User:Ganaram inukshuk/Sandbox

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

Deprecated template params

No params given

The following parameters of Template:NoTemplateGiven have been deprecated: NoParamsGiven.
It is advised to save or relocate any information passed into these parameters to avoid information loss.

A template param is deprecated without a new one given

The following parameters of Template:Example Template have been deprecated: Scale Info.
It is advised to save or relocate any information passed into these parameters to avoid information loss.

A template param is deprecated with a new one to be used

The following parameters of Template:Example Template have been deprecated: Scale Info.
Please use the following parameters instead: Step Pattern, Step Ratio

A template param is deprecated, but the functionality of those params are now part of a new template

The following parameters of Template:Example Template have been deprecated: Scale Info.
Please use the following parameters in Template:Scale Info instead: Step Pattern, Step Ratio

More data given

The following parameters of Template:Example Template have been deprecated: Scale Info.
Please use the following parameters in Template:Scale Info instead: Scale Signature, Step Ratio
Editors, please remember to separate the step pattern from the step ratio; for example, "3331331" becomes "LLLsLLs" and "3:1"

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

NOTE: tables can be substituted, but it's at least a two-step process.

Simple Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 18edo		Soft (3:2) 21edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\18	0.0	0\21	0.0	1/1
Minor 1-oneirodegree	m1oneid	1\13	92.3	1\18	66.7	2\21	114.3	26/25, 21/20
Major 1-oneirodegree	M1oneid	2\13	184.6	3\18	200.0	3\21	171.4	10/9, 9/8
Minor 2-oneirodegree	m2oneid	3\13	276.9	4\18	266.7	5\21	285.7	7/6, 25/21
Major 2-oneirodegree	M2oneid	4\13	369.2	6\18	400.0	6\21	342.9	16/13, 26/21, 5/4
Diminished 3-oneirodegree	d3oneid	4\13	369.2	5\18	333.3	7\21	400.0	16/13, 26/21, 5/4
Perfect 3-oneirodegree	P3oneid	5\13	461.5	7\18	466.7	8\21	457.1	13/10, 21/16
Minor 4-oneirodegree	m4oneid	6\13	553.8	8\18	533.3	10\21	571.4	18/13, 25/18
Major 4-oneirodegree	M4oneid	7\13	646.2	10\18	666.7	11\21	628.6	13/9
Perfect 5-oneirodegree	P5oneid	8\13	738.5	11\18	733.3	13\21	742.9	20/13
Augmented 5-oneirodegree	A5oneid	9\13	830.8	13\18	866.7	14\21	800.0	8/5, 21/13, 13/8
Minor 6-oneirodegree	m6oneid	9\13	830.8	12\18	800.0	15\21	857.1	8/5, 21/13, 13/8
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	16/9, 9/5
Major 7-oneirodegree	M7oneid	12\13	1107.7	17\18	1133.3	19\21	1085.7	25/13
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	18\18	1200.0	21\21	1200.0	2/1

* Ratios shown are within the 2.5.9.13.21 subgroup. Automatic search may be inexact. Other interpretations are possible.

5L 3s only

Simple Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 18edo		Soft (3:2) 21edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\18	0.0	0\21	0.0	1/1
Minor 1-oneirodegree	m1oneid	1\13	92.3	1\18	66.7	2\21	114.3	16/15
Major 1-oneirodegree	M1oneid	2\13	184.6	3\18	200.0	3\21	171.4	11/10, 10/9, 9/8
Minor 2-oneirodegree	m2oneid	3\13	276.9	4\18	266.7	5\21	285.7	7/6
Major 2-oneirodegree	M2oneid	4\13	369.2	6\18	400.0	6\21	342.9	11/9, 16/13, 5/4
Diminished 3-oneirodegree	d3oneid	4\13	369.2	5\18	333.3	7\21	400.0	11/9, 16/13, 5/4
Perfect 3-oneirodegree	P3oneid	5\13	461.5	7\18	466.7	8\21	457.1	9/7
Minor 4-oneirodegree	m4oneid	6\13	553.8	8\18	533.3	10\21	571.4	11/8, 18/13
Major 4-oneirodegree	M4oneid	7\13	646.2	10\18	666.7	11\21	628.6	13/9, 16/11
Perfect 5-oneirodegree	P5oneid	8\13	738.5	11\18	733.3	13\21	742.9	14/9
Augmented 5-oneirodegree	A5oneid	9\13	830.8	13\18	866.7	14\21	800.0	8/5, 13/8, 18/11
Minor 6-oneirodegree	m6oneid	9\13	830.8	12\18	800.0	15\21	857.1	8/5, 13/8, 18/11
Major 6-oneirodegree	M6oneid	10\13	923.1	14\18	933.3	16\21	914.3	12/7
Minor 7-oneirodegree	m7oneid	11\13	1015.4	15\18	1000.0	18\21	1028.6	16/9, 9/5, 20/11
Major 7-oneirodegree	M7oneid	12\13	1107.7	17\18	1133.3	19\21	1085.7	15/8
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	18\18	1200.0	21\21	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Soft-of-basic Tunings of 5L 3s
Scale degree	Abbrev.	Supersoft (4:3) 29edo		Soft (3:2) 21edo		Basic (2:1) 13edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\29	0.0	0\21	0.0	0\13	0.0	1/1
Minor 1-oneirodegree	m1oneid	3\29	124.1	2\21	114.3	1\13	92.3	16/15, 14/13
Major 1-oneirodegree	M1oneid	4\29	165.5	3\21	171.4	2\13	184.6	12/11, 11/10, 10/9
Minor 2-oneirodegree	m2oneid	7\29	289.7	5\21	285.7	3\13	276.9	7/6, 6/5
Major 2-oneirodegree	M2oneid	8\29	331.0	6\21	342.9	4\13	369.2	6/5, 11/9, 16/13
Diminished 3-oneirodegree	d3oneid	10\29	413.8	7\21	400.0	4\13	369.2	5/4, 14/11
Perfect 3-oneirodegree	P3oneid	11\29	455.2	8\21	457.1	5\13	461.5	9/7
Minor 4-oneirodegree	m4oneid	14\29	579.3	10\21	571.4	6\13	553.8	11/8, 18/13, 7/5
Major 4-oneirodegree	M4oneid	15\29	620.7	11\21	628.6	7\13	646.2	10/7, 13/9, 16/11
Perfect 5-oneirodegree	P5oneid	18\29	744.8	13\21	742.9	8\13	738.5	14/9
Augmented 5-oneirodegree	A5oneid	19\29	786.2	14\21	800.0	9\13	830.8	11/7, 8/5
Minor 6-oneirodegree	m6oneid	21\29	869.0	15\21	857.1	9\13	830.8	13/8, 18/11, 5/3
Major 6-oneirodegree	M6oneid	22\29	910.3	16\21	914.3	10\13	923.1	5/3, 12/7
Minor 7-oneirodegree	m7oneid	25\29	1034.5	18\21	1028.6	11\13	1015.4	9/5, 20/11, 11/6
Major 7-oneirodegree	M7oneid	26\29	1075.9	19\21	1085.7	12\13	1107.7	13/7, 15/8
Perfect 8-oneirodegree	P8oneid	29\29	1200.0	21\21	1200.0	13\13	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Hyposoft Tunings of 5L 3s
Scale degree	Abbrev.	Soft (3:2) 21edo		Semisoft (5:3) 34edo		Basic (2:1) 13edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\21	0.0	0\34	0.0	0\13	0.0	1/1
Minor 1-oneirodegree	m1oneid	2\21	114.3	3\34	105.9	1\13	92.3	16/15, 14/13
Major 1-oneirodegree	M1oneid	3\21	171.4	5\34	176.5	2\13	184.6	12/11, 11/10, 10/9, 9/8
Minor 2-oneirodegree	m2oneid	5\21	285.7	8\34	282.4	3\13	276.9	7/6
Major 2-oneirodegree	M2oneid	6\21	342.9	10\34	352.9	4\13	369.2	11/9, 16/13
Diminished 3-oneirodegree	d3oneid	7\21	400.0	11\34	388.2	4\13	369.2	16/13, 5/4, 14/11
Perfect 3-oneirodegree	P3oneid	8\21	457.1	13\34	458.8	5\13	461.5	9/7
Minor 4-oneirodegree	m4oneid	10\21	571.4	16\34	564.7	6\13	553.8	11/8, 18/13, 7/5
Major 4-oneirodegree	M4oneid	11\21	628.6	18\34	635.3	7\13	646.2	10/7, 13/9, 16/11
Perfect 5-oneirodegree	P5oneid	13\21	742.9	21\34	741.2	8\13	738.5	14/9
Augmented 5-oneirodegree	A5oneid	14\21	800.0	23\34	811.8	9\13	830.8	11/7, 8/5, 13/8
Minor 6-oneirodegree	m6oneid	15\21	857.1	24\34	847.1	9\13	830.8	13/8, 18/11
Major 6-oneirodegree	M6oneid	16\21	914.3	26\34	917.6	10\13	923.1	12/7
Minor 7-oneirodegree	m7oneid	18\21	1028.6	29\34	1023.5	11\13	1015.4	16/9, 9/5, 20/11, 11/6
Major 7-oneirodegree	M7oneid	19\21	1085.7	31\34	1094.1	12\13	1107.7	13/7, 15/8
Perfect 8-oneirodegree	P8oneid	21\21	1200.0	34\34	1200.0	13\13	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Hypohard Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Semihard (5:2) 31edo		Hard (3:1) 18edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\31	0.0	0\18	0.0	1/1
Minor 1-oneirodegree	m1oneid	1\13	92.3	2\31	77.4	1\18	66.7
Major 1-oneirodegree	M1oneid	2\13	184.6	5\31	193.5	3\18	200.0	10/9, 9/8
Minor 2-oneirodegree	m2oneid	3\13	276.9	7\31	271.0	4\18	266.7	7/6
Major 2-oneirodegree	M2oneid	4\13	369.2	10\31	387.1	6\18	400.0	5/4
Diminished 3-oneirodegree	d3oneid	4\13	369.2	9\31	348.4	5\18	333.3	11/9, 16/13
Perfect 3-oneirodegree	P3oneid	5\13	461.5	12\31	464.5	7\18	466.7
Minor 4-oneirodegree	m4oneid	6\13	553.8	14\31	541.9	8\18	533.3	11/8, 18/13
Major 4-oneirodegree	M4oneid	7\13	646.2	17\31	658.1	10\18	666.7	13/9, 16/11
Perfect 5-oneirodegree	P5oneid	8\13	738.5	19\31	735.5	11\18	733.3
Augmented 5-oneirodegree	A5oneid	9\13	830.8	22\31	851.6	13\18	866.7	13/8, 18/11
Minor 6-oneirodegree	m6oneid	9\13	830.8	21\31	812.9	12\18	800.0	8/5
Major 6-oneirodegree	M6oneid	10\13	923.1	24\31	929.0	14\18	933.3	12/7
Minor 7-oneirodegree	m7oneid	11\13	1015.4	26\31	1006.5	15\18	1000.0	16/9, 9/5
Major 7-oneirodegree	M7oneid	12\13	1107.7	29\31	1122.6	17\18	1133.3
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	31\31	1200.0	18\18	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Hard-of-basic Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 18edo		Superhard (4:1) 23edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\18	0.0	0\23	0.0	1/1
Minor 1-oneirodegree	m1oneid	1\13	92.3	1\18	66.7	1\23	52.2
Major 1-oneirodegree	M1oneid	2\13	184.6	3\18	200.0	4\23	208.7	10/9, 9/8
Minor 2-oneirodegree	m2oneid	3\13	276.9	4\18	266.7	5\23	260.9	7/6
Major 2-oneirodegree	M2oneid	4\13	369.2	6\18	400.0	8\23	417.4	5/4, 14/11
Diminished 3-oneirodegree	d3oneid	4\13	369.2	5\18	333.3	6\23	313.0	6/5, 11/9
Perfect 3-oneirodegree	P3oneid	5\13	461.5	7\18	466.7	9\23	469.6
Minor 4-oneirodegree	m4oneid	6\13	553.8	8\18	533.3	10\23	521.7	11/8
Major 4-oneirodegree	M4oneid	7\13	646.2	10\18	666.7	13\23	678.3	16/11
Perfect 5-oneirodegree	P5oneid	8\13	738.5	11\18	733.3	14\23	730.4
Augmented 5-oneirodegree	A5oneid	9\13	830.8	13\18	866.7	17\23	887.0	18/11, 5/3
Minor 6-oneirodegree	m6oneid	9\13	830.8	12\18	800.0	15\23	782.6	11/7, 8/5
Major 6-oneirodegree	M6oneid	10\13	923.1	14\18	933.3	18\23	939.1	12/7
Minor 7-oneirodegree	m7oneid	11\13	1015.4	15\18	1000.0	19\23	991.3	16/9, 9/5
Major 7-oneirodegree	M7oneid	12\13	1107.7	17\18	1133.3	22\23	1147.8
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	18\18	1200.0	23\23	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

