User:Ganaram inukshuk/Sandbox: Difference between revisions

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== MOS tunings==
== MOS tunings==
{{{{#ifeq: 1 |1|subst:|}}#invoke: MOS_tunings| mos_tunings
NOTE: tables can be substituted, but it's at least a two-step process.
{{#invoke: MOS_tunings| mos_tunings
| Scale Signature=5L 3s
| Scale Signature=5L 3s
| MOS Prefix=
| MOS Prefix=
Line 30: Line 31:
| Collapsed=
| Collapsed=
| Step Ratios=
| Step Ratios=
| JI Ratios=
| JI Ratios=Subgroup: 2.5.9.13.21; Int Limit: 30
}}
}}


Line 44: Line 45:
{{MOS tunings|Scale Signature=5L 3s|Step Ratios=Hard-of-basic}}
{{MOS tunings|Scale Signature=5L 3s|Step Ratios=Hard-of-basic}}


===6-note mosses===
=== 6-note mosses===


{{MOS tunings|Scale Signature=1L 5s}}
{{MOS tunings|Scale Signature=1L 5s}}
Line 56: Line 57:
{{MOS tunings|Scale Signature=5L 1s}}
{{MOS tunings|Scale Signature=5L 1s}}


===7-note mosses===
=== 7-note mosses===


{{MOS tunings|Scale Signature=1L 6s}}
{{MOS tunings|Scale Signature=1L 6s}}
Line 70: Line 71:
{{MOS tunings|Scale Signature=6L 1s}}
{{MOS tunings|Scale Signature=6L 1s}}


===8-note mosses===
=== 8-note mosses===


{{MOS tunings|Scale Signature=1L 7s}}
{{MOS tunings|Scale Signature=1L 7s}}
Line 86: Line 87:
{{MOS tunings|Scale Signature=7L 1s}}
{{MOS tunings|Scale Signature=7L 1s}}


===9-note mosses===
=== 9-note mosses===


{{MOS tunings|Scale Signature=1L 8s}}
{{MOS tunings|Scale Signature=1L 8s}}
Line 104: Line 105:
{{MOS tunings|Scale Signature=8L 1s}}
{{MOS tunings|Scale Signature=8L 1s}}


=== 10-note mosses===
===10-note mosses===


{{MOS tunings|Scale Signature=1L 9s}}
{{MOS tunings|Scale Signature=1L 9s}}
Line 124: Line 125:
{{MOS tunings|Scale Signature=9L 1s}}
{{MOS tunings|Scale Signature=9L 1s}}


===Misc ===
===Misc===


{{MOS tunings|Scale Signature=8L 3s <3/1>|Step Ratios=17/12; 10/7; 7/5|JI Ratios=Int Limit: 25; Tenney Height: 8}}
{{MOS tunings|Scale Signature=8L 3s <3/1>|Step Ratios=17/12; 10/7; 7/5|JI Ratios=Int Limit: 25; Tenney Height: 8}}
Line 131: Line 132:


==Name==
==Name==
===6-note mosses===
=== 6-note mosses===
{{Template:TAMNAMS name|1L 5s}}
{{Template:TAMNAMS name|1L 5s}}


Line 142: Line 143:
{{Template:TAMNAMS name|5L 1s}}
{{Template:TAMNAMS name|5L 1s}}


===7-note mosses===
=== 7-note mosses===
{{Template:TAMNAMS name|1L 6s}}
{{Template:TAMNAMS name|1L 6s}}


Line 155: Line 156:
{{Template:TAMNAMS name|6L 1s}}
{{Template:TAMNAMS name|6L 1s}}


===8-note mosses===
=== 8-note mosses===
{{Template:TAMNAMS name|1L 7s}}
{{Template:TAMNAMS name|1L 7s}}


Line 170: Line 171:
{{Template:TAMNAMS name|7L 1s}}
{{Template:TAMNAMS name|7L 1s}}


=== 9-note mosses===
===9-note mosses===
{{Template:TAMNAMS name|1L 8s}}
{{Template:TAMNAMS name|1L 8s}}


