3/1-equivalent: 3/1-equivalent nxL nys, also called other-name, is a twelfth-repeating moment of symmetry scale that divides the tritave or perfect 12th (3/1, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.
  • Single-period 3/2-equivalent: 3/2-equivalent xL ys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, c cents) into x large and y small steps.
  • Multi-period 3/2-equivalent: 3/2-equivalent nxL nys, also called other-name, is a fifth-repeating moment of symmetry scale that divides the perfect 5th (3/2, nc cents) into nx large steps and ny small steps, with n periods of c cents containing x large and y small steps each.

Second sentence:

  • Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.

Octave-equivalent relational info:

  • Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
  • Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.

Rothenprop:

  • Single-period: Scales of this form are always proper because there is only one small step.
  • Multi-period: Scales of this form, where every period is the same, are proper because there is only one small step per period.

Sandbox for proposed templates

Cent ruler

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L
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s

MOS characteristics

NOTE: not suitable for displaying intervals or scale degrees. Repurpose for other content.

Scale degrees of the modes of 5L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.
Intervals of 5L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-diastep Perfect 0-diastep P0dias 0 0.0 ¢
1-diastep Minor 1-diastep m1dias s 0.0 ¢ to 171.4 ¢
Major 1-diastep M1dias L 171.4 ¢ to 240.0 ¢
2-diastep Minor 2-diastep m2dias L + s 240.0 ¢ to 342.9 ¢
Major 2-diastep M2dias 2L 342.9 ¢ to 480.0 ¢
3-diastep Perfect 3-diastep P3dias 2L + s 480.0 ¢ to 514.3 ¢
Augmented 3-diastep A3dias 3L 514.3 ¢ to 720.0 ¢
4-diastep Diminished 4-diastep d4dias 2L + 2s 480.0 ¢ to 685.7 ¢
Perfect 4-diastep P4dias 3L + s 685.7 ¢ to 720.0 ¢
5-diastep Minor 5-diastep m5dias 3L + 2s 720.0 ¢ to 857.1 ¢
Major 5-diastep M5dias 4L + s 857.1 ¢ to 960.0 ¢
6-diastep Minor 6-diastep m6dias 4L + 2s 960.0 ¢ to 1028.6 ¢
Major 6-diastep M6dias 5L + s 1028.6 ¢ to 1200.0 ¢
7-diastep Perfect 7-diastep P7dias 5L + 2s 1200.0 ¢
Tamnams suggests the name NAME for this scale, which comes from ORIGIN. Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
4
5
6
7
8
9

MOS intervals (using large/small instead of MmAPd)

Intervals of 5L 2s
Interval Size(s) Steps Range in cents Abbrev.
0-diastep (root) Perfect 0-diastep 0 0.0¢ P0ms
1-diastep Small 1-diastep s 0.0¢ to 171.4¢ s1ms
Large 1-diastep L 171.4¢ to 240.0¢ L1ms
2-diastep Small 2-diastep L + s 240.0¢ to 342.9¢ s2ms
Large 2-diastep 2L 342.9¢ to 480.0¢ L2ms
3-diastep Small 3-diastep 2L + s 480.0¢ to 514.3¢ s3ms
Large 3-diastep 3L 514.3¢ to 720.0¢ L3ms
4-diastep Small 4-diastep 2L + 2s 480.0¢ to 685.7¢ s4ms
Large 4-diastep 3L + s 685.7¢ to 720.0¢ L4ms
5-diastep Small 5-diastep 3L + 2s 720.0¢ to 857.1¢ s5ms
Large 5-diastep 4L + s 857.1¢ to 960.0¢ L5ms
6-diastep Small 6-diastep 4L + 2s 960.0¢ to 1028.6¢ s6ms
Large 6-diastep 5L + s 1028.6¢ to 1200.0¢ L6ms
7-diastep (octave) Perfect 7-diastep 5L + 2s 1200.0¢ P7ms

MOS mode degrees (using large/small instead of MmAPd)