6-note mosses

Simple Tunings of 1L 5s
Scale degree	Abbrev.	Basic (2:1) 7edo		Hard (3:1) 8edo		Soft (3:2) 13edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-amechdegree	P0amkd	0\7	0.0	0\8	0.0	0\13	0.0	1/1
Perfect 1-amechdegree	P1amkd	1\7	171.4	1\8	150.0	2\13	184.6	12/11, 11/10, 10/9
Augmented 1-amechdegree	A1amkd	2\7	342.9	3\8	450.0	3\13	276.9	6/5, 11/9, 16/13
Minor 2-amechdegree	m2amkd	2\7	342.9	2\8	300.0	4\13	369.2	6/5, 11/9, 16/13
Major 2-amechdegree	M2amkd	3\7	514.3	4\8	600.0	5\13	461.5	4/3
Minor 3-amechdegree	m3amkd	3\7	514.3	3\8	450.0	6\13	553.8	4/3
Major 3-amechdegree	M3amkd	4\7	685.7	5\8	750.0	7\13	646.2	3/2
Minor 4-amechdegree	m4amkd	4\7	685.7	4\8	600.0	8\13	738.5	3/2
Major 4-amechdegree	M4amkd	5\7	857.1	6\8	900.0	9\13	830.8	13/8, 18/11, 5/3
Diminished 5-amechdegree	d5amkd	5\7	857.1	5\8	750.0	10\13	923.1	13/8, 18/11, 5/3
Perfect 5-amechdegree	P5amkd	6\7	1028.6	7\8	1050.0	11\13	1015.4	9/5, 20/11, 11/6
Perfect 6-amechdegree	P6amkd	7\7	1200.0	8\8	1200.0	13\13	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 2L 4s
Scale degree	Abbrev.	Basic (2:1) 8edo		Hard (3:1) 10edo		Soft (3:2) 14edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-maldegree	P0mald	0\8	0.0	0\10	0.0	0\14	0.0	1/1
Perfect 1-maldegree	P1mald	1\8	150.0	1\10	120.0	2\14	171.4	14/13, 12/11, 11/10
Augmented 1-maldegree	A1mald	2\8	300.0	3\10	360.0	3\14	257.1	6/5
Diminished 2-maldegree	d2mald	2\8	300.0	2\10	240.0	4\14	342.9	6/5
Perfect 2-maldegree	P2mald	3\8	450.0	4\10	480.0	5\14	428.6	9/7
Perfect 3-maldegree	P3mald	4\8	600.0	5\10	600.0	7\14	600.0	7/5, 10/7
Perfect 4-maldegree	P4mald	5\8	750.0	6\10	720.0	9\14	771.4	14/9
Augmented 4-maldegree	A4mald	6\8	900.0	8\10	960.0	10\14	857.1	5/3
Diminished 5-maldegree	d5mald	6\8	900.0	7\10	840.0	11\14	942.9	5/3
Perfect 5-maldegree	P5mald	7\8	1050.0	9\10	1080.0	12\14	1028.6	20/11, 11/6, 13/7
Perfect 6-maldegree	P6mald	8\8	1200.0	10\10	1200.0	14\14	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 3L 3s
Scale degree	Abbrev.	Basic (2:1) 9edo		Hard (3:1) 12edo		Soft (3:2) 15edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-triwddegree	P0twd	0\9	0.0	0\12	0.0	0\15	0.0	1/1
Minor 1-triwddegree	m1twd	1\9	133.3	1\12	100.0	2\15	160.0	16/15, 14/13, 12/11
Major 1-triwddegree	M1twd	2\9	266.7	3\12	300.0	3\15	240.0	7/6
Perfect 2-triwddegree	P2twd	3\9	400.0	4\12	400.0	5\15	400.0	5/4, 14/11
Minor 3-triwddegree	m3twd	4\9	533.3	5\12	500.0	7\15	560.0	11/8
Major 3-triwddegree	M3twd	5\9	666.7	7\12	700.0	8\15	640.0	16/11
Perfect 4-triwddegree	P4twd	6\9	800.0	8\12	800.0	10\15	800.0	11/7, 8/5
Minor 5-triwddegree	m5twd	7\9	933.3	9\12	900.0	12\15	960.0	12/7
Major 5-triwddegree	M5twd	8\9	1066.7	11\12	1100.0	13\15	1040.0	11/6, 13/7, 15/8
Perfect 6-triwddegree	P6twd	9\9	1200.0	12\12	1200.0	15\15	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 4L 2s
Scale degree	Abbrev.	Basic (2:1) 10edo		Hard (3:1) 14edo		Soft (3:2) 16edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-citrodegree	P0citd	0\10	0.0	0\14	0.0	0\16	0.0	1/1
Diminished 1-citrodegree	d1citd	1\10	120.0	1\14	85.7	2\16	150.0	16/15, 14/13
Perfect 1-citrodegree	P1citd	2\10	240.0	3\14	257.1	3\16	225.0	8/7, 7/6
Perfect 2-citrodegree	P2citd	3\10	360.0	4\14	342.9	5\16	375.0	11/9, 16/13, 5/4
Augmented 2-citrodegree	A2citd	4\10	480.0	6\14	514.3	6\16	450.0	4/3
Perfect 3-citrodegree	P3citd	5\10	600.0	7\14	600.0	8\16	600.0	7/5, 10/7
Diminished 4-citrodegree	d4citd	6\10	720.0	8\14	685.7	10\16	750.0	3/2
Perfect 4-citrodegree	P4citd	7\10	840.0	10\14	857.1	11\16	825.0	8/5, 13/8, 18/11
Perfect 5-citrodegree	P5citd	8\10	960.0	11\14	942.9	13\16	975.0	12/7, 7/4
Augmented 5-citrodegree	A5citd	9\10	1080.0	13\14	1114.3	14\16	1050.0	13/7, 15/8
Perfect 6-citrodegree	P6citd	10\10	1200.0	14\14	1200.0	16\16	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 5L 1s
Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 16edo		Soft (3:2) 17edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-mechdegree	P0mkd	0\11	0.0	0\16	0.0	0\17	0.0	1/1
Diminished 1-mechdegree	d1mkd	1\11	109.1	1\16	75.0	2\17	141.2	16/15, 14/13
Perfect 1-mechdegree	P1mkd	2\11	218.2	3\16	225.0	3\17	211.8	9/8, 8/7
Minor 2-mechdegree	m2mkd	3\11	327.3	4\16	300.0	5\17	352.9	6/5, 11/9
Major 2-mechdegree	M2mkd	4\11	436.4	6\16	450.0	6\17	423.5	14/11, 9/7
Minor 3-mechdegree	m3mkd	5\11	545.5	7\16	525.0	8\17	564.7	11/8, 18/13
Major 3-mechdegree	M3mkd	6\11	654.5	9\16	675.0	9\17	635.3	13/9, 16/11
Minor 4-mechdegree	m4mkd	7\11	763.6	10\16	750.0	11\17	776.5	14/9, 11/7
Major 4-mechdegree	M4mkd	8\11	872.7	12\16	900.0	12\17	847.1	18/11, 5/3
Perfect 5-mechdegree	P5mkd	9\11	981.8	13\16	975.0	14\17	988.2	7/4, 16/9
Augmented 5-mechdegree	A5mkd	10\11	1090.9	15\16	1125.0	15\17	1058.8	13/7, 15/8
Perfect 6-mechdegree	P6mkd	11\11	1200.0	16\16	1200.0	17\17	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