Line 332: Line 333:
|Perfect 0-diastep
|Perfect 0-diastep
|0
|0
| 0.0¢
|0.0¢
|P0ms
|P0ms
|-
|-
Line 343: Line 344:
|Large 1-diastep
|Large 1-diastep
|L
|L
| 171.4¢ to 240.0¢
|171.4¢ to 240.0¢
| L1ms
|L1ms
|-
|-
| rowspan="2" |2-diastep
| rowspan="2" |2-diastep
Line 350: Line 351:
|L + s
|L + s
|240.0¢ to 342.9¢
|240.0¢ to 342.9¢
| s2ms
|s2ms
|-
|-
|Large 2-diastep
|Large 2-diastep
Line 370: Line 371:
| rowspan="2" |'''4-diastep'''
| rowspan="2" |'''4-diastep'''
|Small 4-diastep
|Small 4-diastep
| 2L + 2s
|2L + 2s
|480.0¢ to 685.7¢
|480.0¢ to 685.7¢
|s4ms
|s4ms
Line 376: Line 377:
|'''Large 4-diastep'''
|'''Large 4-diastep'''
|3L + s
|3L + s
| 685.7¢ to 720.0¢
|685.7¢ to 720.0¢
|L4ms
|L4ms
|-
|-
Line 393: Line 394:
|Small 6-diastep
|Small 6-diastep
|4L + 2s
|4L + 2s
| 960.0¢ to 1028.6¢
|960.0¢ to 1028.6¢
|s6ms
|s6ms
|-
|-
Line 405: Line 406:
|5L + 2s
|5L + 2s
|1200.0¢
|1200.0¢
| P7ms
|P7ms
|}
|}


Line 419: Line 420:
!Names
!Names
!Bri.
!Bri.
!Rot.
! Rot.
! 0
!0
!1
! 1
!2
!2
! 3
!3
!4
!4
! 5
!5
! 6
!6
!7
!7
|-
|-
Line 435: Line 436:
|LLLsLLs
|LLLsLLs
|Perf.
|Perf.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
| Lg.
|Lg.
|Lg.
|Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
| Ionian (major)
|2
|2
|5
|5
Line 452: Line 453:
|Lg.
|Lg.
|Sm.
|Sm.
| Lg.
|Lg.
|Lg.
|Lg.
|Lg.
|Lg.
Line 459: Line 460:
|<nowiki>5L 2s 4|2</nowiki>
|<nowiki>5L 2s 4|2</nowiki>
|Mixolydian
|Mixolydian
| 3
|3
|2
|2
|LLsLLsL
|LLsLLsL
|Perf.
|Perf.
| Lg.
|Lg.
|Lg.
|Lg.
|Sm.
|Sm.
Line 469: Line 470:
|Lg.
|Lg.
|Sm.
|Sm.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 3|3</nowiki>
|<nowiki>5L 2s 3|3</nowiki>
|Dorian
|Dorian
|4
|4
| 6
|6
| LsLLLsL
|LsLLLsL
| Perf.
|Perf.
| Lg.
|Lg.
|Sm.
|Sm.
|Sm.
|Sm.
Line 483: Line 484:
|Lg.
|Lg.
| Sm.
| Sm.
| Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
| Aeolian (minor)
|Aeolian (minor)
|5
|5
| 3
|3
|LsLLsLL
|LsLLsLL
|Perf.
|Perf.
Line 496: Line 497:
|Lg.
|Lg.
|Sm.
|Sm.
| Sm.
|Sm.
|Perf.
|Perf.
|-
|-
|<nowiki>5L 2s 1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
| Phrygian
|Phrygian
| 6
|6
|7
|7
| sLLLsLL
|sLLLsLL
|Perf.
|Perf.
|Sm.
|Sm.
Line 509: Line 510:
|Sm.
|Sm.
|Lg.
|Lg.
| Sm.
|Sm.
|Sm.
| Perf.
|Sm.
|Perf.
|-
|-
|<nowiki>5L 2s 0|6</nowiki>
|<nowiki>5L 2s 0|6</nowiki>
Line 531: Line 532:
{| class="wikitable"
{| class="wikitable"
|+
|+
! rowspan="2" |Type
! rowspan="2" | Type
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="4" | Individual steps
! colspan="4" |Individual steps
! rowspan="2" | Notes
! rowspan="2" |Notes
|-
|-
!Start
!Start
Line 604: Line 605:
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Type
! rowspan="2" | Type
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="7" |Individual steps
! colspan="7" |Individual steps
Line 610: Line 611:
|-
|-
!Start
!Start
! Size 1
!Size 1
!Size 2
!Size 2
!Size 3
!Size 3
Line 752: Line 753:


</pre>
</pre>
| X's are placeholders for note names.
|X's are placeholders for note names.
Naturals only, as there is not enough room for accidentals.
Naturals only, as there is not enough room for accidentals.


