User:Ganaram inukshuk/Sandbox: Difference between revisions

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== MOS intro ==
== 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:


* Single-period 2/1-equivalent: '''xL ys''' (TAMNAMS name ''tamnams-name''), also called ''other-name'', is a moment of symmetry scale that divides the octave (2/1) into x large and y small steps.
* Generators that produce this scale range from g1 cents to g2 cents, or from d1 cents to d2 cents.
* Multi-period 2/1-equivalent: '''nxL nys''' (TAMNAMS name ''tamnams-name''), also called ''other-name'', is a 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 moment of symmetry scale that divides the tritave or perfect 12th (3/1, c cents) into x large and y small steps.
Octave-equivalent relational info:
* Multi-period 3/1-equivalent: '''3/1-equivalent nxL nys''', also called ''other-name'', is a 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 moment of symmetry scale that divides the perfect 5th (3/2, c cents) into x large and y small steps.
* Parents of mosses with 6-10 steps: xL ys is the parent scale of both child-soft and child-hard.
* Multi-period 3/2-equivalent: '''3/2-equivalent nxL nys''', also called ''other-name'', is a 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.
* Children of mosses with 6-10 steps: xL ys expands parent-scale by adding step-count-difference tones.
''Rest of intro pending...''
 
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.


== MOS tunings==
== MOS tunings==

Revision as of 06:47, 26 August 2024

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

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.

MOS tunings

Simple Tunings of 5L 3s
Scale degree Abbrev. Basic (2:1)
13edo 		Hard (3:1)
18edo 		Soft (3:2)
21edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-oneirodegree P0oneid 0\13 0.0 0\18 0.0 0\21 0.0
Minor 1-oneirodegree m1oneid 1\13 92.3 1\18 66.7 2\21 114.3
Major 1-oneirodegree M1oneid 2\13 184.6 3\18 200.0 3\21 171.4
Minor 2-oneirodegree m2oneid 3\13 276.9 4\18 266.7 5\21 285.7
Major 2-oneirodegree M2oneid 4\13 369.2 6\18 400.0 6\21 342.9
Diminished 3-oneirodegree d3oneid 4\13 369.2 5\18 333.3 7\21 400.0
Perfect 3-oneirodegree P3oneid 5\13 461.5 7\18 466.7 8\21 457.1
Minor 4-oneirodegree m4oneid 6\13 553.8 8\18 533.3 10\21 571.4
Major 4-oneirodegree M4oneid 7\13 646.2 10\18 666.7 11\21 628.6
Perfect 5-oneirodegree P5oneid 8\13 738.5 11\18 733.3 13\21 742.9
Augmented 5-oneirodegree A5oneid 9\13 830.8 13\18 866.7 14\21 800.0
Minor 6-oneirodegree m6oneid 9\13 830.8 12\18 800.0 15\21 857.1
Major 6-oneirodegree M6oneid 10\13 923.1 14\18 933.3 16\21 914.3
Minor 7-oneirodegree m7oneid 11\13 1015.4 15\18 1000.0 18\21 1028.6
Major 7-oneirodegree M7oneid 12\13 1107.7 17\18 1133.3 19\21 1085.7
Perfect 8-oneirodegree P8oneid 13\13 1200.0 18\18 1200.0 21\21 1200.0
Hypohard Tunings of 5L 4s
Scale degree Abbrev. Basic (2:1)
14edo 		Hard (3:1)
19edo
Steps ¢ Steps ¢
Perfect 0-cthondegree P0ctd 0\14 0.0 0\19 0.0
Minor 1-cthondegree m1ctd 1\14 85.7 1\19 63.2
Major 1-cthondegree M1ctd 2\14 171.4 3\19 189.5
Perfect 2-cthondegree P2ctd 3\14 257.1 4\19 252.6
Augmented 2-cthondegree A2ctd 4\14 342.9 6\19 378.9
Minor 3-cthondegree m3ctd 4\14 342.9 5\19 315.8
Major 3-cthondegree M3ctd 5\14 428.6 7\19 442.1
Minor 4-cthondegree m4ctd 6\14 514.3 8\19 505.3
Major 4-cthondegree M4ctd 7\14 600.0 10\19 631.6
Minor 5-cthondegree m5ctd 7\14 600.0 9\19 568.4
Major 5-cthondegree M5ctd 8\14 685.7 11\19 694.7
Minor 6-cthondegree m6ctd 9\14 771.4 12\19 757.9
Major 6-cthondegree M6ctd 10\14 857.1 14\19 884.2
Diminished 7-cthondegree d7ctd 10\14 857.1 13\19 821.1
Perfect 7-cthondegree P7ctd 11\14 942.9 15\19 947.4
Minor 8-cthondegree m8ctd 12\14 1028.6 16\19 1010.5
Major 8-cthondegree M8ctd 13\14 1114.3 18\19 1136.8
Perfect 9-cthondegree P9ctd 14\14 1200.0 19\19 1200.0