7-note mosses

Simple Tunings of 1L 6s
Scale degree	Abbrev.	Basic (2:1) 8edo		Hard (3:1) 9edo		Soft (3:2) 15edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-ondegree	P0ond	0\8	0.0	0\9	0.0	0\15	0.0	1/1
Perfect 1-ondegree	P1ond	1\8	150.0	1\9	133.3	2\15	160.0	14/13, 12/11, 11/10
Augmented 1-ondegree	A1ond	2\8	300.0	3\9	400.0	3\15	240.0	6/5
Minor 2-ondegree	m2ond	2\8	300.0	2\9	266.7	4\15	320.0	6/5
Major 2-ondegree	M2ond	3\8	450.0	4\9	533.3	5\15	400.0	9/7
Minor 3-ondegree	m3ond	3\8	450.0	3\9	400.0	6\15	480.0	9/7
Major 3-ondegree	M3ond	4\8	600.0	5\9	666.7	7\15	560.0	7/5, 10/7
Minor 4-ondegree	m4ond	4\8	600.0	4\9	533.3	8\15	640.0	7/5, 10/7
Major 4-ondegree	M4ond	5\8	750.0	6\9	800.0	9\15	720.0	14/9
Minor 5-ondegree	m5ond	5\8	750.0	5\9	666.7	10\15	800.0	14/9
Major 5-ondegree	M5ond	6\8	900.0	7\9	933.3	11\15	880.0	5/3
Diminished 6-ondegree	d6ond	6\8	900.0	6\9	800.0	12\15	960.0	5/3
Perfect 6-ondegree	P6ond	7\8	1050.0	8\9	1066.7	13\15	1040.0	20/11, 11/6, 13/7
Perfect 7-ondegree	P7ond	8\8	1200.0	9\9	1200.0	15\15	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 2L 5s
Scale degree	Abbrev.	Basic (2:1) 9edo		Hard (3:1) 11edo		Soft (3:2) 16edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-peldegree	P0peld	0\9	0.0	0\11	0.0	0\16	0.0	1/1
Minor 1-peldegree	m1peld	1\9	133.3	1\11	109.1	2\16	150.0	16/15, 14/13, 12/11
Major 1-peldegree	M1peld	2\9	266.7	3\11	327.3	3\16	225.0	7/6
Minor 2-peldegree	m2peld	2\9	266.7	2\11	218.2	4\16	300.0	7/6
Major 2-peldegree	M2peld	3\9	400.0	4\11	436.4	5\16	375.0	5/4, 14/11
Diminished 3-peldegree	d3peld	3\9	400.0	3\11	327.3	6\16	450.0	5/4, 14/11
Perfect 3-peldegree	P3peld	4\9	533.3	5\11	545.5	7\16	525.0	11/8
Perfect 4-peldegree	P4peld	5\9	666.7	6\11	654.5	9\16	675.0	16/11
Augmented 4-peldegree	A4peld	6\9	800.0	8\11	872.7	10\16	750.0	11/7, 8/5
Minor 5-peldegree	m5peld	6\9	800.0	7\11	763.6	11\16	825.0	11/7, 8/5
Major 5-peldegree	M5peld	7\9	933.3	9\11	981.8	12\16	900.0	12/7
Minor 6-peldegree	m6peld	7\9	933.3	8\11	872.7	13\16	975.0	12/7
Major 6-peldegree	M6peld	8\9	1066.7	10\11	1090.9	14\16	1050.0	11/6, 13/7, 15/8
Perfect 7-peldegree	P7peld	9\9	1200.0	11\11	1200.0	16\16	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 3L 4s
Scale degree	Abbrev.	Basic (2:1) 10edo		Hard (3:1) 13edo		Soft (3:2) 17edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-moshdegree	P0moshd	0\10	0.0	0\13	0.0	0\17	0.0	1/1
Minor 1-moshdegree	m1moshd	1\10	120.0	1\13	92.3	2\17	141.2	16/15, 14/13
Major 1-moshdegree	M1moshd	2\10	240.0	3\13	276.9	3\17	211.8	8/7, 7/6
Diminished 2-moshdegree	d2moshd	2\10	240.0	2\13	184.6	4\17	282.4	8/7, 7/6
Perfect 2-moshdegree	P2moshd	3\10	360.0	4\13	369.2	5\17	352.9	11/9, 16/13, 5/4
Minor 3-moshdegree	m3moshd	4\10	480.0	5\13	461.5	7\17	494.1	4/3
Major 3-moshdegree	M3moshd	5\10	600.0	7\13	646.2	8\17	564.7	7/5, 10/7
Minor 4-moshdegree	m4moshd	5\10	600.0	6\13	553.8	9\17	635.3	7/5, 10/7
Major 4-moshdegree	M4moshd	6\10	720.0	8\13	738.5	10\17	705.9	3/2
Perfect 5-moshdegree	P5moshd	7\10	840.0	9\13	830.8	12\17	847.1	8/5, 13/8, 18/11
Augmented 5-moshdegree	A5moshd	8\10	960.0	11\13	1015.4	13\17	917.6	12/7, 7/4
Minor 6-moshdegree	m6moshd	8\10	960.0	10\13	923.1	14\17	988.2	12/7, 7/4
Major 6-moshdegree	M6moshd	9\10	1080.0	12\13	1107.7	15\17	1058.8	13/7, 15/8
Perfect 7-moshdegree	P7moshd	10\10	1200.0	13\13	1200.0	17\17	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 4L 3s
Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 15edo		Soft (3:2) 18edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-smidegree	P0smid	0\11	0.0	0\15	0.0	0\18	0.0	1/1
Minor 1-smidegree	m1smid	1\11	109.1	1\15	80.0	2\18	133.3	16/15, 14/13
Major 1-smidegree	M1smid	2\11	218.2	3\15	240.0	3\18	200.0	9/8, 8/7
Perfect 2-smidegree	P2smid	3\11	327.3	4\15	320.0	5\18	333.3	6/5, 11/9
Augmented 2-smidegree	A2smid	4\11	436.4	6\15	480.0	6\18	400.0	14/11, 9/7
Minor 3-smidegree	m3smid	4\11	436.4	5\15	400.0	7\18	466.7	14/11, 9/7
Major 3-smidegree	M3smid	5\11	545.5	7\15	560.0	8\18	533.3	11/8, 18/13
Minor 4-smidegree	m4smid	6\11	654.5	8\15	640.0	10\18	666.7	13/9, 16/11
Major 4-smidegree	M4smid	7\11	763.6	10\15	800.0	11\18	733.3	14/9, 11/7
Diminished 5-smidegree	d5smid	7\11	763.6	9\15	720.0	12\18	800.0	14/9, 11/7
Perfect 5-smidegree	P5smid	8\11	872.7	11\15	880.0	13\18	866.7	18/11, 5/3
Minor 6-smidegree	m6smid	9\11	981.8	12\15	960.0	15\18	1000.0	7/4, 16/9
Major 6-smidegree	M6smid	10\11	1090.9	14\15	1120.0	16\18	1066.7	13/7, 15/8
Perfect 7-smidegree	P7smid	11\11	1200.0	15\15	1200.0	18\18	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 5L 2s
Scale degree	Abbrev.	Basic (2:1) 12edo		Hard (3:1) 17edo		Soft (3:2) 19edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-diadegree	P0diad	0\12	0.0	0\17	0.0	0\19	0.0	1/1
Minor 1-diadegree	m1diad	1\12	100.0	1\17	70.6	2\19	126.3	16/15, 14/13
Major 1-diadegree	M1diad	2\12	200.0	3\17	211.8	3\19	189.5	10/9, 9/8
Minor 2-diadegree	m2diad	3\12	300.0	4\17	282.4	5\19	315.8	6/5
Major 2-diadegree	M2diad	4\12	400.0	6\17	423.5	6\19	378.9	5/4, 14/11
Perfect 3-diadegree	P3diad	5\12	500.0	7\17	494.1	8\19	505.3	4/3
Augmented 3-diadegree	A3diad	6\12	600.0	9\17	635.3	9\19	568.4	7/5, 10/7
Diminished 4-diadegree	d4diad	6\12	600.0	8\17	564.7	10\19	631.6	7/5, 10/7
Perfect 4-diadegree	P4diad	7\12	700.0	10\17	705.9	11\19	694.7	3/2
Minor 5-diadegree	m5diad	8\12	800.0	11\17	776.5	13\19	821.1	11/7, 8/5
Major 5-diadegree	M5diad	9\12	900.0	13\17	917.6	14\19	884.2	5/3
Minor 6-diadegree	m6diad	10\12	1000.0	14\17	988.2	16\19	1010.5	16/9, 9/5
Major 6-diadegree	M6diad	11\12	1100.0	16\17	1129.4	17\19	1073.7	13/7, 15/8
Perfect 7-diadegree	P7diad	12\12	1200.0	17\17	1200.0	19\19	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 6L 1s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 19edo		Soft (3:2) 20edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-archdegree	P0arcd	0\13	0.0	0\19	0.0	0\20	0.0	1/1
Diminished 1-archdegree	d1arcd	1\13	92.3	1\19	63.2	2\20	120.0	16/15
Perfect 1-archdegree	P1arcd	2\13	184.6	3\19	189.5	3\20	180.0	11/10, 10/9, 9/8
Minor 2-archdegree	m2arcd	3\13	276.9	4\19	252.6	5\20	300.0	7/6
Major 2-archdegree	M2arcd	4\13	369.2	6\19	378.9	6\20	360.0	11/9, 16/13, 5/4
Minor 3-archdegree	m3arcd	5\13	461.5	7\19	442.1	8\20	480.0	9/7
Major 3-archdegree	M3arcd	6\13	553.8	9\19	568.4	9\20	540.0	11/8, 18/13
Minor 4-archdegree	m4arcd	7\13	646.2	10\19	631.6	11\20	660.0	13/9, 16/11
Major 4-archdegree	M4arcd	8\13	738.5	12\19	757.9	12\20	720.0	14/9
Minor 5-archdegree	m5arcd	9\13	830.8	13\19	821.1	14\20	840.0	8/5, 13/8, 18/11
Major 5-archdegree	M5arcd	10\13	923.1	15\19	947.4	15\20	900.0	12/7
Perfect 6-archdegree	P6arcd	11\13	1015.4	16\19	1010.5	17\20	1020.0	16/9, 9/5, 20/11
Augmented 6-archdegree	A6arcd	12\13	1107.7	18\19	1136.8	18\20	1080.0	15/8
Perfect 7-archdegree	P7arcd	13\13	1200.0	19\19	1200.0	20\20	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

