User:Ganaram inukshuk/Sandbox: Difference between revisions

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== Scale properties templates ==
== Scale properties templates ==
{{MOS intervals|Scale Signature=5L 3s}}{{MOS genchain|Scale Signature=5L 3s}}
{{MOS intervals
|Scale Signature=5L 3s
|MOS Prefix = test
|MOS Abbrev = ts
}}


{{MOS mode degrees|Scale Signature=5L 3s}}
{{MOS genchain
|Scale Signature=5L 3s
|MOS Prefix = test
|MOS Abbrev = ts
}}


== 5L 2s modes and modmos modes ==
{{MOS mode degrees
{{MOS mode degrees|Scale Signature=5L 2s}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs}}
|Scale Signature=5L 3s
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LALdLAd}}
|MOS Prefix = test
|MOS Abbrev = ts
}}
 
 
== 5L 2s modes and modmos modes==
{{MOS mode degrees|Scale Signature=5L 2s}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLLLs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLsLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AAdAdAd}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LLLLLLd}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LALdLAd}}


== 4L 4s modes and modmos modes ==
== 4L 4s modes and modmos modes ==
{{MOS mode degrees|Scale Signature=4L 4s}}{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLLss}}{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLsLs}}
{{MOS mode degrees|Scale Signature=4L 4s}}
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLLss}}
{{MOS mode degrees|Scale Signature=4L 4s|MODMOS Step Pattern=LLssLsLs}}


==Sandbox for proposed templates==
==Sandbox for proposed templates==
Line 45: Line 67:


<div style="height: 100px; width: 1200px; background-color: powderblue; font-size: 0;">
<div style="height: 100px; width: 1200px; background-color: powderblue; font-size: 0;">
<div style="border-bottom: 100px solid #555; border-left: 0px solid transparent; border-right: 30px solid transparent; display: inline-block; height: 0px; width: 33.333%;></div>
<div style="border-bottom: 100px solid #555; border-left: 0px solid transparent; border-right: 30px solid transparent; display: inline-block; height: 0px; width: 33.333%;"></div>
</div>
</div>


Line 145: Line 167:
|Small 1-diastep
|Small 1-diastep
|s
|s
|0.0¢ to 171.4¢
| 0.0¢ to 171.4¢
|s1ms
|s1ms
|-
|-
Line 153: Line 175:
|L1ms
|L1ms
|-
|-
| rowspan="2" | 2-diastep
| rowspan="2" |2-diastep
|Small 2-diastep
|Small 2-diastep
|L + s
|L + s
Line 160: Line 182:
|-
|-
|Large 2-diastep
|Large 2-diastep
| 2L
|2L
|342.9¢ to 480.0¢
|342.9¢ to 480.0¢
|L2ms
|L2ms
Line 177: Line 199:
| 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
|-
|-
|'''Large 4-diastep'''
|'''Large 4-diastep'''
|3L + s
| 3L + s
|685.7¢ to 720.0¢
|685.7¢ to 720.0¢
|L4ms
|L4ms
Line 188: Line 210:
| rowspan="2" |5-diastep
| rowspan="2" |5-diastep
|Small 5-diastep
|Small 5-diastep
|3L + 2s
| 3L + 2s
|720.0¢ to 857.1¢
|720.0¢ to 857.1¢
|s5ms
|s5ms
Line 205: Line 227:
| Large 6-diastep
| Large 6-diastep
|5L + s
|5L + s
| 1028.6¢ to 1200.0¢
|1028.6¢ to 1200.0¢
|L6ms
|L6ms
|-
|-
Line 212: Line 234:
|5L + 2s
|5L + 2s
|1200.0¢
|1200.0¢
| P7ms
|P7ms
|}
|}


Line 262: Line 284:
|Lg.
|Lg.
|Lg.
|Lg.
|Perf.
| Perf.
|-
|-
|<nowiki>5L 2s 4|2</nowiki>
|<nowiki>5L 2s 4|2</nowiki>
Line 304: Line 326:
|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.
|Sm.
|Sm.
|Sm.
| Sm.
|Lg.
|Lg.
|Sm.
|Sm.
Line 326: Line 348:
|sLLsLLL
|sLLsLLL
|Perf.
|Perf.
| Sm.
|Sm.
|Sm.
|Sm.
|Sm.
|Sm.
Line 332: Line 354:
| Sm.
| Sm.
|Sm.
|Sm.
| Perf.
|Perf.
|}
|}