Mos intervals and mos interval HE

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 ¢
Harmonic entropy info for 5L 2s
Interval Range in cents Average of HE
(from HE Calc)		 Min of HE
Perfect 0-diastep 0.0 ¢ ~2.4654 nats ~2.4654 nats
Minor 1-diastep 0.0 ¢ to 171.4 ¢ ~4.6969 nats ~4.6333 nats
Major 1-diastep 171.4 ¢ to 240.0 ¢ ~4.5872 nats ~4.5842 nats
Minor 2-diastep 240.0 ¢ to 342.9 ¢ ~4.5596 nats ~4.5379 nats
Major 2-diastep 342.9 ¢ to 480.0 ¢ ~4.5540 nats ~4.4846 nats
Perfect 3-diastep 480.0 ¢ to 514.3 ¢ ~4.3841 nats ~4.3665 nats
Augmented 3-diastep 514.3 ¢ to 720.0 ¢ ~4.6012 nats ~4.5615 nats
Diminished 4-diastep 480.0 ¢ to 685.7 ¢ ~4.6013 nats ~4.5630 nats
Perfect 4-diastep 685.7 ¢ to 720.0 ¢ ~4.1634 nats ~4.1224 nats
Minor 5-diastep 720.0 ¢ to 857.1 ¢ ~4.5942 nats ~4.5711 nats
Major 5-diastep 857.1 ¢ to 960.0 ¢ ~4.5145 nats ~4.4208 nats
Minor 6-diastep 960.0 ¢ to 1028.6 ¢ ~4.5760 nats ~4.5502 nats
Major 6-diastep 1028.6 ¢ to 1200.0 ¢ ~4.6377 nats ~4.6078 nats
Perfect 7-diastep 1200.0 ¢ ~3.3273 nats ~3.3273 nats

Name

6-note mosses

TAMNAMS suggests the temperament-agnostic name antimachinoid as the name of 1L 5s. The name is based on being the opposite pattern of 5L 1s (machinoid).

TAMNAMS suggests the temperament-agnostic name malic as the name of 2L 4s. The name derives from Latin malus, since apples have two concave ends.

TAMNAMS suggests the temperament-agnostic name triwood as the name of 3L 3s. The name generalizes blackwood[10] and whitewood[14] to 3 periods.

TAMNAMS suggests the temperament-agnostic name citric as the name of 4L 2s. The name references its daughter scales 4L 6s (lime) and 6L 4s (lemon).

TAMNAMS suggests the temperament-agnostic name machinoid as the name of 5L 1s. The name derives from machine temperament. Although this name is directly based off of a temperament, tunings of machine cover the entire tuning range of 5L 1s see TAMNAMS/Appendix #Machinoid (5L 1s) for more information.

7-note mosses

TAMNAMS suggests the temperament-agnostic name onyx as the name of 1L 6s.

TAMNAMS suggests the temperament-agnostic name antidiatonic as the name of 2L 5s. The name is based on being the opposite pattern of 5L 2s (diatonic).

TAMNAMS suggests the temperament-agnostic name mosh as the name of 3L 4s. The name derives from "mohajira-ish", a name from Graham Breed's naming scheme.

TAMNAMS suggests the temperament-agnostic name smitonic as the name of 4L 3s. The name derives from "sharp minor third", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name diatonic as the name of 5L 2s. The name commonly refers to a scale with 5 whole and 2 half steps, or 5 large and 2 small steps; see TAMNAMS/Appendix #On the term diatonic for more information.