Line 805: Line 806:
|
|
|-
|-
|Bright generator
| Bright generator
|3
|3
|360¢
|360¢
Line 835: Line 836:
|(2x+y)L xs
|(2x+y)L xs
|-
|-
| rowspan="2" |(x+y)L xs
| rowspan="2" | (x+y)L xs
|(2x+y)L (x+y)s
|(2x+y)L (x+y)s
|-
|-
|(x+y)L (2x+y)s
| (x+y)L (2x+y)s
|}
|}


===Navbox MOS===
=== Navbox MOS===
<div class="wikitable mw-collapsible" style="overflow:auto">
<div class="wikitable mw-collapsible" style="overflow:auto">
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>[[MOS scale|Moment-of-symmetry scales]]</b></center></div>
<div style="width: 100%; background-color:#eaecf0; padding-top:0.2em; padding-bottom:0.2em;"><center><b>[[MOS scale|Moment-of-symmetry scales]]</b></center></div>
Line 904: Line 905:
!Intervals with 1 size
!Intervals with 1 size
!Nonperfectable intervals
!Nonperfectable intervals
!Bright gen
! Bright gen
!Dark gen
!Dark gen
! Period intervals
!Period intervals
|-
|-
|2
|2
|Large plus 2 chromas
|Large plus 2 chromas
|Perfect plus 2 chromas
|Perfect plus 2 chromas
| 2× Augmented
|2× Augmented
|2× Augmented
|2× Augmented
|3× Augmented
|3× Augmented
Line 972: Line 973:
|-
|-
!Mossteps
!Mossteps
! Chroma
!Chroma
|-
|-
|0
|0
| 0
|0
|0
|0
|Perfect 0-diastep
|Perfect 0-diastep
|F
|F
|-
|-
|s
| s
|1
|1
| -1
| -1
Line 987: Line 988:
|-
|-
|L
|L
|1
| 1
|0
|0
| Major 1-diastep
| Major 1-diastep
Line 1,010: Line 1,011:
|Bb
|Bb
|-
|-
| 3L
|3L
| 3
|3
|0
|0
|Augmented 3-diastep
|Augmented 3-diastep
Line 1,019: Line 1,020:
|4
|4
| -1
| -1
| Diminished 4-diastep
|Diminished 4-diastep
|Cb
|Cb
|-
|-
|3L + s
|3L + s
|4
|4
| 0
|0
|Perfect 4-diastep
|Perfect 4-diastep
| C
|C
|-
|-
| 3L + 2s
|3L + 2s
|5
|5
| -1
| -1
|Minor 5-diastep
|Minor 5-diastep
|Db
|Db
|-
|-
| 4L + s
|4L + s
|5
|5
|0
|0
Line 1,053: Line 1,054:
|-
|-
|5L + 2s
|5L + 2s
| 7
|7
|0
|0
|Perfect 7-diastep
|Perfect 7-diastep
Line 1,061: Line 1,062:
! colspan="2" |Mode names
! colspan="2" |Mode names
! colspan="2" |Ordering
! colspan="2" |Ordering
! rowspan="2" | Step pattern
! rowspan="2" |Step pattern
! colspan="8" |Scale degree (encoded)
! colspan="8" |Scale degree (encoded)
|-
|-
!Default
!Default
! Names
!Names
!Bri.
!Bri.
!Rot.
!Rot.
Line 1,079: Line 1,080:
|<nowiki>5L 2s 6|0</nowiki>
|<nowiki>5L 2s 6|0</nowiki>
|Lydian
|Lydian
| 1
|1
|1
|1
|LLLsLLs
| LLLsLLs
|0
|0
|0
|0
Line 1,087: Line 1,088:
|0
|0
|0
|0
| 0
|0
|0
|0
|0
| 0
|-
|-
|<nowiki>5L 2s 5|1</nowiki>
|<nowiki>5L 2s 5|1</nowiki>
|Ionian (major)
| Ionian (major)
| 2
|2
|5
|5
|LLsLLLs
|LLsLLLs
|0
|0
| 0
|0
|0
|0
| -1
|  -1
|0
|0
|0
|0
Line 1,111: Line 1,112:
|LLsLLsL
|LLsLLsL
|0
|0
|0
| 0
|1
|1
| -1
| -1
| 0
|0
|0
| -1
|0
|0
| -1
| 0
|-
|-
|<nowiki>5L 2s 3|3</nowiki>
|<nowiki>5L 2s 3|3</nowiki>
Line 1,125: Line 1,126:
|LsLLLsL
|LsLLLsL
|0
|0
| 0
|0
| -1
| -1
| -1
| -1
| 0
|0
|0
| -1
|0
|0
| -1
| 0
|-
|-
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
Line 1,138: Line 1,139:
|3
|3
|LsLLsLL
|LsLLsLL
| 0
|0
|0
|0
| -1
| -1
| -1
| -1
| 0
|0
|  -1
|  -1
| -1
| -1