8-note mosses

Simple Tunings of 1L 7s
Scale degree	Abbrev.	Basic (2:1) 9edo		Hard (3:1) 10edo		Soft (3:2) 17edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-apinedegree	P0apd	0\9	0.0	0\10	0.0	0\17	0.0	1/1
Perfect 1-apinedegree	P1apd	1\9	133.3	1\10	120.0	2\17	141.2	16/15, 14/13, 12/11
Augmented 1-apinedegree	A1apd	2\9	266.7	3\10	360.0	3\17	211.8	7/6
Minor 2-apinedegree	m2apd	2\9	266.7	2\10	240.0	4\17	282.4	7/6
Major 2-apinedegree	M2apd	3\9	400.0	4\10	480.0	5\17	352.9	5/4, 14/11
Minor 3-apinedegree	m3apd	3\9	400.0	3\10	360.0	6\17	423.5	5/4, 14/11
Major 3-apinedegree	M3apd	4\9	533.3	5\10	600.0	7\17	494.1	11/8
Minor 4-apinedegree	m4apd	4\9	533.3	4\10	480.0	8\17	564.7	11/8
Major 4-apinedegree	M4apd	5\9	666.7	6\10	720.0	9\17	635.3	16/11
Minor 5-apinedegree	m5apd	5\9	666.7	5\10	600.0	10\17	705.9	16/11
Major 5-apinedegree	M5apd	6\9	800.0	7\10	840.0	11\17	776.5	11/7, 8/5
Minor 6-apinedegree	m6apd	6\9	800.0	6\10	720.0	12\17	847.1	11/7, 8/5
Major 6-apinedegree	M6apd	7\9	933.3	8\10	960.0	13\17	917.6	12/7
Diminished 7-apinedegree	d7apd	7\9	933.3	7\10	840.0	14\17	988.2	12/7
Perfect 7-apinedegree	P7apd	8\9	1066.7	9\10	1080.0	15\17	1058.8	11/6, 13/7, 15/8
Perfect 8-apinedegree	P8apd	9\9	1200.0	10\10	1200.0	17\17	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 2L 6s
Scale degree	Abbrev.	Basic (2:1) 10edo		Hard (3:1) 12edo		Soft (3:2) 18edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-subardegree	P0sbd	0\10	0.0	0\12	0.0	0\18	0.0	1/1
Perfect 1-subardegree	P1sbd	1\10	120.0	1\12	100.0	2\18	133.3	16/15, 14/13
Augmented 1-subardegree	A1sbd	2\10	240.0	3\12	300.0	3\18	200.0	8/7, 7/6
Minor 2-subardegree	m2sbd	2\10	240.0	2\12	200.0	4\18	266.7	8/7, 7/6
Major 2-subardegree	M2sbd	3\10	360.0	4\12	400.0	5\18	333.3	11/9, 16/13, 5/4
Diminished 3-subardegree	d3sbd	3\10	360.0	3\12	300.0	6\18	400.0	11/9, 16/13, 5/4
Perfect 3-subardegree	P3sbd	4\10	480.0	5\12	500.0	7\18	466.7	4/3
Perfect 4-subardegree	P4sbd	5\10	600.0	6\12	600.0	9\18	600.0	7/5, 10/7
Perfect 5-subardegree	P5sbd	6\10	720.0	7\12	700.0	11\18	733.3	3/2
Augmented 5-subardegree	A5sbd	7\10	840.0	9\12	900.0	12\18	800.0	8/5, 13/8, 18/11
Minor 6-subardegree	m6sbd	7\10	840.0	8\12	800.0	13\18	866.7	8/5, 13/8, 18/11
Major 6-subardegree	M6sbd	8\10	960.0	10\12	1000.0	14\18	933.3	12/7, 7/4
Diminished 7-subardegree	d7sbd	8\10	960.0	9\12	900.0	15\18	1000.0	12/7, 7/4
Perfect 7-subardegree	P7sbd	9\10	1080.0	11\12	1100.0	16\18	1066.7	13/7, 15/8
Perfect 8-subardegree	P8sbd	10\10	1200.0	12\12	1200.0	18\18	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 3L 5s
Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 14edo		Soft (3:2) 19edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-checkdegree	P0chkd	0\11	0.0	0\14	0.0	0\19	0.0	1/1
Minor 1-checkdegree	m1chkd	1\11	109.1	1\14	85.7	2\19	126.3	16/15, 14/13
Major 1-checkdegree	M1chkd	2\11	218.2	3\14	257.1	3\19	189.5	9/8, 8/7
Minor 2-checkdegree	m2chkd	2\11	218.2	2\14	171.4	4\19	252.6	9/8, 8/7
Major 2-checkdegree	M2chkd	3\11	327.3	4\14	342.9	5\19	315.8	6/5, 11/9
Perfect 3-checkdegree	P3chkd	4\11	436.4	5\14	428.6	7\19	442.1	14/11, 9/7
Augmented 3-checkdegree	A3chkd	5\11	545.5	7\14	600.0	8\19	505.3	11/8, 18/13
Minor 4-checkdegree	m4chkd	5\11	545.5	6\14	514.3	9\19	568.4	11/8, 18/13
Major 4-checkdegree	M4chkd	6\11	654.5	8\14	685.7	10\19	631.6	13/9, 16/11
Diminished 5-checkdegree	d5chkd	6\11	654.5	7\14	600.0	11\19	694.7	13/9, 16/11
Perfect 5-checkdegree	P5chkd	7\11	763.6	9\14	771.4	12\19	757.9	14/9, 11/7
Minor 6-checkdegree	m6chkd	8\11	872.7	10\14	857.1	14\19	884.2	18/11, 5/3
Major 6-checkdegree	M6chkd	9\11	981.8	12\14	1028.6	15\19	947.4	7/4, 16/9
Minor 7-checkdegree	m7chkd	9\11	981.8	11\14	942.9	16\19	1010.5	7/4, 16/9
Major 7-checkdegree	M7chkd	10\11	1090.9	13\14	1114.3	17\19	1073.7	13/7, 15/8
Perfect 8-checkdegree	P8chkd	11\11	1200.0	14\14	1200.0	19\19	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 4L 4s
Scale degree	Abbrev.	Basic (2:1) 12edo		Hard (3:1) 16edo		Soft (3:2) 20edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-tetrawddegree	P0ttwd	0\12	0.0	0\16	0.0	0\20	0.0	1/1
Minor 1-tetrawddegree	m1ttwd	1\12	100.0	1\16	75.0	2\20	120.0	16/15, 14/13
Major 1-tetrawddegree	M1ttwd	2\12	200.0	3\16	225.0	3\20	180.0	10/9, 9/8
Perfect 2-tetrawddegree	P2ttwd	3\12	300.0	4\16	300.0	5\20	300.0	6/5
Minor 3-tetrawddegree	m3ttwd	4\12	400.0	5\16	375.0	7\20	420.0	5/4, 14/11
Major 3-tetrawddegree	M3ttwd	5\12	500.0	7\16	525.0	8\20	480.0	4/3
Perfect 4-tetrawddegree	P4ttwd	6\12	600.0	8\16	600.0	10\20	600.0	7/5, 10/7
Minor 5-tetrawddegree	m5ttwd	7\12	700.0	9\16	675.0	12\20	720.0	3/2
Major 5-tetrawddegree	M5ttwd	8\12	800.0	11\16	825.0	13\20	780.0	11/7, 8/5
Perfect 6-tetrawddegree	P6ttwd	9\12	900.0	12\16	900.0	15\20	900.0	5/3
Minor 7-tetrawddegree	m7ttwd	10\12	1000.0	13\16	975.0	17\20	1020.0	16/9, 9/5
Major 7-tetrawddegree	M7ttwd	11\12	1100.0	15\16	1125.0	18\20	1080.0	13/7, 15/8
Perfect 8-tetrawddegree	P8ttwd	12\12	1200.0	16\16	1200.0	20\20	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 5L 3s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 18edo		Soft (3:2) 21edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-oneirodegree	P0oneid	0\13	0.0	0\18	0.0	0\21	0.0	1/1
Minor 1-oneirodegree	m1oneid	1\13	92.3	1\18	66.7	2\21	114.3	16/15
Major 1-oneirodegree	M1oneid	2\13	184.6	3\18	200.0	3\21	171.4	11/10, 10/9, 9/8
Minor 2-oneirodegree	m2oneid	3\13	276.9	4\18	266.7	5\21	285.7	7/6
Major 2-oneirodegree	M2oneid	4\13	369.2	6\18	400.0	6\21	342.9	11/9, 16/13, 5/4
Diminished 3-oneirodegree	d3oneid	4\13	369.2	5\18	333.3	7\21	400.0	11/9, 16/13, 5/4
Perfect 3-oneirodegree	P3oneid	5\13	461.5	7\18	466.7	8\21	457.1	9/7
Minor 4-oneirodegree	m4oneid	6\13	553.8	8\18	533.3	10\21	571.4	11/8, 18/13
Major 4-oneirodegree	M4oneid	7\13	646.2	10\18	666.7	11\21	628.6	13/9, 16/11
Perfect 5-oneirodegree	P5oneid	8\13	738.5	11\18	733.3	13\21	742.9	14/9
Augmented 5-oneirodegree	A5oneid	9\13	830.8	13\18	866.7	14\21	800.0	8/5, 13/8, 18/11
Minor 6-oneirodegree	m6oneid	9\13	830.8	12\18	800.0	15\21	857.1	8/5, 13/8, 18/11
Major 6-oneirodegree	M6oneid	10\13	923.1	14\18	933.3	16\21	914.3	12/7
Minor 7-oneirodegree	m7oneid	11\13	1015.4	15\18	1000.0	18\21	1028.6	16/9, 9/5, 20/11
Major 7-oneirodegree	M7oneid	12\13	1107.7	17\18	1133.3	19\21	1085.7	15/8
Perfect 8-oneirodegree	P8oneid	13\13	1200.0	18\18	1200.0	21\21	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 6L 2s
Scale degree	Abbrev.	Basic (2:1) 14edo		Hard (3:1) 20edo		Soft (3:2) 22edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-ekdegree	P0ekd	0\14	0.0	0\20	0.0	0\22	0.0	1/1
Diminished 1-ekdegree	d1ekd	1\14	85.7	1\20	60.0	2\22	109.1
Perfect 1-ekdegree	P1ekd	2\14	171.4	3\20	180.0	3\22	163.6	12/11, 11/10, 10/9
Minor 2-ekdegree	m2ekd	3\14	257.1	4\20	240.0	5\22	272.7	7/6
Major 2-ekdegree	M2ekd	4\14	342.9	6\20	360.0	6\22	327.3	11/9, 16/13
Perfect 3-ekdegree	P3ekd	5\14	428.6	7\20	420.0	8\22	436.4	14/11, 9/7
Augmented 3-ekdegree	A3ekd	6\14	514.3	9\20	540.0	9\22	490.9	4/3
Perfect 4-ekdegree	P4ekd	7\14	600.0	10\20	600.0	11\22	600.0	7/5, 10/7
Diminished 5-ekdegree	d5ekd	8\14	685.7	11\20	660.0	13\22	709.1	3/2
Perfect 5-ekdegree	P5ekd	9\14	771.4	13\20	780.0	14\22	763.6	14/9, 11/7
Minor 6-ekdegree	m6ekd	10\14	857.1	14\20	840.0	16\22	872.7	13/8, 18/11
Major 6-ekdegree	M6ekd	11\14	942.9	16\20	960.0	17\22	927.3	12/7
Perfect 7-ekdegree	P7ekd	12\14	1028.6	17\20	1020.0	19\22	1036.4	9/5, 20/11, 11/6
Augmented 7-ekdegree	A7ekd	13\14	1114.3	19\20	1140.0	20\22	1090.9
Perfect 8-ekdegree	P8ekd	14\14	1200.0	20\20	1200.0	22\22	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 7L 1s
Scale degree	Abbrev.	Basic (2:1) 15edo		Hard (3:1) 22edo		Soft (3:2) 23edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-pinedegree	P0pd	0\15	0.0	0\22	0.0	0\23	0.0	1/1
Diminished 1-pinedegree	d1pd	1\15	80.0	1\22	54.5	2\23	104.3
Perfect 1-pinedegree	P1pd	2\15	160.0	3\22	163.6	3\23	156.5	12/11, 11/10, 10/9
Minor 2-pinedegree	m2pd	3\15	240.0	4\22	218.2	5\23	260.9	8/7
Major 2-pinedegree	M2pd	4\15	320.0	6\22	327.3	6\23	313.0	6/5
Minor 3-pinedegree	m3pd	5\15	400.0	7\22	381.8	8\23	417.4	5/4, 14/11
Major 3-pinedegree	M3pd	6\15	480.0	9\22	490.9	9\23	469.6	4/3
Minor 4-pinedegree	m4pd	7\15	560.0	10\22	545.5	11\23	573.9	11/8, 18/13, 7/5
Major 4-pinedegree	M4pd	8\15	640.0	12\22	654.5	12\23	626.1	10/7, 13/9, 16/11
Minor 5-pinedegree	m5pd	9\15	720.0	13\22	709.1	14\23	730.4	3/2
Major 5-pinedegree	M5pd	10\15	800.0	15\22	818.2	15\23	782.6	11/7, 8/5
Minor 6-pinedegree	m6pd	11\15	880.0	16\22	872.7	17\23	887.0	5/3
Major 6-pinedegree	M6pd	12\15	960.0	18\22	981.8	18\23	939.1	7/4
Perfect 7-pinedegree	P7pd	13\15	1040.0	19\22	1036.4	20\23	1043.5	9/5, 20/11, 11/6
Augmented 7-pinedegree	A7pd	14\15	1120.0	21\22	1145.5	21\23	1095.7
Perfect 8-pinedegree	P8pd	15\15	1200.0	22\22	1200.0	23\23	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