TAMNAMS suggests the temperament-agnostic name archaeotonic as the name of 6L 1s. The name was originally used as a name for the 6L 1s scale in 13edo.

8-note mosses

TAMNAMS suggests the temperament-agnostic name antipine as the name of 1L 7s. The name is based on being the opposite pattern of 7L 1s (pine).

TAMNAMS suggests the temperament-agnostic name subaric as the name of 2L 6s. The name references to how 2L 6s is the parent scale (or subset scale) of 2L 8s (jaric) and 8L 2s (taric).

TAMNAMS suggests the temperament-agnostic name checkertonic as the name of 3L 5s. The name derives from the Kite guitar checkerboard scale.

TAMNAMS suggests the temperament-agnostic name tetrawood as the name of 4L 4s. The name generalizes blackwood[10] and whitewood[14] to 4 periods.

TAMNAMS suggests the temperament-agnostic name oneirotonic as the name of 5L 3s. The name was originally used as a name for the 5L 3s scale in 13edo.

TAMNAMS suggests the temperament-agnostic name ekic as the name of 6L 2s. The name is an abstraction of echidna and hedgehog temperaments.

TAMNAMS suggests the temperament-agnostic name pine as the name of 7L 1s. The name is an abstraction of porcupine temperament.

9-note mosses

TAMNAMS suggests the temperament-agnostic name antisubneutralic as the name of 1L 8s. The name is based on being the opposite pattern of 8L 1s (subneutralic).

TAMNAMS suggests the temperament-agnostic name balzano as the name of 2L 7s. The name was originally used as a name for the 2L 7s scale in 20edo.

TAMNAMS suggests the temperament-agnostic name tcherepnin as the name of 3L 6s. The name references Alexander Tcherepnin's nine-note scale, corresponding to to 3L 6s in 12edo.

TAMNAMS suggests the temperament-agnostic name gramitonic as the name of 4L 5s. The name derives from "grave minor third", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name semiquartal as the name of 5L 4s. The name derives from "half-fourth", referring to the generator's quality.

TAMNAMS suggests the temperament-agnostic name hyrulic as the name of 6L 3s. The name is an abstraction of triforce temperament.

TAMNAMS suggests the temperament-agnostic name armotonic as the name of 7L 2s. The name references Armodue, a system of theory for the 7L 2s scale in 16edo.

TAMNAMS suggests the temperament-agnostic name subneutralic as the name of 8L 1s. The name derives from "subneutral", referring to the generator's quality.

10-note mosses

TAMNAMS suggests the temperament-agnostic name antisinatonic as the name of 1L 9s. The name is based on being the opposite pattern of 9L 1s (sinatonic).

TAMNAMS suggests the temperament-agnostic name jaric as the name of 2L 8s. The name is an abstraction of pajara, injera, and diaschismic temperaments.

TAMNAMS suggests the temperament-agnostic name sephiroid as the name of 3L 7s. The name derives from sephiroth temperament. Although this name is directly based off of a temperament, tunings of sephiroth cover the entire tuning range of 3L 7s; see TAMNAMS/Appendix #Sephiroid (3L 7s) for more information.

TAMNAMS suggests the temperament-agnostic name lime as the name of 4L 6s. The name references its parent scale 4L 2s (citric).

TAMNAMS suggests the temperament-agnostic name pentawood as the name of 5L 5s. The name generalizes blackwood[10] and whitewood[14] to 5 periods.

TAMNAMS suggests the temperament-agnostic name lemon as the name of 6L 4s. The name references its parent scale 4L 2s (citric), as well as indirectly referencing lemba temperament.

TAMNAMS suggests the temperament-agnostic name dicoid as the name of 7L 3s. The name derives from dichotic and dicot temperament. Although this name is directly based off of a temperament, tunings of dichotic and dicot cover the entire tuning range of 7L 3s; see TAMNAMS/Appendix #Dicoid (7L 3s) for more information.

TAMNAMS suggests the temperament-agnostic name taric as the name of 8L 2s. The name derives from Hindi aṭhārah for 18, in reference to 18edo containing a basic 8L 2s scale.