===KB vis ===
===KB vis===
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 341: Line 363:
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="4" |Individual steps
! colspan="4" |Individual steps
! rowspan="2" |Notes
! rowspan="2" | Notes
|-
|-
!Start
!Start
!Large step
!Large step
!Small step
!Small step
!End
! End
|-
|-
|Small vis
|Small vis
Line 413: Line 435:
! rowspan="2" |Type
! rowspan="2" |Type
! rowspan="2" |Visualization
! rowspan="2" |Visualization
! colspan="7" | Individual steps
! colspan="7" |Individual steps
! rowspan="2" |Notes
! rowspan="2" |Notes
|-
|-
Line 579: Line 601:
|+3L 4s step sizes
|+3L 4s step sizes
! rowspan="2" |Interval
! rowspan="2" |Interval
! colspan="2" | Basic 3L 4s
! colspan="2" |Basic 3L 4s
(10edo, L:s = 2:1)
(10edo, L:s = 2:1)
! colspan="2" |Hard 3L 4s
! colspan="2" |Hard 3L 4s
Line 599: Line 621:
|3
|3
|276.9¢
|276.9¢
| 3
|3
|211.8¢
|211.8¢
|Hide column if no ratios given
|Hide column if no ratios given
Line 607: Line 629:
|120¢
|120¢
|1
|1
|92.3¢
| 92.3¢
|2
|2
|141.2¢
| 141.2¢
|
|
|-
|-
| Bright generator
|Bright generator
|3
|3
|360¢
|360¢
Line 626: Line 648:
*JI ratios column only shows if there are any ratios to show
*JI ratios column only shows if there are any ratios to show


===Mos ancestors and descendants ===
===Mos ancestors and descendants===
{| class="wikitable"
{| class="wikitable"
!2nd ancestor
!2nd ancestor
Line 692: Line 714:
</div>
</div>


== Encoding scheme for module:mos==
==Encoding scheme for module:mos==


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


Line 706: Line 728:
! rowspan="2" |Value
! rowspan="2" |Value
! colspan="2" |Encoded
! colspan="2" |Encoded
! colspan="4" | Decoded
! colspan="4" |Decoded
|-
|-
!Intervals with 2 sizes
!Intervals with 2 sizes
Line 721: Line 743:
|2× Augmented
|2× Augmented
|3× Augmented
|3× Augmented
| 2× Augmented
|2× Augmented
|-
|-
|1
|1
Line 739: Line 761:
|'''Perfect'''
|'''Perfect'''
|-
|-
| -1
| -1
|'''Small'''
|'''Small'''
|Perfect minus 1 chroma
|Perfect minus 1 chroma
Line 748: Line 770:
|-
|-
| -2
| -2
| Small minus 1 chroma
|Small minus 1 chroma
|Perfect minus 2 chromas
|Perfect minus 2 chromas
| Diminished
|Diminished
|2× Diminished
|2× Diminished
|Diminished
|Diminished
Line 759: Line 781:
|Perfect minus 3 chromas
|Perfect minus 3 chromas
|2× Diminished
|2× Diminished
| 3× Diminished
|3× Diminished
|2× Diminished
|2× Diminished
|3× Diminished
|3× Diminished
Line 765: Line 787:
Rationale:
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.
* 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.
**Alterations by entire large steps or small steps is considered interval arithmetic.


Line 781: Line 803:
!Chroma
!Chroma
|-
|-
|0
| 0
|0
|0
|0
|0
Line 787: Line 809:
|F
|F
|-
|-
|s
| s
|1
|1
| -1
| -1
Line 793: Line 815:
|Gb
|Gb
|-
|-
| L
|L
|1
|1
|0
|0
Line 818: Line 840:
|-
|-
|3L
|3L
|3
| 3
|0
|0
|Augmented 3-diastep
|Augmented 3-diastep
Line 824: Line 846:
|-
|-
|2L + 2s
|2L + 2s
|4
| 4
| -1
| -1
|Diminished 4-diastep
|Diminished 4-diastep
Line 839: Line 861:
| -1
| -1
|Minor 5-diastep
|Minor 5-diastep
| Db
|Db
|-
|-
|4L + s
|4L + s
Line 847: Line 869:
|D
|D
|-
|-
| 4L + 2s
|4L + 2s
|6
|6
| -1
| -1
Line 855: Line 877:
|5L + s
|5L + s
|6
|6
|0
| 0
|Major 6-diastep
|Major 6-diastep
|E
|E
Line 890: Line 912:
|LLLsLLs
|LLLsLLs
|0
|0
|0
| 0
|0
| 0
|0
|0
|0
|0
Line 904: Line 926:
|LLsLLLs
|LLsLLLs
|0
|0
|0
| 0
|0
| 0
| -1
| -1
|0
|0
Line 918: Line 940:
|LLsLLsL
|LLsLLsL
|0
|0
|0
| 0
|1
| 1
| -1
| -1
|0
|0
Line 930: Line 952:
|4
|4
|6
|6
|LsLLLsL
| LsLLLsL
|0
|0
|0
|0
Line 942: Line 964:
|<nowiki>5L 2s 2|4</nowiki>
|<nowiki>5L 2s 2|4</nowiki>
|Aeolian (minor)
|Aeolian (minor)
| 5
|5
|3
|3
|LsLLsLL
|LsLLsLL
Line 949: Line 971:
| -1
| -1
| -1
| -1
|0
| 0
| -1
| -1
| -1
| -1
Line 955: Line 977:
|-
|-
|<nowiki>5L 2s 1|5</nowiki>
|<nowiki>5L 2s 1|5</nowiki>
|Phrygian
| Phrygian
|6
| 6
|7
|7
|sLLLsLL
|sLLLsLL