9-note mosses

Simple Tunings of 1L 8s
Scale degree	Abbrev.	Basic (2:1) 10edo		Hard (3:1) 11edo		Soft (3:2) 19edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-abludegree	P0ablud	0\10	0.0	0\11	0.0	0\19	0.0	1/1
Perfect 1-abludegree	P1ablud	1\10	120.0	1\11	109.1	2\19	126.3	16/15, 14/13
Augmented 1-abludegree	A1ablud	2\10	240.0	3\11	327.3	3\19	189.5	8/7, 7/6
Minor 2-abludegree	m2ablud	2\10	240.0	2\11	218.2	4\19	252.6	8/7, 7/6
Major 2-abludegree	M2ablud	3\10	360.0	4\11	436.4	5\19	315.8	11/9, 16/13, 5/4
Minor 3-abludegree	m3ablud	3\10	360.0	3\11	327.3	6\19	378.9	11/9, 16/13, 5/4
Major 3-abludegree	M3ablud	4\10	480.0	5\11	545.5	7\19	442.1	4/3
Minor 4-abludegree	m4ablud	4\10	480.0	4\11	436.4	8\19	505.3	4/3
Major 4-abludegree	M4ablud	5\10	600.0	6\11	654.5	9\19	568.4	7/5, 10/7
Minor 5-abludegree	m5ablud	5\10	600.0	5\11	545.5	10\19	631.6	7/5, 10/7
Major 5-abludegree	M5ablud	6\10	720.0	7\11	763.6	11\19	694.7	3/2
Minor 6-abludegree	m6ablud	6\10	720.0	6\11	654.5	12\19	757.9	3/2
Major 6-abludegree	M6ablud	7\10	840.0	8\11	872.7	13\19	821.1	8/5, 13/8, 18/11
Minor 7-abludegree	m7ablud	7\10	840.0	7\11	763.6	14\19	884.2	8/5, 13/8, 18/11
Major 7-abludegree	M7ablud	8\10	960.0	9\11	981.8	15\19	947.4	12/7, 7/4
Diminished 8-abludegree	d8ablud	8\10	960.0	8\11	872.7	16\19	1010.5	12/7, 7/4
Perfect 8-abludegree	P8ablud	9\10	1080.0	10\11	1090.9	17\19	1073.7	13/7, 15/8
Perfect 9-abludegree	P9ablud	10\10	1200.0	11\11	1200.0	19\19	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 2L 7s
Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 13edo		Soft (3:2) 20edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-baldegree	P0bzd	0\11	0.0	0\13	0.0	0\20	0.0	1/1
Minor 1-baldegree	m1bzd	1\11	109.1	1\13	92.3	2\20	120.0	16/15, 14/13
Major 1-baldegree	M1bzd	2\11	218.2	3\13	276.9	3\20	180.0	9/8, 8/7
Minor 2-baldegree	m2bzd	2\11	218.2	2\13	184.6	4\20	240.0	9/8, 8/7
Major 2-baldegree	M2bzd	3\11	327.3	4\13	369.2	5\20	300.0	6/5, 11/9
Minor 3-baldegree	m3bzd	3\11	327.3	3\13	276.9	6\20	360.0	6/5, 11/9
Major 3-baldegree	M3bzd	4\11	436.4	5\13	461.5	7\20	420.0	14/11, 9/7
Diminished 4-baldegree	d4bzd	4\11	436.4	4\13	369.2	8\20	480.0	14/11, 9/7
Perfect 4-baldegree	P4bzd	5\11	545.5	6\13	553.8	9\20	540.0	11/8, 18/13
Perfect 5-baldegree	P5bzd	6\11	654.5	7\13	646.2	11\20	660.0	13/9, 16/11
Augmented 5-baldegree	A5bzd	7\11	763.6	9\13	830.8	12\20	720.0	14/9, 11/7
Minor 6-baldegree	m6bzd	7\11	763.6	8\13	738.5	13\20	780.0	14/9, 11/7
Major 6-baldegree	M6bzd	8\11	872.7	10\13	923.1	14\20	840.0	18/11, 5/3
Minor 7-baldegree	m7bzd	8\11	872.7	9\13	830.8	15\20	900.0	18/11, 5/3
Major 7-baldegree	M7bzd	9\11	981.8	11\13	1015.4	16\20	960.0	7/4, 16/9
Minor 8-baldegree	m8bzd	9\11	981.8	10\13	923.1	17\20	1020.0	7/4, 16/9
Major 8-baldegree	M8bzd	10\11	1090.9	12\13	1107.7	18\20	1080.0	13/7, 15/8
Perfect 9-baldegree	P9bzd	11\11	1200.0	13\13	1200.0	20\20	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 3L 6s
Scale degree	Abbrev.	Basic (2:1) 12edo		Hard (3:1) 15edo		Soft (3:2) 21edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-cherdegree	P0chd	0\12	0.0	0\15	0.0	0\21	0.0	1/1
Perfect 1-cherdegree	P1chd	1\12	100.0	1\15	80.0	2\21	114.3	16/15, 14/13
Augmented 1-cherdegree	A1chd	2\12	200.0	3\15	240.0	3\21	171.4	10/9, 9/8
Diminished 2-cherdegree	d2chd	2\12	200.0	2\15	160.0	4\21	228.6	10/9, 9/8
Perfect 2-cherdegree	P2chd	3\12	300.0	4\15	320.0	5\21	285.7	6/5
Perfect 3-cherdegree	P3chd	4\12	400.0	5\15	400.0	7\21	400.0	5/4, 14/11
Perfect 4-cherdegree	P4chd	5\12	500.0	6\15	480.0	9\21	514.3	4/3
Augmented 4-cherdegree	A4chd	6\12	600.0	8\15	640.0	10\21	571.4	7/5, 10/7
Diminished 5-cherdegree	d5chd	6\12	600.0	7\15	560.0	11\21	628.6	7/5, 10/7
Perfect 5-cherdegree	P5chd	7\12	700.0	9\15	720.0	12\21	685.7	3/2
Perfect 6-cherdegree	P6chd	8\12	800.0	10\15	800.0	14\21	800.0	11/7, 8/5
Perfect 7-cherdegree	P7chd	9\12	900.0	11\15	880.0	16\21	914.3	5/3
Augmented 7-cherdegree	A7chd	10\12	1000.0	13\15	1040.0	17\21	971.4	16/9, 9/5
Diminished 8-cherdegree	d8chd	10\12	1000.0	12\15	960.0	18\21	1028.6	16/9, 9/5
Perfect 8-cherdegree	P8chd	11\12	1100.0	14\15	1120.0	19\21	1085.7	13/7, 15/8
Perfect 9-cherdegree	P9chd	12\12	1200.0	15\15	1200.0	21\21	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 4L 5s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 17edo		Soft (3:2) 22edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-gramdegree	P0gmd	0\13	0.0	0\17	0.0	0\22	0.0	1/1
Minor 1-gramdegree	m1gmd	1\13	92.3	1\17	70.6	2\22	109.1	16/15
Major 1-gramdegree	M1gmd	2\13	184.6	3\17	211.8	3\22	163.6	11/10, 10/9, 9/8
Diminished 2-gramdegree	d2gmd	2\13	184.6	2\17	141.2	4\22	218.2	11/10, 10/9, 9/8
Perfect 2-gramdegree	P2gmd	3\13	276.9	4\17	282.4	5\22	272.7	7/6
Minor 3-gramdegree	m3gmd	4\13	369.2	5\17	352.9	7\22	381.8	11/9, 16/13, 5/4
Major 3-gramdegree	M3gmd	5\13	461.5	7\17	494.1	8\22	436.4	9/7
Minor 4-gramdegree	m4gmd	5\13	461.5	6\17	423.5	9\22	490.9	9/7
Major 4-gramdegree	M4gmd	6\13	553.8	8\17	564.7	10\22	545.5	11/8, 18/13
Minor 5-gramdegree	m5gmd	7\13	646.2	9\17	635.3	12\22	654.5	13/9, 16/11
Major 5-gramdegree	M5gmd	8\13	738.5	11\17	776.5	13\22	709.1	14/9
Minor 6-gramdegree	m6gmd	8\13	738.5	10\17	705.9	14\22	763.6	14/9
Major 6-gramdegree	M6gmd	9\13	830.8	12\17	847.1	15\22	818.2	8/5, 13/8, 18/11
Perfect 7-gramdegree	P7gmd	10\13	923.1	13\17	917.6	17\22	927.3	12/7
Augmented 7-gramdegree	A7gmd	11\13	1015.4	15\17	1058.8	18\22	981.8	16/9, 9/5, 20/11
Minor 8-gramdegree	m8gmd	11\13	1015.4	14\17	988.2	19\22	1036.4	16/9, 9/5, 20/11
Major 8-gramdegree	M8gmd	12\13	1107.7	16\17	1129.4	20\22	1090.9	15/8
Perfect 9-gramdegree	P9gmd	13\13	1200.0	17\17	1200.0	22\22	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 5L 4s
Scale degree	Abbrev.	Basic (2:1) 14edo		Hard (3:1) 19edo		Soft (3:2) 23edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-cthondegree	P0ctd	0\14	0.0	0\19	0.0	0\23	0.0	1/1
Minor 1-cthondegree	m1ctd	1\14	85.7	1\19	63.2	2\23	104.3
Major 1-cthondegree	M1ctd	2\14	171.4	3\19	189.5	3\23	156.5	12/11, 11/10, 10/9
Perfect 2-cthondegree	P2ctd	3\14	257.1	4\19	252.6	5\23	260.9	7/6
Augmented 2-cthondegree	A2ctd	4\14	342.9	6\19	378.9	6\23	313.0	11/9, 16/13
Minor 3-cthondegree	m3ctd	4\14	342.9	5\19	315.8	7\23	365.2	11/9, 16/13
Major 3-cthondegree	M3ctd	5\14	428.6	7\19	442.1	8\23	417.4	14/11, 9/7
Minor 4-cthondegree	m4ctd	6\14	514.3	8\19	505.3	10\23	521.7	4/3
Major 4-cthondegree	M4ctd	7\14	600.0	10\19	631.6	11\23	573.9	7/5, 10/7
Minor 5-cthondegree	m5ctd	7\14	600.0	9\19	568.4	12\23	626.1	7/5, 10/7
Major 5-cthondegree	M5ctd	8\14	685.7	11\19	694.7	13\23	678.3	3/2
Minor 6-cthondegree	m6ctd	9\14	771.4	12\19	757.9	15\23	782.6	14/9, 11/7
Major 6-cthondegree	M6ctd	10\14	857.1	14\19	884.2	16\23	834.8	13/8, 18/11
Diminished 7-cthondegree	d7ctd	10\14	857.1	13\19	821.1	17\23	887.0	13/8, 18/11
Perfect 7-cthondegree	P7ctd	11\14	942.9	15\19	947.4	18\23	939.1	12/7
Minor 8-cthondegree	m8ctd	12\14	1028.6	16\19	1010.5	20\23	1043.5	9/5, 20/11, 11/6
Major 8-cthondegree	M8ctd	13\14	1114.3	18\19	1136.8	21\23	1095.7
Perfect 9-cthondegree	P9ctd	14\14	1200.0	19\19	1200.0	23\23	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 6L 3s
Scale degree	Abbrev.	Basic (2:1) 15edo		Hard (3:1) 21edo		Soft (3:2) 24edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-hyrudegree	P0hyd	0\15	0.0	0\21	0.0	0\24	0.0	1/1
Diminished 1-hyrudegree	d1hyd	1\15	80.0	1\21	57.1	2\24	100.0
Perfect 1-hyrudegree	P1hyd	2\15	160.0	3\21	171.4	3\24	150.0	12/11, 11/10, 10/9
Perfect 2-hyrudegree	P2hyd	3\15	240.0	4\21	228.6	5\24	250.0	8/7
Augmented 2-hyrudegree	A2hyd	4\15	320.0	6\21	342.9	6\24	300.0	6/5
Perfect 3-hyrudegree	P3hyd	5\15	400.0	7\21	400.0	8\24	400.0	5/4, 14/11
Diminished 4-hyrudegree	d4hyd	6\15	480.0	8\21	457.1	10\24	500.0	4/3
Perfect 4-hyrudegree	P4hyd	7\15	560.0	10\21	571.4	11\24	550.0	11/8, 18/13, 7/5
Perfect 5-hyrudegree	P5hyd	8\15	640.0	11\21	628.6	13\24	650.0	10/7, 13/9, 16/11
Augmented 5-hyrudegree	A5hyd	9\15	720.0	13\21	742.9	14\24	700.0	3/2
Perfect 6-hyrudegree	P6hyd	10\15	800.0	14\21	800.0	16\24	800.0	11/7, 8/5
Diminished 7-hyrudegree	d7hyd	11\15	880.0	15\21	857.1	18\24	900.0	5/3
Perfect 7-hyrudegree	P7hyd	12\15	960.0	17\21	971.4	19\24	950.0	7/4
Perfect 8-hyrudegree	P8hyd	13\15	1040.0	18\21	1028.6	21\24	1050.0	9/5, 20/11, 11/6
Augmented 8-hyrudegree	A8hyd	14\15	1120.0	20\21	1142.9	22\24	1100.0
Perfect 9-hyrudegree	P9hyd	15\15	1200.0	21\21	1200.0	24\24	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 7L 2s
Scale degree	Abbrev.	Basic (2:1) 16edo		Hard (3:1) 23edo		Soft (3:2) 25edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-armdegree	P0armd	0\16	0.0	0\23	0.0	0\25	0.0	1/1
Minor 1-armdegree	m1armd	1\16	75.0	1\23	52.2	2\25	96.0
Major 1-armdegree	M1armd	2\16	150.0	3\23	156.5	3\25	144.0	14/13, 12/11, 11/10
Minor 2-armdegree	m2armd	3\16	225.0	4\23	208.7	5\25	240.0	9/8, 8/7
Major 2-armdegree	M2armd	4\16	300.0	6\23	313.0	6\25	288.0	6/5
Minor 3-armdegree	m3armd	5\16	375.0	7\23	365.2	8\25	384.0	16/13, 5/4
Major 3-armdegree	M3armd	6\16	450.0	9\23	469.6	9\25	432.0	9/7
Perfect 4-armdegree	P4armd	7\16	525.0	10\23	521.7	11\25	528.0
Augmented 4-armdegree	A4armd	8\16	600.0	12\23	626.1	12\25	576.0	7/5, 10/7
Diminished 5-armdegree	d5armd	8\16	600.0	11\23	573.9	13\25	624.0	7/5, 10/7
Perfect 5-armdegree	P5armd	9\16	675.0	13\23	678.3	14\25	672.0
Minor 6-armdegree	m6armd	10\16	750.0	14\23	730.4	16\25	768.0	14/9
Major 6-armdegree	M6armd	11\16	825.0	16\23	834.8	17\25	816.0	8/5, 13/8
Minor 7-armdegree	m7armd	12\16	900.0	17\23	887.0	19\25	912.0	5/3
Major 7-armdegree	M7armd	13\16	975.0	19\23	991.3	20\25	960.0	7/4, 16/9
Minor 8-armdegree	m8armd	14\16	1050.0	20\23	1043.5	22\25	1056.0	20/11, 11/6, 13/7
Major 8-armdegree	M8armd	15\16	1125.0	22\23	1147.8	23\25	1104.0
Perfect 9-armdegree	P9armd	16\16	1200.0	23\23	1200.0	25\25	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 8L 1s
Scale degree	Abbrev.	Basic (2:1) 17edo		Hard (3:1) 25edo		Soft (3:2) 26edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-bludegree	P0blud	0\17	0.0	0\25	0.0	0\26	0.0	1/1
Diminished 1-bludegree	d1blud	1\17	70.6	1\25	48.0	2\26	92.3
Perfect 1-bludegree	P1blud	2\17	141.2	3\25	144.0	3\26	138.5	14/13, 12/11
Minor 2-bludegree	m2blud	3\17	211.8	4\25	192.0	5\26	230.8	9/8, 8/7
Major 2-bludegree	M2blud	4\17	282.4	6\25	288.0	6\26	276.9	7/6
Minor 3-bludegree	m3blud	5\17	352.9	7\25	336.0	8\26	369.2	11/9, 16/13
Major 3-bludegree	M3blud	6\17	423.5	9\25	432.0	9\26	415.4	14/11, 9/7
Minor 4-bludegree	m4blud	7\17	494.1	10\25	480.0	11\26	507.7	4/3
Major 4-bludegree	M4blud	8\17	564.7	12\25	576.0	12\26	553.8	11/8, 18/13, 7/5
Minor 5-bludegree	m5blud	9\17	635.3	13\25	624.0	14\26	646.2	10/7, 13/9, 16/11
Major 5-bludegree	M5blud	10\17	705.9	15\25	720.0	15\26	692.3	3/2
Minor 6-bludegree	m6blud	11\17	776.5	16\25	768.0	17\26	784.6	14/9, 11/7
Major 6-bludegree	M6blud	12\17	847.1	18\25	864.0	18\26	830.8	13/8, 18/11
Minor 7-bludegree	m7blud	13\17	917.6	19\25	912.0	20\26	923.1	12/7
Major 7-bludegree	M7blud	14\17	988.2	21\25	1008.0	21\26	969.2	7/4, 16/9
Perfect 8-bludegree	P8blud	15\17	1058.8	22\25	1056.0	23\26	1061.5	11/6, 13/7
Augmented 8-bludegree	A8blud	16\17	1129.4	24\25	1152.0	24\26	1107.7
Perfect 9-bludegree	P9blud	17\17	1200.0	25\25	1200.0	26\26	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