TAMNAMS suggests the temperament-agnostic name sinatonic as the name of 9L 1s. The name derives from the sinaic, referring to the generator's quality.

Scale data

User:MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

5L 2s modes and modmos modes

Scale degrees of the modes of 5L 2s (cscscsscscss)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
6|0 A0md M1md A1md M2md A2md A3md P4md A4md M5md A5md M6md P7md
0|6 A0md M1md A1md M2md A2md A3md P4md A4md M5md A5md M6md P7md 		1 cscscsscscss Perf. Aug. Maj. Aug. Maj. Aug. Aug. Perf. Aug. Maj. Aug. Maj. Perf.
1|5 M1md m2md M2md P3md d4md P4md m5md M5md m6md d7md P7md
0|6 M1md m2md M2md P3md d4md P4md m5md M5md m6md d7md P7md 		2 scscsscscssc Perf. Min. Maj. Min. Maj. Perf. Dim. Perf. Min. Maj. Min. Dim. Perf.
6|0 A0md M1md A1md M2md P3md A3md P4md A4md M5md m6md M6md P7md
0|6 A0md M1md A1md M2md P3md A3md P4md A4md M5md m6md M6md P7md 		3 cscsscscsscs Perf. Aug. Maj. Aug. Maj. Perf. Aug. Perf. Aug. Maj. Min. Maj. Perf.
1|5 M1md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md
0|6 M1md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md 		4 scsscscsscsc Perf. Min. Maj. Min. Dim. Perf. Dim. Perf. Min. Dim. Min. Dim. Perf.
6|0 A0md M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md
0|6 A0md M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md 		5 csscscsscscs Perf. Aug. Maj. Min. Maj. Perf. Aug. Perf. Min. Maj. Min. Maj. Perf.
1|5 d2md m2md d3md P3md d4md d5md m5md d6md m6md d7md P7md
0|6 d2md m2md d3md P3md d4md d5md m5md d6md m6md d7md P7md 		6 sscscsscscsc Perf. Min. Dim. Min. Dim. Perf. Dim. Dim. Min. Dim. Min. Dim. Perf.
1|5 M1md m2md M2md P3md d4md P4md m5md M5md m6md M6md P7md
0|6 M1md m2md M2md P3md d4md P4md m5md M5md m6md M6md P7md 		7 scscsscscscs Perf. Min. Maj. Min. Maj. Perf. Dim. Perf. Min. Maj. Min. Maj. Perf.
6|0 A0md M1md A1md M2md P3md A3md P4md A4md M5md A5md M6md P7md
0|6 A0md M1md A1md M2md P3md A3md P4md A4md M5md A5md M6md P7md 		8 cscsscscscss Perf. Aug. Maj. Aug. Maj. Perf. Aug. Perf. Aug. Maj. Aug. Maj. Perf.
1|5 M1md m2md d3md P3md d4md P4md m5md M5md m6md d7md P7md
0|6 M1md m2md d3md P3md d4md P4md m5md M5md m6md d7md P7md 		9 scsscscscssc Perf. Min. Maj. Min. Dim. Perf. Dim. Perf. Min. Maj. Min. Dim. Perf.
6|0 A0md M1md m2md M2md P3md A3md P4md A4md M5md m6md M6md P7md
0|6 A0md M1md m2md M2md P3md A3md P4md A4md M5md m6md M6md P7md 		10 csscscscsscs Perf. Aug. Maj. Min. Maj. Perf. Aug. Perf. Aug. Maj. Min. Maj. Perf.
1|5 d2md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md
0|6 d2md m2md d3md P3md d4md P4md m5md d6md m6md d7md P7md 		11 sscscscsscsc Perf. Min. Dim. Min. Dim. Perf. Dim. Perf. Min. Dim. Min. Dim. Perf.
1|5 M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md
0|6 M1md m2md M2md P3md A3md P4md m5md M5md m6md M6md P7md 		12 scscscsscscs Perf. Min. Maj. Min. Maj. Perf. Aug. Perf. Min. Maj. Min. Maj. Perf.
Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.
Scale degrees of the modes of 5L 2s (LsLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m2md
3|3 M6md 		1 LsLLLLs Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md
1|5 M5md 		2 sLLLLsL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