Scale degree qualities of 5L 2s modes
Mode names Ordering Step pattern Scale degree
Default Names Bri. Rot. 0 1 2 3 4 5 6 7
5L 2s 6|0 Lydian 1 1 LLLsLLs Perf. Lg. Lg. Lg. Lg. Lg. Lg. Perf.
5L 2s 5|1 Ionian (major) 2 5 LLsLLLs Perf. Lg. Lg. Sm. Lg. Lg. Lg. Perf.
5L 2s 4|2 Mixolydian 3 2 LLsLLsL Perf. Lg. Lg. Sm. Lg. Lg. Sm. Perf.
5L 2s 3|3 Dorian 4 6 LsLLLsL Perf. Lg. Sm. Sm. Lg. Lg. Sm. Perf.
5L 2s 2|4 Aeolian (minor) 5 3 LsLLsLL Perf. Lg. Sm. Sm. Lg. Sm. Sm. Perf.
5L 2s 1|5 Phrygian 6 7 sLLLsLL Perf. Sm. Sm. Sm. Lg. Sm. Sm. Perf.
5L 2s 0|6 Locrian 7 4 sLLsLLL Perf. Sm. Sm. Sm. Sm. Sm. Sm. Perf.

KB vis

Type Visualization Individual steps Notes
Start Large step Small step End
Small vis 
┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘
 
┌
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└
 
╥
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┴
 
┬
│
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┴
 
┐
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┘
 Not enough room for note names.
Large vis 
┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
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│░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│
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└───┴───┴───┴───┴───┴───┴───┴───┘
 
┌──
│  
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└──
 
┬─┬─
│ │ 
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─┴──
 
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─┴──
 
─┐
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─┘
 Black squares indicate notes one equave apart.

Contains shading characters, meant for spacing.

Type Visualization Individual steps Notes
Start Size 1 Size 2 Size 3 Size 4 Size 5 End
Multisize vis (large) 
┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
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│░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│
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│░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│
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X's are placeholders for note names.

Naturals only, as there is not enough room for accidentals.

May not display correctly on some devices.

Testing with unintrusive filler characters

TAMNAMS use

This article assumes TAMNAMS conventions for naming scale degrees, intervals, and step ratios.

Names for the scale degrees of xL ys, the position of the scales tones, are called mosdegrees, or prefixdegrees. Its intervals, the pitch difference between any two tones, are based on the number of large and small steps between them and are called mossteps, or prefixsteps. Both mosdegrees and mossteps use 0-indexed numbering, as opposed to using 1-indexed ordinals, such as mos-1st instead of 0-mosstep. The use of 1-indexed ordinal names is discouraged for nondiatonic MOS scales.

JI ratio intro

For general ratios: m/n, also called interval-name, is a p-limit just intonation ratio of exactly/about r¢.

For harmonics: m/1, also called interval-name, is a just intonation ration that represents the mth harmonic of exactly/about r¢.

MOS step sizes

3L 4s step sizes
Interval Basic 3L 4s

(10edo, L:s = 2:1)

Hard 3L 4s

(13edo, L:s = 3:1)

Soft 3L 4s

(17edo, L:s = 3:2)

Approx. JI ratios
Steps Cents Steps Cents Steps Cents
Large step 2 240¢ 3 276.9¢ 3 211.8¢ Hide column if no ratios given
Small step 1 120¢ 1 92.3¢ 2 141.2¢
Bright generator 3 360¢ 4 369.2¢ 5 355.6¢

Notes:

  • Allow option to show the bright generator, dark generator, or no generator.
  • JI ratios column only shows if there are any ratios to show

Mos ancestors and descendants

2nd ancestor 1st ancestor Mos 1st descendants 2nd descendants
uL vs zL ws xL ys xL (x+y)s xL (2x+y)s
(2x+y)L xs
(x+y)L xs (2x+y)L (x+y)s
(x+y)L (2x+y)s


Encoding scheme for module:mos

Mossteps as a vector of L's and s's

For an arbitrary step sequence consisting of L's and s's, the sum of the quantities of L's and s's denotes what mosstep it is. EG, "LLLsL" is a 5-mosstep since it has 5 L's and s's total. This can be expressed as a vector denoting how many L's and s's there are. EG, "LLLsL" becomes { 4, 1 }, denoting 4 large steps and 1 small step.