10-note mosses

Simple Tunings of 1L 9s
Scale degree	Abbrev.	Basic (2:1) 11edo		Hard (3:1) 12edo		Soft (3:2) 21edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-asinadegree	P0asid	0\11	0.0	0\12	0.0	0\21	0.0	1/1
Perfect 1-asinadegree	P1asid	1\11	109.1	1\12	100.0	2\21	114.3	16/15, 14/13
Augmented 1-asinadegree	A1asid	2\11	218.2	3\12	300.0	3\21	171.4	9/8, 8/7
Minor 2-asinadegree	m2asid	2\11	218.2	2\12	200.0	4\21	228.6	9/8, 8/7
Major 2-asinadegree	M2asid	3\11	327.3	4\12	400.0	5\21	285.7	6/5, 11/9
Minor 3-asinadegree	m3asid	3\11	327.3	3\12	300.0	6\21	342.9	6/5, 11/9
Major 3-asinadegree	M3asid	4\11	436.4	5\12	500.0	7\21	400.0	14/11, 9/7
Minor 4-asinadegree	m4asid	4\11	436.4	4\12	400.0	8\21	457.1	14/11, 9/7
Major 4-asinadegree	M4asid	5\11	545.5	6\12	600.0	9\21	514.3	11/8, 18/13
Minor 5-asinadegree	m5asid	5\11	545.5	5\12	500.0	10\21	571.4	11/8, 18/13
Major 5-asinadegree	M5asid	6\11	654.5	7\12	700.0	11\21	628.6	13/9, 16/11
Minor 6-asinadegree	m6asid	6\11	654.5	6\12	600.0	12\21	685.7	13/9, 16/11
Major 6-asinadegree	M6asid	7\11	763.6	8\12	800.0	13\21	742.9	14/9, 11/7
Minor 7-asinadegree	m7asid	7\11	763.6	7\12	700.0	14\21	800.0	14/9, 11/7
Major 7-asinadegree	M7asid	8\11	872.7	9\12	900.0	15\21	857.1	18/11, 5/3
Minor 8-asinadegree	m8asid	8\11	872.7	8\12	800.0	16\21	914.3	18/11, 5/3
Major 8-asinadegree	M8asid	9\11	981.8	10\12	1000.0	17\21	971.4	7/4, 16/9
Diminished 9-asinadegree	d9asid	9\11	981.8	9\12	900.0	18\21	1028.6	7/4, 16/9
Perfect 9-asinadegree	P9asid	10\11	1090.9	11\12	1100.0	19\21	1085.7	13/7, 15/8
Perfect 10-asinadegree	P10asid	11\11	1200.0	12\12	1200.0	21\21	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 2L 8s
Scale degree	Abbrev.	Basic (2:1) 12edo		Hard (3:1) 14edo		Soft (3:2) 22edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-jaradegree	P0jad	0\12	0.0	0\14	0.0	0\22	0.0	1/1
Perfect 1-jaradegree	P1jad	1\12	100.0	1\14	85.7	2\22	109.1	16/15, 14/13
Augmented 1-jaradegree	A1jad	2\12	200.0	3\14	257.1	3\22	163.6	10/9, 9/8
Minor 2-jaradegree	m2jad	2\12	200.0	2\14	171.4	4\22	218.2	10/9, 9/8
Major 2-jaradegree	M2jad	3\12	300.0	4\14	342.9	5\22	272.7	6/5
Minor 3-jaradegree	m3jad	3\12	300.0	3\14	257.1	6\22	327.3	6/5
Major 3-jaradegree	M3jad	4\12	400.0	5\14	428.6	7\22	381.8	5/4, 14/11
Diminished 4-jaradegree	d4jad	4\12	400.0	4\14	342.9	8\22	436.4	5/4, 14/11
Perfect 4-jaradegree	P4jad	5\12	500.0	6\14	514.3	9\22	490.9	4/3
Perfect 5-jaradegree	P5jad	6\12	600.0	7\14	600.0	11\22	600.0	7/5, 10/7
Perfect 6-jaradegree	P6jad	7\12	700.0	8\14	685.7	13\22	709.1	3/2
Augmented 6-jaradegree	A6jad	8\12	800.0	10\14	857.1	14\22	763.6	11/7, 8/5
Minor 7-jaradegree	m7jad	8\12	800.0	9\14	771.4	15\22	818.2	11/7, 8/5
Major 7-jaradegree	M7jad	9\12	900.0	11\14	942.9	16\22	872.7	5/3
Minor 8-jaradegree	m8jad	9\12	900.0	10\14	857.1	17\22	927.3	5/3
Major 8-jaradegree	M8jad	10\12	1000.0	12\14	1028.6	18\22	981.8	16/9, 9/5
Diminished 9-jaradegree	d9jad	10\12	1000.0	11\14	942.9	19\22	1036.4	16/9, 9/5
Perfect 9-jaradegree	P9jad	11\12	1100.0	13\14	1114.3	20\22	1090.9	13/7, 15/8
Perfect 10-jaradegree	P10jad	12\12	1200.0	14\14	1200.0	22\22	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 3L 7s
Scale degree	Abbrev.	Basic (2:1) 13edo		Hard (3:1) 16edo		Soft (3:2) 23edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-sephdegree	P0spd	0\13	0.0	0\16	0.0	0\23	0.0	1/1
Minor 1-sephdegree	m1spd	1\13	92.3	1\16	75.0	2\23	104.3	16/15
Major 1-sephdegree	M1spd	2\13	184.6	3\16	225.0	3\23	156.5	11/10, 10/9, 9/8
Minor 2-sephdegree	m2spd	2\13	184.6	2\16	150.0	4\23	208.7	11/10, 10/9, 9/8
Major 2-sephdegree	M2spd	3\13	276.9	4\16	300.0	5\23	260.9	7/6
Diminished 3-sephdegree	d3spd	3\13	276.9	3\16	225.0	6\23	313.0	7/6
Perfect 3-sephdegree	P3spd	4\13	369.2	5\16	375.0	7\23	365.2	11/9, 16/13, 5/4
Minor 4-sephdegree	m4spd	5\13	461.5	6\16	450.0	9\23	469.6	9/7
Major 4-sephdegree	M4spd	6\13	553.8	8\16	600.0	10\23	521.7	11/8, 18/13
Minor 5-sephdegree	m5spd	6\13	553.8	7\16	525.0	11\23	573.9	11/8, 18/13
Major 5-sephdegree	M5spd	7\13	646.2	9\16	675.0	12\23	626.1	13/9, 16/11
Minor 6-sephdegree	m6spd	7\13	646.2	8\16	600.0	13\23	678.3	13/9, 16/11
Major 6-sephdegree	M6spd	8\13	738.5	10\16	750.0	14\23	730.4	14/9
Perfect 7-sephdegree	P7spd	9\13	830.8	11\16	825.0	16\23	834.8	8/5, 13/8, 18/11
Augmented 7-sephdegree	A7spd	10\13	923.1	13\16	975.0	17\23	887.0	12/7
Minor 8-sephdegree	m8spd	10\13	923.1	12\16	900.0	18\23	939.1	12/7
Major 8-sephdegree	M8spd	11\13	1015.4	14\16	1050.0	19\23	991.3	16/9, 9/5, 20/11
Minor 9-sephdegree	m9spd	11\13	1015.4	13\16	975.0	20\23	1043.5	16/9, 9/5, 20/11
Major 9-sephdegree	M9spd	12\13	1107.7	15\16	1125.0	21\23	1095.7	15/8
Perfect 10-sephdegree	P10spd	13\13	1200.0	16\16	1200.0	23\23	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 4L 6s
Scale degree	Abbrev.	Basic (2:1) 14edo		Hard (3:1) 18edo		Soft (3:2) 24edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-limedegree	P0lmd	0\14	0.0	0\18	0.0	0\24	0.0	1/1
Minor 1-limedegree	m1lmd	1\14	85.7	1\18	66.7	2\24	100.0
Major 1-limedegree	M1lmd	2\14	171.4	3\18	200.0	3\24	150.0	12/11, 11/10, 10/9
Diminished 2-limedegree	d2lmd	2\14	171.4	2\18	133.3	4\24	200.0	12/11, 11/10, 10/9
Perfect 2-limedegree	P2lmd	3\14	257.1	4\18	266.7	5\24	250.0	7/6
Perfect 3-limedegree	P3lmd	4\14	342.9	5\18	333.3	7\24	350.0	11/9, 16/13
Augmented 3-limedegree	A3lmd	5\14	428.6	7\18	466.7	8\24	400.0	14/11, 9/7
Minor 4-limedegree	m4lmd	5\14	428.6	6\18	400.0	9\24	450.0	14/11, 9/7
Major 4-limedegree	M4lmd	6\14	514.3	8\18	533.3	10\24	500.0	4/3
Perfect 5-limedegree	P5lmd	7\14	600.0	9\18	600.0	12\24	600.0	7/5, 10/7
Minor 6-limedegree	m6lmd	8\14	685.7	10\18	666.7	14\24	700.0	3/2
Major 6-limedegree	M6lmd	9\14	771.4	12\18	800.0	15\24	750.0	14/9, 11/7
Diminished 7-limedegree	d7lmd	9\14	771.4	11\18	733.3	16\24	800.0	14/9, 11/7
Perfect 7-limedegree	P7lmd	10\14	857.1	13\18	866.7	17\24	850.0	13/8, 18/11
Perfect 8-limedegree	P8lmd	11\14	942.9	14\18	933.3	19\24	950.0	12/7
Augmented 8-limedegree	A8lmd	12\14	1028.6	16\18	1066.7	20\24	1000.0	9/5, 20/11, 11/6
Minor 9-limedegree	m9lmd	12\14	1028.6	15\18	1000.0	21\24	1050.0	9/5, 20/11, 11/6
Major 9-limedegree	M9lmd	13\14	1114.3	17\18	1133.3	22\24	1100.0
Perfect 10-limedegree	P10lmd	14\14	1200.0	18\18	1200.0	24\24	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 5L 5s
Scale degree	Abbrev.	Basic (2:1) 15edo		Hard (3:1) 20edo		Soft (3:2) 25edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-pentawddegree	P0pwd	0\15	0.0	0\20	0.0	0\25	0.0	1/1
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	12/11, 11/10, 10/9
Perfect 2-pentawddegree	P2pwd	3\15	240.0	4\20	240.0	5\25	240.0	8/7
Minor 3-pentawddegree	m3pwd	4\15	320.0	5\20	300.0	7\25	336.0	6/5
Major 3-pentawddegree	M3pwd	5\15	400.0	7\20	420.0	8\25	384.0	5/4, 14/11
Perfect 4-pentawddegree	P4pwd	6\15	480.0	8\20	480.0	10\25	480.0	4/3
Minor 5-pentawddegree	m5pwd	7\15	560.0	9\20	540.0	12\25	576.0	11/8, 18/13, 7/5
Major 5-pentawddegree	M5pwd	8\15	640.0	11\20	660.0	13\25	624.0	10/7, 13/9, 16/11
Perfect 6-pentawddegree	P6pwd	9\15	720.0	12\20	720.0	15\25	720.0	3/2
Minor 7-pentawddegree	m7pwd	10\15	800.0	13\20	780.0	17\25	816.0	11/7, 8/5
Major 7-pentawddegree	M7pwd	11\15	880.0	15\20	900.0	18\25	864.0	5/3
Perfect 8-pentawddegree	P8pwd	12\15	960.0	16\20	960.0	20\25	960.0	7/4
Minor 9-pentawddegree	m9pwd	13\15	1040.0	17\20	1020.0	22\25	1056.0	9/5, 20/11, 11/6
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	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 6L 4s
Scale degree	Abbrev.	Basic (2:1) 16edo		Hard (3:1) 22edo		Soft (3:2) 26edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-lemdegree	P0led	0\16	0.0	0\22	0.0	0\26	0.0	1/1
Minor 1-lemdegree	m1led	1\16	75.0	1\22	54.5	2\26	92.3
Major 1-lemdegree	M1led	2\16	150.0	3\22	163.6	3\26	138.5	14/13, 12/11, 11/10
Perfect 2-lemdegree	P2led	3\16	225.0	4\22	218.2	5\26	230.8	9/8, 8/7
Augmented 2-lemdegree	A2led	4\16	300.0	6\22	327.3	6\26	276.9	6/5
Diminished 3-lemdegree	d3led	4\16	300.0	5\22	272.7	7\26	323.1	6/5
Perfect 3-lemdegree	P3led	5\16	375.0	7\22	381.8	8\26	369.2	16/13, 5/4
Minor 4-lemdegree	m4led	6\16	450.0	8\22	436.4	10\26	461.5	9/7
Major 4-lemdegree	M4led	7\16	525.0	10\22	545.5	11\26	507.7
Perfect 5-lemdegree	P5led	8\16	600.0	11\22	600.0	13\26	600.0	7/5, 10/7
Minor 6-lemdegree	m6led	9\16	675.0	12\22	654.5	15\26	692.3
Major 6-lemdegree	M6led	10\16	750.0	14\22	763.6	16\26	738.5	14/9
Perfect 7-lemdegree	P7led	11\16	825.0	15\22	818.2	18\26	830.8	8/5, 13/8
Augmented 7-lemdegree	A7led	12\16	900.0	17\22	927.3	19\26	876.9	5/3
Diminished 8-lemdegree	d8led	12\16	900.0	16\22	872.7	20\26	923.1	5/3
Perfect 8-lemdegree	P8led	13\16	975.0	18\22	981.8	21\26	969.2	7/4, 16/9
Minor 9-lemdegree	m9led	14\16	1050.0	19\22	1036.4	23\26	1061.5	20/11, 11/6, 13/7
Major 9-lemdegree	M9led	15\16	1125.0	21\22	1145.5	24\26	1107.7
Perfect 10-lemdegree	P10led	16\16	1200.0	22\22	1200.0	26\26	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 7L 3s
Scale degree	Abbrev.	Basic (2:1) 17edo		Hard (3:1) 24edo		Soft (3:2) 27edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-dicodegree	P0did	0\17	0.0	0\24	0.0	0\27	0.0	1/1
Minor 1-dicodegree	m1did	1\17	70.6	1\24	50.0	2\27	88.9
Major 1-dicodegree	M1did	2\17	141.2	3\24	150.0	3\27	133.3	14/13, 12/11
Minor 2-dicodegree	m2did	3\17	211.8	4\24	200.0	5\27	222.2	9/8, 8/7
Major 2-dicodegree	M2did	4\17	282.4	6\24	300.0	6\27	266.7	7/6
Perfect 3-dicodegree	P3did	5\17	352.9	7\24	350.0	8\27	355.6	11/9, 16/13
Augmented 3-dicodegree	A3did	6\17	423.5	9\24	450.0	9\27	400.0	14/11, 9/7
Minor 4-dicodegree	m4did	6\17	423.5	8\24	400.0	10\27	444.4	14/11, 9/7
Major 4-dicodegree	M4did	7\17	494.1	10\24	500.0	11\27	488.9	4/3
Minor 5-dicodegree	m5did	8\17	564.7	11\24	550.0	13\27	577.8	11/8, 18/13, 7/5
Major 5-dicodegree	M5did	9\17	635.3	13\24	650.0	14\27	622.2	10/7, 13/9, 16/11
Minor 6-dicodegree	m6did	10\17	705.9	14\24	700.0	16\27	711.1	3/2
Major 6-dicodegree	M6did	11\17	776.5	16\24	800.0	17\27	755.6	14/9, 11/7
Diminished 7-dicodegree	d7did	11\17	776.5	15\24	750.0	18\27	800.0	14/9, 11/7
Perfect 7-dicodegree	P7did	12\17	847.1	17\24	850.0	19\27	844.4	13/8, 18/11
Minor 8-dicodegree	m8did	13\17	917.6	18\24	900.0	21\27	933.3	12/7
Major 8-dicodegree	M8did	14\17	988.2	20\24	1000.0	22\27	977.8	7/4, 16/9
Minor 9-dicodegree	m9did	15\17	1058.8	21\24	1050.0	24\27	1066.7	11/6, 13/7
Major 9-dicodegree	M9did	16\17	1129.4	23\24	1150.0	25\27	1111.1
Perfect 10-dicodegree	P10did	17\17	1200.0	24\24	1200.0	27\27	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 8L 2s
Scale degree	Abbrev.	Basic (2:1) 18edo		Hard (3:1) 26edo		Soft (3:2) 28edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-taradegree	P0tad	0\18	0.0	0\26	0.0	0\28	0.0	1/1
Diminished 1-taradegree	d1tad	1\18	66.7	1\26	46.2	2\28	85.7
Perfect 1-taradegree	P1tad	2\18	133.3	3\26	138.5	3\28	128.6	14/13, 12/11
Minor 2-taradegree	m2tad	3\18	200.0	4\26	184.6	5\28	214.3	10/9, 9/8
Major 2-taradegree	M2tad	4\18	266.7	6\26	276.9	6\28	257.1	7/6
Minor 3-taradegree	m3tad	5\18	333.3	7\26	323.1	8\28	342.9	6/5, 11/9
Major 3-taradegree	M3tad	6\18	400.0	9\26	415.4	9\28	385.7	5/4, 14/11
Perfect 4-taradegree	P4tad	7\18	466.7	10\26	461.5	11\28	471.4
Augmented 4-taradegree	A4tad	8\18	533.3	12\26	553.8	12\28	514.3	11/8
Perfect 5-taradegree	P5tad	9\18	600.0	13\26	600.0	14\28	600.0	7/5, 10/7
Diminished 6-taradegree	d6tad	10\18	666.7	14\26	646.2	16\28	685.7	16/11
Perfect 6-taradegree	P6tad	11\18	733.3	16\26	738.5	17\28	728.6
Minor 7-taradegree	m7tad	12\18	800.0	17\26	784.6	19\28	814.3	11/7, 8/5
Major 7-taradegree	M7tad	13\18	866.7	19\26	876.9	20\28	857.1	18/11, 5/3
Minor 8-taradegree	m8tad	14\18	933.3	20\26	923.1	22\28	942.9	12/7
Major 8-taradegree	M8tad	15\18	1000.0	22\26	1015.4	23\28	985.7	16/9, 9/5
Perfect 9-taradegree	P9tad	16\18	1066.7	23\26	1061.5	25\28	1071.4	11/6, 13/7
Augmented 9-taradegree	A9tad	17\18	1133.3	25\26	1153.8	26\28	1114.3
Perfect 10-taradegree	P10tad	18\18	1200.0	26\26	1200.0	28\28	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Simple Tunings of 9L 1s
Scale degree	Abbrev.	Basic (2:1) 19edo		Hard (3:1) 28edo		Soft (3:2) 29edo		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-sinadegree	P0sid	0\19	0.0	0\28	0.0	0\29	0.0	1/1
Diminished 1-sinadegree	d1sid	1\19	63.2	1\28	42.9	2\29	82.8
Perfect 1-sinadegree	P1sid	2\19	126.3	3\28	128.6	3\29	124.1	16/15, 14/13
Minor 2-sinadegree	m2sid	3\19	189.5	4\28	171.4	5\29	206.9	10/9, 9/8
Major 2-sinadegree	M2sid	4\19	252.6	6\28	257.1	6\29	248.3	7/6
Minor 3-sinadegree	m3sid	5\19	315.8	7\28	300.0	8\29	331.0	6/5
Major 3-sinadegree	M3sid	6\19	378.9	9\28	385.7	9\29	372.4	5/4
Minor 4-sinadegree	m4sid	7\19	442.1	10\28	428.6	11\29	455.2	9/7
Major 4-sinadegree	M4sid	8\19	505.3	12\28	514.3	12\29	496.6	4/3
Minor 5-sinadegree	m5sid	9\19	568.4	13\28	557.1	14\29	579.3	11/8, 18/13, 7/5
Major 5-sinadegree	M5sid	10\19	631.6	15\28	642.9	15\29	620.7	10/7, 13/9, 16/11
Minor 6-sinadegree	m6sid	11\19	694.7	16\28	685.7	17\29	703.4	3/2
Major 6-sinadegree	M6sid	12\19	757.9	18\28	771.4	18\29	744.8	14/9
Minor 7-sinadegree	m7sid	13\19	821.1	19\28	814.3	20\29	827.6	8/5
Major 7-sinadegree	M7sid	14\19	884.2	21\28	900.0	21\29	869.0	5/3
Minor 8-sinadegree	m8sid	15\19	947.4	22\28	942.9	23\29	951.7	12/7
Major 8-sinadegree	M8sid	16\19	1010.5	24\28	1028.6	24\29	993.1	16/9, 9/5
Perfect 9-sinadegree	P9sid	17\19	1073.7	25\28	1071.4	26\29	1075.9	13/7, 15/8
Augmented 9-sinadegree	A9sid	18\19	1136.8	27\28	1157.1	27\29	1117.2
Perfect 10-sinadegree	P10sid	19\19	1200.0	28\28	1200.0	29\29	1200.0	2/1