6|0 A4md 3 LLLLsLs Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md
4|2 A3md 		4 LLLsLsL Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md
2|4 M2md 		5 LLsLsLL Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md
0|6 M1md 		6 LsLsLLL Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md 7 sLsLLLL Perf. Min. Min. Dim. Dim. Min. Min. Perf.
Scale degrees of the modes of 5L 2s (LLsLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m5md 1 LLsLsAs Perf. Maj. Maj. Perf. Perf. Min. Maj. Perf.
3|3 d4md 2 LsLsAsL Perf. Maj. Min. Perf. Dim. Maj. Min. Perf.
1|5 d3md 3 sLsAsLL Perf. Min. Min. Dim. Perf. Min. Min. Perf.
6|0 m2md 4 LsAsLLs Perf. Maj. Min. Aug. Perf. Maj. Maj. Perf.
4|2 m1md 5 sAsLLsL Perf. Min. Maj. Perf. Perf. Maj. Min. Perf.
6|0 A1md A4md 6 AsLLsLs Perf. Aug. Maj. Aug. Aug. Maj. Maj. Perf.
0|6 d6md 7 sLLsLsA Perf. Min. Min. Perf. Dim. Min. Dim. Perf.
Scale degrees of the modes of 5L 2s (AAdAdAd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 A1md AA2md AA4md A6md 1 AAdAdAd Perf. Aug. 2× Aug. Aug. 2× Aug. Maj. Aug. Perf.
6|0 A1md m2md d4md d6md
0|6 A1md A3md M5md d6md 		2 AdAdAdA Perf. Aug. Min. Aug. Dim. Maj. Dim. Perf.
0|6 d1md dd3md dd5md d6md 3 dAdAdAA Perf. Dim. Min. 2× Dim. Dim. 2× Dim. Dim. Perf.
6|0 A1md m2md d4md A6md
0|6 A1md A3md M5md A6md 		4 AdAdAAd Perf. Aug. Min. Aug. Dim. Maj. Aug. Perf.
3|3 d1md dd3md d4md d6md
0|6 d1md dd3md M5md d6md 		5 dAdAAdA Perf. Dim. Min. 2× Dim. Dim. Maj. Dim. Perf.
6|0 A1md m2md AA4md A6md
3|3 A1md A3md AA4md A6md 		6 AdAAdAd Perf. Aug. Min. Aug. 2× Aug. Maj. Aug. Perf.
6|0 d1md m2md d4md d6md
0|6 d1md A3md M5md d6md 		7 dAAdAdA Perf. Dim. Min. Aug. Dim. Maj. Dim. Perf.
Scale degrees of the modes of 5L 2s (LLLLLLd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 A4md A5md A6md 1 LLLLLLd Perf. Maj. Maj. Aug. Aug. Aug. Aug. Perf.
6|0 A4md A5md m6md
4|2 A3md A4md A5md 		2 LLLLLdL Perf. Maj. Maj. Aug. Aug. Aug. Min. Perf.
6|0 A4md m5md m6md
2|4 M2md A3md A4md 		3 LLLLdLL Perf. Maj. Maj. Aug. Aug. Min. Min. Perf.
6|0 d4md m5md m6md
0|6 M1md M2md A3md 		4 LLLdLLL Perf. Maj. Maj. Aug. Dim. Min. Min. Perf.
4|2 d3md d4md m5md
0|6 M1md M2md d3md 		5 LLdLLLL Perf. Maj. Maj. Dim. Dim. Min. Min. Perf.
2|4 d2md d3md d4md
0|6 M1md d2md d3md 		6 LdLLLLL Perf. Maj. Dim. Dim. Dim. Min. Min. Perf.
0|6 d1md d2md d3md 7 dLLLLLL Perf. Dim. Dim. Dim. Dim. Min. Min. Perf.
Scale degrees of the modes of 5L 2s (LALdLAd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
6|0 A2md AA3md A6md
3|3 A2md AA3md A6md 		1 LALdLAd Perf. Maj. Aug. 2× Aug. Perf. Maj. Aug. Perf.
4|2 A1md A2md A5md
1|5 A1md A2md A5md 		2 ALdLAdL Perf. Aug. Aug. Perf. Perf. Aug. Min. Perf.
6|0 d2md d3md d5md d6md
2|4 d2md d3md d5md d6md 		3 LdLAdLA Perf. Maj. Dim. Dim. Perf. Dim. Dim. Perf.
4|2 d1md d2md dd4md d5md
0|6 d1md d2md dd4md d5md 		4 dLAdLAL Perf. Dim. Dim. Perf. 2× Dim. Dim. Min. Perf.
5|1 A2md A5md A6md
2|4 A2md A5md A6md 		5 LAdLALd Perf. Maj. Aug. Perf. Perf. Aug. Aug. Perf.
3|3 A1md A4md A5md
0|6 A1md A4md A5md 		6 AdLALdL Perf. Aug. Min. Perf. Aug. Aug. Min. Perf.
5|1 d1md d2md d5md d6md
1|5 d1md d2md d5md d6md 		7 dLALdLA Perf. Dim. Dim. Perf. Perf. Dim. Dim. Perf.