Revision as of 07:57, 19 September 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

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
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

5L 3s only

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


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


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


Hypohard Tunings of 5L 3s
Scale degree Abbrev. Basic (2:1)
13edo 		Semihard (5:2)
31edo 		Hard (3:1)
18edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-oneirodegree P0oneid 0\13 0.0 0\31 0.0 0\18 0.0
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
Minor 2-oneirodegree m2oneid 3\13 276.9 7\31 271.0 4\18 266.7
Major 2-oneirodegree M2oneid 4\13 369.2 10\31 387.1 6\18 400.0
Diminished 3-oneirodegree d3oneid 4\13 369.2 9\31 348.4 5\18 333.3
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
Major 4-oneirodegree M4oneid 7\13 646.2 17\31 658.1 10\18 666.7
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
Minor 6-oneirodegree m6oneid 9\13 830.8 21\31 812.9 12\18 800.0
Major 6-oneirodegree M6oneid 10\13 923.1 24\31 929.0 14\18 933.3
Minor 7-oneirodegree m7oneid 11\13 1015.4 26\31 1006.5 15\18 1000.0
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


Hard-of-basic Tunings of 5L 3s
Scale degree Abbrev. Basic (2:1)
13edo 		Hard (3:1)
18edo 		Superhard (4:1)
23edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-oneirodegree P0oneid 0\13 0.0 0\18 0.0 0\23 0.0
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
Minor 2-oneirodegree m2oneid 3\13 276.9 4\18 266.7 5\23 260.9
Major 2-oneirodegree M2oneid 4\13 369.2 6\18 400.0 8\23 417.4
Diminished 3-oneirodegree d3oneid 4\13 369.2 5\18 333.3 6\23 313.0
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
Major 4-oneirodegree M4oneid 7\13 646.2 10\18 666.7 13\23 678.3
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
Minor 6-oneirodegree m6oneid 9\13 830.8 12\18 800.0 15\23 782.6
Major 6-oneirodegree M6oneid 10\13 923.1 14\18 933.3 18\23 939.1
Minor 7-oneirodegree m7oneid 11\13 1015.4 15\18 1000.0 19\23 991.3
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

6-note mosses

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


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


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


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


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

7-note mosses

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


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


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


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


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


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

8-note mosses

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


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


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


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


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


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


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

9-note mosses

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


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


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


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


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


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


Simple Tunings of 7L 2s
Scale degree Abbrev. Basic (2:1)
16edo 		Hard (3:1)
23edo 		Soft (3:2)
25edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-armdegree P0armd 0\16 0.0 0\23 0.0 0\25 0.0
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
Minor 2-armdegree m2armd 3\16 225.0 4\23 208.7 5\25 240.0
Major 2-armdegree M2armd 4\16 300.0 6\23 313.0 6\25 288.0
Minor 3-armdegree m3armd 5\16 375.0 7\23 365.2 8\25 384.0
Major 3-armdegree M3armd 6\16 450.0 9\23 469.6 9\25 432.0
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
Diminished 5-armdegree d5armd 8\16 600.0 11\23 573.9 13\25 624.0
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
Major 6-armdegree M6armd 11\16 825.0 16\23 834.8 17\25 816.0
Minor 7-armdegree m7armd 12\16 900.0 17\23 887.0 19\25 912.0
Major 7-armdegree M7armd 13\16 975.0 19\23 991.3 20\25 960.0
Minor 8-armdegree m8armd 14\16 1050.0 20\23 1043.5 22\25 1056.0
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