* Ratios shown are within the 50-integer limit. Automatic search may be inexact. Other interpretations are possible.

Misc

Parasoft Tunings of 8L 3s⟨3/1⟩
Scale degree	Abbrev.	7:5 71edt		17:12 172edt		10:7 101edt		Approx. ratios*
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Approx. ratios*
Perfect 0-mosdegree	P0md	0\71	0.0	0\172	0.0	0\101	0.0	1/1
Minor 1-mosdegree	m1md	5\71	133.9	12\172	132.7	7\101	131.8	16/15, 15/14, 14/13, 13/12, 12/11
Major 1-mosdegree	M1md	7\71	187.5	17\172	188.0	10\101	188.3	11/10, 10/9, 9/8, 17/15
Minor 2-mosdegree	m2md	12\71	321.5	29\172	320.7	17\101	320.1	6/5, 17/14, 11/9
Major 2-mosdegree	M2md	14\71	375.0	34\172	376.0	20\101	376.6	11/9, 16/13, 5/4
Minor 3-mosdegree	m3md	19\71	509.0	46\172	508.7	27\101	508.4	4/3, 15/11
Major 3-mosdegree	M3md	21\71	562.6	51\172	564.0	30\101	564.9	15/11, 11/8, 18/13, 7/5
Diminished 4-mosdegree	d4md	24\71	642.9	58\172	641.4	34\101	640.3	10/7, 13/9, 16/11, 19/13
Perfect 4-mosdegree	P4md	26\71	696.5	63\172	696.6	37\101	696.8	3/2
Minor 5-mosdegree	m5md	31\71	830.4	75\172	829.3	44\101	828.6	8/5, 13/8, 18/11
Major 5-mosdegree	M5md	33\71	884.0	80\172	884.6	47\101	885.1	5/3
Minor 6-mosdegree	m6md	38\71	1017.9	92\172	1017.3	54\101	1016.9	16/9, 9/5, 20/11
Major 6-mosdegree	M6md	40\71	1071.5	97\172	1072.6	57\101	1073.4	11/6, 13/7, 15/8, 17/9
Perfect 7-mosdegree	P7md	45\71	1205.5	109\172	1205.3	64\101	1205.2	2/1
Augmented 7-mosdegree	A7md	47\71	1259.0	114\172	1260.6	67\101	1261.7	23/11, 21/10
Minor 8-mosdegree	m8md	50\71	1339.4	121\172	1338.0	71\101	1337.0	15/7, 13/6, 11/5
Major 8-mosdegree	M8md	52\71	1393.0	126\172	1393.3	74\101	1393.5	11/5, 20/9, 9/4
Minor 9-mosdegree	m9md	57\71	1526.9	138\172	1526.0	81\101	1525.3	19/8, 12/5, 17/7, 22/9
Major 9-mosdegree	M9md	59\71	1580.5	143\172	1581.3	84\101	1581.8	5/2
Minor 10-mosdegree	m10md	64\71	1714.4	155\172	1714.0	91\101	1713.6	8/3, 19/7
Major 10-mosdegree	M10md	66\71	1768.0	160\172	1769.3	94\101	1770.1	11/4, 25/9, 14/5
Perfect 11-mosdegree	P11md	71\71	1902.0	172\172	1902.0	101\101	1902.0	3/1

* Ratios shown are within the 25-integer limit. Automatic search may be inexact. Other interpretations are possible.