Revision as of 09:45, 1 August 2024

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

Scale properties templates

Intervals of 5L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-oneirostep Perfect 0-oneirostep P0oneis 0 0.0 ¢
1-oneirostep Minor 1-oneirostep m1oneis s 0.0 ¢ to 150.0 ¢
Major 1-oneirostep M1oneis L 150.0 ¢ to 240.0 ¢
2-oneirostep Minor 2-oneirostep m2oneis L + s 240.0 ¢ to 300.0 ¢
Major 2-oneirostep M2oneis 2L 300.0 ¢ to 480.0 ¢
3-oneirostep Diminished 3-oneirostep d3oneis L + 2s 240.0 ¢ to 450.0 ¢
Perfect 3-oneirostep P3oneis 2L + s 450.0 ¢ to 480.0 ¢
4-oneirostep Minor 4-oneirostep m4oneis 2L + 2s 480.0 ¢ to 600.0 ¢
Major 4-oneirostep M4oneis 3L + s 600.0 ¢ to 720.0 ¢
5-oneirostep Perfect 5-oneirostep P5oneis 3L + 2s 720.0 ¢ to 750.0 ¢
Augmented 5-oneirostep A5oneis 4L + s 750.0 ¢ to 960.0 ¢
6-oneirostep Minor 6-oneirostep m6oneis 3L + 3s 720.0 ¢ to 900.0 ¢
Major 6-oneirostep M6oneis 4L + 2s 900.0 ¢ to 960.0 ¢
7-oneirostep Minor 7-oneirostep m7oneis 4L + 3s 960.0 ¢ to 1050.0 ¢
Major 7-oneirostep M7oneis 5L + 2s 1050.0 ¢ to 1200.0 ¢
8-oneirostep Perfect 8-oneirostep P8oneis 5L + 3s 1200.0 ¢


Generator chain of 5L 3s
Bright gens Scale degree Abbrev.
12 Augmented 4-oneirodegree A4oneid
11 Augmented 1-oneirodegree A1oneid
10 Augmented 6-oneirodegree A6oneid
9 Augmented 3-oneirodegree A3oneid
8 Augmented 0-oneirodegree A0oneid
7 Augmented 5-oneirodegree A5oneid
6 Major 2-oneirodegree M2oneid
5 Major 7-oneirodegree M7oneid
4 Major 4-oneirodegree M4oneid
3 Major 1-oneirodegree M1oneid
2 Major 6-oneirodegree M6oneid
1 Perfect 3-oneirodegree P3oneid
0 Perfect 0-oneirodegree
Perfect 8-oneirodegree		 P0oneid
P8oneid
−1 Perfect 5-oneirodegree P5oneid
−2 Minor 2-oneirodegree m2oneid
−3 Minor 7-oneirodegree m7oneid
−4 Minor 4-oneirodegree m4oneid
−5 Minor 1-oneirodegree m1oneid
−6 Minor 6-oneirodegree m6oneid
−7 Diminished 3-oneirodegree d3oneid
−8 Diminished 8-oneirodegree d8oneid
−9 Diminished 5-oneirodegree d5oneid
−10 Diminished 2-oneirodegree d2oneid
−11 Diminished 7-oneirodegree d7oneid
−12 Diminished 4-oneirodegree d4oneid


Scale degrees of the modes of 5L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (oneirodegree)
0 1 2 3 4 5 6 7 8
7|0 1 LLsLLsLs Perf. Maj. Maj. Perf. Maj. Aug. Maj. Maj. Perf.
6|1 4 LLsLsLLs Perf. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Perf.
5|2 7 LsLLsLLs Perf. Maj. Min. Perf. Maj. Perf. Maj. Maj. Perf.
4|3 2 LsLLsLsL Perf. Maj. Min. Perf. Maj. Perf. Maj. Min. Perf.
3|4 5 LsLsLLsL Perf. Maj. Min. Perf. Min. Perf. Maj. Min. Perf.
2|5 8 sLLsLLsL Perf. Min. Min. Perf. Min. Perf. Maj. Min. Perf.
1|6 3 sLLsLsLL Perf. Min. Min. Perf. Min. Perf. Min. Min. Perf.
0|7 6 sLsLLsLL Perf. Min. Min. Dim. Min. Perf. Min. Min. Perf.


5L 2s modes and modmos modes

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

4L 4s modes and modmos modes

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

Sandbox for proposed templates

Cent ruler

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MOS characteristics

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

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

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

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

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

KB vis

Type Visualization Individual steps Notes
Start Large step Small step End
Small vis 
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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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