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

10-note mosses

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


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


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


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


Simple Tunings of 5L 5s
Scale degree Abbrev. Basic (2:1)
15edo 		Hard (3:1)
20edo 		Soft (3:2)
25edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-pentawddegree P0pwd 0\15 0.0 0\20 0.0 0\25 0.0
Minor 1-pentawddegree m1pwd 1\15 80.0 1\20 60.0 2\25 96.0
Major 1-pentawddegree M1pwd 2\15 160.0 3\20 180.0 3\25 144.0
Perfect 2-pentawddegree P2pwd 3\15 240.0 4\20 240.0 5\25 240.0
Minor 3-pentawddegree m3pwd 4\15 320.0 5\20 300.0 7\25 336.0
Major 3-pentawddegree M3pwd 5\15 400.0 7\20 420.0 8\25 384.0
Perfect 4-pentawddegree P4pwd 6\15 480.0 8\20 480.0 10\25 480.0
Minor 5-pentawddegree m5pwd 7\15 560.0 9\20 540.0 12\25 576.0
Major 5-pentawddegree M5pwd 8\15 640.0 11\20 660.0 13\25 624.0
Perfect 6-pentawddegree P6pwd 9\15 720.0 12\20 720.0 15\25 720.0
Minor 7-pentawddegree m7pwd 10\15 800.0 13\20 780.0 17\25 816.0
Major 7-pentawddegree M7pwd 11\15 880.0 15\20 900.0 18\25 864.0
Perfect 8-pentawddegree P8pwd 12\15 960.0 16\20 960.0 20\25 960.0
Minor 9-pentawddegree m9pwd 13\15 1040.0 17\20 1020.0 22\25 1056.0
Major 9-pentawddegree M9pwd 14\15 1120.0 19\20 1140.0 23\25 1104.0
Perfect 10-pentawddegree P10pwd 15\15 1200.0 20\20 1200.0 25\25 1200.0


Simple Tunings of 6L 4s
Scale degree Abbrev. Basic (2:1)
16edo 		Hard (3:1)
22edo 		Soft (3:2)
26edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-lemdegree P0led 0\16 0.0 0\22 0.0 0\26 0.0
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
Perfect 2-lemdegree P2led 3\16 225.0 4\22 218.2 5\26 230.8
Augmented 2-lemdegree A2led 4\16 300.0 6\22 327.3 6\26 276.9
Diminished 3-lemdegree d3led 4\16 300.0 5\22 272.7 7\26 323.1
Perfect 3-lemdegree P3led 5\16 375.0 7\22 381.8 8\26 369.2
Minor 4-lemdegree m4led 6\16 450.0 8\22 436.4 10\26 461.5
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
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
Perfect 7-lemdegree P7led 11\16 825.0 15\22 818.2 18\26 830.8
Augmented 7-lemdegree A7led 12\16 900.0 17\22 927.3 19\26 876.9
Diminished 8-lemdegree d8led 12\16 900.0 16\22 872.7 20\26 923.1
Perfect 8-lemdegree P8led 13\16 975.0 18\22 981.8 21\26 969.2
Minor 9-lemdegree m9led 14\16 1050.0 19\22 1036.4 23\26 1061.5
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


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


Simple Tunings of 8L 2s
Scale degree Abbrev. Basic (2:1)
18edo 		Hard (3:1)
26edo 		Soft (3:2)
28edo
Steps ¢ Steps ¢ Steps ¢
Perfect 0-taradegree P0tad 0\18 0.0 0\26 0.0 0\28 0.0
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
Minor 2-taradegree m2tad 3\18 200.0 4\26 184.6 5\28 214.3
Major 2-taradegree M2tad 4\18 266.7 6\26 276.9 6\28 257.1
Minor 3-taradegree m3tad 5\18 333.3 7\26 323.1 8\28 342.9
Major 3-taradegree M3tad 6\18 400.0 9\26 415.4 9\28 385.7
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
Perfect 5-taradegree P5tad 9\18 600.0 13\26 600.0 14\28 600.0
Diminished 6-taradegree d6tad 10\18 666.7 14\26 646.2 16\28 685.7
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
Major 7-taradegree M7tad 13\18 866.7 19\26 876.9 20\28 857.1
Minor 8-taradegree m8tad 14\18 933.3 20\26 923.1 22\28 942.9
Major 8-taradegree M8tad 15\18 1000.0 22\26 1015.4 23\28 985.7
Perfect 9-taradegree P9tad 16\18 1066.7 23\26 1061.5 25\28 1071.4
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


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

Misc

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

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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Large 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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