Tunings of 9L 4s⟨7/2⟩
Scale degree	Abbrev.	Supersoft (4:3) 48ed7/2		Soft (3:2) 35ed7/2		Semisoft (5:3) 57ed7/2		Basic (2:1) 22ed7/2		Semihard (5:2) 53ed7/2		Hard (3:1) 31ed7/2		Superhard (4:1) 40ed7/2
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\48	0.0	0\35	0.0	0\57	0.0	0\22	0.0	0\53	0.0	0\31	0.0	0\40	0.0
Minor 1-mosdegree	m1md	3\48	135.6	2\35	123.9	3\57	114.1	1\22	98.6	2\53	81.8	1\31	70.0	1\40	54.2
Major 1-mosdegree	M1md	4\48	180.7	3\35	185.9	5\57	190.2	2\22	197.2	5\53	204.6	3\31	209.9	4\40	216.9
Minor 2-mosdegree	m2md	7\48	316.3	5\35	309.8	8\57	304.4	3\22	295.7	7\53	286.4	4\31	279.8	5\40	271.1
Major 2-mosdegree	M2md	8\48	361.5	6\35	371.8	10\57	380.5	4\22	394.3	10\53	409.2	6\31	419.8	8\40	433.8
Perfect 3-mosdegree	P3md	11\48	497.0	8\35	495.7	13\57	494.6	5\22	492.9	12\53	491.1	7\31	489.7	9\40	488.0
Augmented 3-mosdegree	A3md	12\48	542.2	9\35	557.7	15\57	570.7	6\22	591.5	15\53	613.8	9\31	629.7	12\40	650.6
Minor 4-mosdegree	m4md	14\48	632.6	10\35	619.7	16\57	608.8	6\22	591.5	14\53	572.9	8\31	559.7	10\40	542.2
Major 4-mosdegree	M4md	15\48	677.8	11\35	681.6	18\57	684.9	7\22	690.1	17\53	695.7	10\31	699.6	13\40	704.9
Minor 5-mosdegree	m5md	18\48	813.3	13\35	805.6	21\57	799.0	8\22	788.7	19\53	777.5	11\31	769.6	14\40	759.1
Major 5-mosdegree	M5md	19\48	858.5	14\35	867.5	23\57	875.1	9\22	887.2	22\53	900.3	13\31	909.5	17\40	921.8
Minor 6-mosdegree	m6md	22\48	994.0	16\35	991.5	26\57	989.3	10\22	985.8	24\53	982.1	14\31	979.5	18\40	976.0
Major 6-mosdegree	M6md	23\48	1039.2	17\35	1053.4	28\57	1065.4	11\22	1084.4	27\53	1104.9	16\31	1119.4	21\40	1138.6
Minor 7-mosdegree	m7md	25\48	1129.6	18\35	1115.4	29\57	1103.4	11\22	1084.4	26\53	1064.0	15\31	1049.4	19\40	1030.2
Major 7-mosdegree	M7md	26\48	1174.8	19\35	1177.4	31\57	1179.5	12\22	1183.0	29\53	1186.7	17\31	1189.4	22\40	1192.9
Minor 8-mosdegree	m8md	29\48	1310.3	21\35	1301.3	34\57	1293.7	13\22	1281.6	31\53	1268.6	18\31	1259.3	23\40	1247.1
Major 8-mosdegree	M8md	30\48	1355.5	22\35	1363.3	36\57	1369.8	14\22	1380.2	34\53	1391.3	20\31	1399.2	26\40	1409.7
Minor 9-mosdegree	m9md	33\48	1491.1	24\35	1487.2	39\57	1483.9	15\22	1478.7	36\53	1473.2	21\31	1469.2	27\40	1464.0
Major 9-mosdegree	M9md	34\48	1536.3	25\35	1549.2	41\57	1560.0	16\22	1577.3	39\53	1595.9	23\31	1609.1	30\40	1626.6
Diminished 10-mosdegree	d10md	36\48	1626.6	26\35	1611.1	42\57	1598.1	16\22	1577.3	38\53	1555.0	22\31	1539.2	28\40	1518.2
Perfect 10-mosdegree	P10md	37\48	1671.8	27\35	1673.1	44\57	1674.2	17\22	1675.9	41\53	1677.8	24\31	1679.1	31\40	1680.8
Minor 11-mosdegree	m11md	40\48	1807.4	29\35	1797.0	47\57	1788.3	18\22	1774.5	43\53	1759.6	25\31	1749.1	32\40	1735.1
Major 11-mosdegree	M11md	41\48	1852.5	30\35	1859.0	49\57	1864.4	19\22	1873.1	46\53	1882.4	27\31	1889.0	35\40	1897.7
Minor 12-mosdegree	m12md	44\48	1988.1	32\35	1982.9	52\57	1978.6	20\22	1971.7	48\53	1964.2	28\31	1958.9	36\40	1951.9
Major 12-mosdegree	M12md	45\48	2033.3	33\35	2044.9	54\57	2054.7	21\22	2070.2	51\53	2087.0	30\31	2098.9	39\40	2114.6
Perfect 13-mosdegree	P13md	48\48	2168.8	35\35	2168.8	57\57	2168.8	22\22	2168.8	53\53	2168.8	31\31	2168.8	40\40	2168.8

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 basic 8L 2s.

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.

Sandbox for proposed templates

Cent ruler

50

L

s

L

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)
UDP	Cyclic order	Step pattern	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.	Steps subtended	Range in cents
0-diastep	Perfect 0-diastep	P0dias	0	0.0¢
1-diastep	Minor 1-diastep	m1dias	s	0.0¢ to 171.4¢
1-diastep	Major 1-diastep	M1dias	L	171.4¢ to 240.0¢
2-diastep	Minor 2-diastep	m2dias	L + s	240.0¢ to 342.9¢
2-diastep	Major 2-diastep	M2dias	2L	342.9¢ to 480.0¢
3-diastep	Perfect 3-diastep	P3dias	2L + s	480.0¢ to 514.3¢
3-diastep	Augmented 3-diastep	A3dias	3L	514.3¢ to 720.0¢
4-diastep	Diminished 4-diastep	d4dias	2L + 2s	480.0¢ to 685.7¢
4-diastep	Perfect 4-diastep	P4dias	3L + s	685.7¢ to 720.0¢
5-diastep	Minor 5-diastep	m5dias	3L + 2s	720.0¢ to 857.1¢
5-diastep	Major 5-diastep	M5dias	4L + s	857.1¢ to 960.0¢
6-diastep	Minor 6-diastep	m6dias	4L + 2s	960.0¢ to 1028.6¢
6-diastep	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
1-diastep	Large 1-diastep	L	171.4¢ to 240.0¢	L1ms
2-diastep	Small 2-diastep	L + s	240.0¢ to 342.9¢	s2ms
2-diastep	Large 2-diastep	2L	342.9¢ to 480.0¢	L2ms
3-diastep	Small 3-diastep	2L + s	480.0¢ to 514.3¢	s3ms
3-diastep	Large 3-diastep	3L	514.3¢ to 720.0¢	L3ms
4-diastep	Small 4-diastep	2L + 2s	480.0¢ to 685.7¢	s4ms
4-diastep	Large 4-diastep	3L + s	685.7¢ to 720.0¢	L4ms
5-diastep	Small 5-diastep	3L + 2s	720.0¢ to 857.1¢	s5ms
5-diastep	Large 5-diastep	4L + s	857.1¢ to 960.0¢	L5ms
6-diastep	Small 6-diastep	4L + 2s	960.0¢ to 1028.6¢	s6ms
6-diastep	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.	Step pattern	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

┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘

┌
│
│
└

╥
║
│
┴

┬
│
│
┴

┐
│
│
┘

Not enough room for note names.

Large vis

┌──┬─┬─┬─┬─┬─┬──┬──┬─┬─┬─┬──┬───┐
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
│░░│▒│░│▒│░│▒│░░│░░│▒│░│▒│░░│░░░│
│░░└┬┘░└┬┘░└┬┘░░│░░└┬┘░└┬┘░░│░░░│
│░░░│░░░│░░░│░░░│░░░│░░░│░░░│░░░│
│░█░│░░░│░░░│░░░│░░░│░░░│░░░│░█░│
└───┴───┴───┴───┴───┴───┴───┴───┘

┌──
│  
│  
│  
│  
│ X
└──

┬─┬─
│ │ 
│ │ 
└┬┘ 
 │  
 │ X
─┴──

─┬──
 │ 
 │ 
 │ 
 │  
 │ X
─┴──

─┐
 │
 │
 │
 │
 │
─┘

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)

┌────┬───┬──┬───┬──┬─┬─┬────┬────┬─┬─┬──┬─┬─┬────┬──────┐
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░├─┼─┤░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒│▒│░░░░│░░░░│▒│▒│░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░├───┤░░├─┴─┤░░░░│░░░░├─┼─┤░░│▒│▒│░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░├─┴─┤░░░░│░░░░░░│
│░░░░│▒▒▒│░░│▒▒▒│░░│▒▒▒│░░░░│░░░░│▒│▒│░░│▒▒▒│░░░░│░░░░░░│
│░░░░└─┬─┘░░└─┬─┘░░└─┬─┘░░░░│░░░░└─┼─┘░░└─┬─┘░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│░░░░░░│
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘

┌────
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
│░░░░
└────

────┬──
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
░░░░│░░
────┴──

┬───┬──
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────

┬───┬──
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
├───┤░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────

┬─┬─┬──
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
├─┴─┤░░
│▓▓▓│░░
│▓▓▓│░░
│▓▓▓│░░
└─┬─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────

┬─┬─┬──
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
├─┼─┤░░
│▓│▓│░░
│▓│▓│░░
│▓│▓│░░
└─┼─┘░░
░░│░░░░
░░│░░░░
░░│░░░░
░░│░░░░
──┴────

──┐
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
░░│
──┘

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
Interval	Steps	Cents	Steps	Cents	Steps	Cents	Approx. JI ratios
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
			xL (x+y)s	(2x+y)L xs
			(x+y)L xs	(2x+y)L (x+y)s
			(x+y)L xs	(x+y)L (2x+y)s

Navbox MOS

Moment-of-symmetry scales

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
Value	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
Interval in mossteps	Mossteps	Chroma	Decoding	Standard notation in the key of F
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
Default	Names	Bri.	Rot.	Step pattern	1	2	3	4	5	6	7
5L 2s 6\|0	Lydian	1	1	LLLsLLs	0	0	0	0	0	0	0
5L 2s 5\|1	Ionian (major)	2	5	LLsLLLs	0	0	-1	0	0	0	0
5L 2s 4\|2	Mixolydian	3	2	LLsLLsL	0	1	-1	0	0	-1	0
5L 2s 3\|3	Dorian	4	6	LsLLLsL	0	-1	-1	0	0	-1	0
5L 2s 2\|4	Aeolian (minor)	5	3	LsLLsLL	0	-1	-1	0	-1	-1	0
5L 2s 1\|5	Phrygian	6	7	sLLLsLL	-1	-1	-1	0	-1	-1	0
5L 2s 0\|6	Locrian	7	4	sLLsLLL	-1	-1	-1	-1	-1	-1	0

User:Ganaram inukshuk/Sandbox

Contents

Deprecated template params

MOS intro

MOS tunings

5L 3s only

6-note mosses

7-note mosses

8-note mosses

9-note mosses

10-note mosses

Misc

Name

6-note mosses

7-note mosses

8-note mosses

9-note mosses

10-note mosses

Sandbox for proposed templates

Cent ruler

MOS characteristics

MOS intervals (using large/small instead of MmAPd)

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

KB vis

TAMNAMS use

JI ratio intro

MOS step sizes

Mos ancestors and descendants

Navbox MOS

Encoding scheme for module:mos

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

Navigation menu

Search