4L 4s modes and modmos modes

Scale degrees of the modes of 4L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (tetrawddegree)
0 1 2 3 4 5 6 7 8
4|0(4) 1 LsLsLsLs Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf.
0|4(4) 2 sLsLsLsL Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf.
Scale degrees of the modes of 4L 4s (LLssLLss)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (tetrawddegree)
0 1 2 3 4 5 6 7 8
4|0(4) A2md A6md 1 LLssLLss Perf. Maj. Aug. Maj. Perf. Maj. Aug. Maj. Perf.
4|0(4) m3md m7md
0|4(4) M1md M5md 		2 LssLLssL Perf. Maj. Perf. Min. Perf. Maj. Perf. Min. Perf.
0|4(4) d2md d6md 3 ssLLssLL Perf. Min. Dim. Min. Perf. Min. Dim. Min. Perf.
4|0(4) m1md m5md
0|4(4) M3md M7md 		4 sLLssLLs Perf. Min. Perf. Maj. Perf. Min. Perf. Maj. Perf.
Scale degrees of the modes of 4L 4s (LLssLsLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (tetrawddegree)
0 1 2 3 4 5 6 7 8
4|0(4) A2md 1 LLssLsLs Perf. Maj. Aug. Maj. Perf. Maj. Perf. Maj. Perf.
0|4(4) M1md 2 LssLsLsL Perf. Maj. Perf. Min. Perf. Min. Perf. Min. Perf.
0|4(4) d2md d4md d6md 3 ssLsLsLL Perf. Min. Dim. Min. Dim. Min. Dim. Min. Perf.
0|4(4) M7md 4 sLsLsLLs Perf. Min. Perf. Min. Perf. Min. Perf. Maj. Perf.
4|0(4) A6md 5 LsLsLLss Perf. Maj. Perf. Maj. Perf. Maj. Aug. Maj. Perf.
0|4(4) M5md 6 sLsLLssL Perf. Min. Perf. Min. Perf. Maj. Perf. Min. Perf.
4|0(4) A4md 7 LsLLssLs Perf. Maj. Perf. Maj. Aug. Maj. Perf. Maj. Perf.
0|4(4) M3md 8 sLLssLsL Perf. Min. Perf. Maj. Perf. Min. Perf. Min. Perf.

Sandbox for proposed templates

Cent ruler

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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.
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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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 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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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

Navbox MOS

6- to 10-note mosses 1L 5s (selenite) | 2L 4s ( | 3L 3s | 4L 2 | 5L 1s
Monolarge family 1L 5s (selenite) | 1L 6s (onyx) | 1L 7s (spinel) | 1L 8s (agate) | 1L 9s (olivine)
Diatonic mos family
Parent mos 5L 2s (diatonic)
Chromatic scales 7L 5s (soft diatonic chromatic) | 5L 7s (hard diatonic chromatic)
Enharmonic scales 7L 12s (soft diatonic enharmonic) | 12L 7s (hyposoft diatonic enharmonic) | 12L 5s (hypohard diatonic enharmonic) | 5L 12s (hard diatonic enharmonic)
Subchromatic scales 7L 19s and 19L 7s | 19L 12s and 12L 19s | 12L 17s and 17L 12s | 17L 5s and 5L 17s

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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