Alterations by adding a chroma always adds one L and subtracts one s (or subtracts one L and adds one s, if lowering by a chroma), so the sum of L's and s's, even if one of the quantities is negative, will always denote what k-mosstep that interval is. EG, raising "LLLsL" by a chroma produces the vector { 5, 0 }, and raising it by another chroma produces the vector { 6, -1 }.

Through this, the "original size" of the interval can always be deduced.

EG, the vector { 6, -2 } is given, assuming a mos of 5L 2s. Adding 6 and -2 shows that the interval is a 4-mosstep. Taking the brightest mode of 5L 2s (LLLsLLs) and truncating it to the first 4 steps (LLLs), the corresponding vector is { 3, 1 }. This is the vector to compare to. Subtracting the given vector from the comparison vector ( as { 6-3, -2-1 }) produces the vector { 3, -3 }, meaning that { 6, -2 } is the large 4-mosstep raised by 3 chromas. (A shortcut can be employed by simply subtracting only the L-values.) The decoding scheme below shows how the "large 4-mosstep plus 3 chromas" can be decoded into more familiar terms. In this example, since the large 4-mosstep is the perfect bright generator, adding 3 chromas makes it triply augmented.

Encoding scheme
Value Encoded Decoded
Intervals with 2 sizes Intervals with 1 size Nonperfectable intervals Bright gen Dark gen Period intervals
2 Large plus 2 chromas Perfect plus 2 chromas 2× Augmented 2× Augmented 3× Augmented 2× Augmented
1 Large plus 1 chroma Perfect plus 1 chroma Augmented Augmented 2× Augmented Augmented
0 Large Perfect Major Perfect Augmented Perfect
-1 Small Perfect minus 1 chroma Minor Diminished Perfect Diminished
-2 Small minus 1 chroma Perfect minus 2 chromas Diminished 2× Diminished Diminished 2× Diminished
-3 Small minus 2 chromas Perfect minus 3 chromas 2× Diminished 3× Diminished 2× Diminished 3× Diminished

Rationale:

  • Vectors of L's and s's can always be translated back to the original k-mosstep, no matter how many chromas were added. The "unmodified" vector (the large k-mosstep, or perfect k-mosstep for period intervals) can be compared with the mosstep vector to produce the number of chromas.
    • Alterations by entire large steps or small steps is considered interval arithmetic.
  • Easy to translate values to number of chromas for mos notation. Best done with notation assigned to the brightest mode, but can be adapted for arbitrary notations by adjusting the approprite chroma offsets.

Examples of encodings for 5L 2s

Interval encodings for 5L 2s
Interval in mossteps Encoding Decoding Standard notation in the key of F
Mossteps Chroma
0 0 0 Perfect 0-diastep F
s 1 -1 Minor 1-diastep Gb
L 1 0 Major 1-diastep G
L + s 2 -1 Minor 2-diastep Ab
2L 2 0 Major 2-diastep A
2L + s 3 -1 Perfect 3-diastep Bb
3L 3 0 Augmented 3-diastep B
2L + 2s 4 -1 Diminished 4-diastep Cb
3L + s 4 0 Perfect 4-diastep C
3L + 2s 5 -1 Minor 5-diastep Db
4L + s 5 0 Major 5-diastep D
4L + 2s 6 -1 Minor 6-diastep Eb
5L + s 6 0 Major 6-diastep E
5L + 2s 7 0 Perfect 7-diastep F
Mode names Ordering Step pattern Scale degree (encoded)
Default Names Bri. Rot. 0 1 2 3 4 5 6 7
5L 2s 6|0 Lydian 1 1 LLLsLLs 0 0 0 0 0 0 0 0
5L 2s 5|1 Ionian (major) 2 5 LLsLLLs 0 0 0 -1 0 0 0 0
5L 2s 4|2 Mixolydian 3 2 LLsLLsL 0 0 1 -1 0 0 -1 0
5L 2s 3|3 Dorian 4 6 LsLLLsL 0 0 -1 -1 0 0 -1 0
5L 2s 2|4 Aeolian (minor) 5 3 LsLLsLL 0 0 -1 -1 0 -1 -1 0
5L 2s 1|5 Phrygian 6 7 sLLLsLL 0 -1 -1 -1 0 -1 -1 0
5L 2s 0|6 Locrian 7 4 sLLsLLL 0 -1 -1 -1 -1 -1 -1 0
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