User:Ganaram inukshuk/Sandbox/Modmosses: Difference between revisions

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Modmosses shown here are chosen for testing purposes and may not correspond to actual scales used in practice.
Modmosses shown here are chosen for testing purposes and may not correspond to actual scales used in practice.
{| class="wikitable"
|+Step types
!Step
!Size
!Value
!Comments
|-
|A
|Augmented step
|2L - s
|Large step plus a chroma.
|-
|L
|Large step
|L
|Large step size.
|-
|s
|Small step
|s
|Small step size. If used in conjunction with diminished steps, a capital S can be used instead, to main lexicographic ordering.
|-
|c
|Chroma
|L - s
|The difference between a large and small step.
Cannot be used as a step size in the template, but is used to change the size of other steps.
|-
|d
|Diminished step
|L - 2s
|Small step minus a chroma.
|}


== 1L 6s ==
== 1L 6s ==
Line 12: Line 46:


* LssssLd - Lssssss, but with a raised 6-degree.
* LssssLd - Lssssss, but with a raised 6-degree.
{{MOS mode degrees|Scale Signature=1L 6s|MODMOS Step Pattern=LssssLd}}
{{MOS mode degrees|Scale Signature=1L 6s|MODMOS Step Pattern=LSSSSLd}}


== 2L 5s ==
== 2L 5s ==
Line 21: Line 55:
* ssLsLdL - The "sister" of LLsLsAs, a modmos of 5L 2s.
* ssLsLdL - The "sister" of LLsLsAs, a modmos of 5L 2s.
* sLssssL - The "sister" of LsLLLLs, a modmos of 5L 2s.
* sLssssL - The "sister" of LsLLLLs, a modmos of 5L 2s.
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=sLssLdL}}
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=SLSSLdL}}
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=ssLsLdL}}
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=SSLSLdL}}
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=sLssssL}}
{{MOS mode degrees|Scale Signature=2L 5s|MODMOS Step Pattern=sLssssL}}


Line 34: Line 68:
* LLssLsL - LsLsLsL, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
* LLssLsL - LsLsLsL, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
* LLssLLs - LsLsLLs, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
* LLssLLs - LsLsLLs, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
{{MOS mode degrees|Scale Signature=4L 3s|MODMOS Step Pattern=LLssLsL}}{{MOS mode degrees|Scale Signature=4L 3s|MODMOS Step Pattern=LLssLLs}}
{{MOS mode degrees|Scale Signature=4L 3s|MODMOS Step Pattern=LLssLsL}}
{{MOS mode degrees|Scale Signature=4L 3s|MODMOS Step Pattern=LLssLLs}}


== 5L 2s ==
== 5L 2s ==
Line 45: Line 80:
* Neapolitan major (sLLLLLs); attested names added for comparison
* Neapolitan major (sLLLLLs); attested names added for comparison
* Neapolitan minor (sLLLsAs); attested names added for comparison
* Neapolitan minor (sLLLsAs); attested names added for comparison
Modmos properties
{| class="wikitable"
|+5L 2s modmosses
!Step pattern
!Common name
!Brightest mode
!Darkest mode
!Is chiral? (Reverses to what modmos?)
|-
|LsLLsAs
|Harmonic minor
|AsLsLLs
|sLsLLsA
|Yes (Harmonic major)
|-
|LLsLsAs
|Harmonic major
|AsLLsLs
|sLLsLsA
|Yes (Harmonic minor)
|-
|LsLLLLs
|Melodic minor
|LLLLsLs
|sLsLLLL
|No (reverses to itself)
|-
|sLLLLLs
|Neapolitan major
|LLLLLss
|ssLLLLL
|No (reverses to itself)
|-
|sLLLsAs
|Neapolitan minor
|LLLsAss
|ssLLLsA
|Yes (AsLLLss, ssAsLLL)
|-
|sAsLsAs
|Double harmonic
|AsLsAss
|ssAsLsA
|No (reverses to itself)
|}{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=AssLAss|Mode Names=Default}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=LsLLsAs}}


Line 54: Line 134:


{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sLLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sLLLsAs}}
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sAsLsAs|Mode Names=Ionian b2 b6 (Double harmonic);
{{MOS mode degrees|Scale Signature=5L 2s|MODMOS Step Pattern=sAsLsAs}}
Lydian #2 #6;
Phrygian b4 bb7 (Altered natural 5 bb7);
Lydian b3 b6 (Aeolian #4 natural 7, Double harmonic minor);
Mixolydian b2 b5;
Ionian #2 #5 (Ionian augmented #2);
Locrian bb3 bb7}}
'''Default names chosen for 5L 2s modmosses'''
'''Default names chosen for 5L 2s modmosses'''


The criteria for closeness is whichever reported UDP (ignoring alterations) matches the common name.
The criteria for closeness is whichever reported UDP (ignoring alterations) matches the common name. In most cases, the brightest closest mode is either closest or exact.
{| class="wikitable"
{| class="wikitable"
! colspan="6" |Modes of harmonic minor
! colspan="5" |Modes of harmonic minor
|-
|-
!Step pattern
!Step pattern
Line 72: Line 146:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|LsLLsAs
|LsLLsAs
Line 79: Line 152:
|<nowiki>2|4 M6md</nowiki>
|<nowiki>2|4 M6md</nowiki>
|Tied
|Tied
|Aeolian ♮7 (Harmonic minor)
|-
|-
|sLLsAsL
|sLLsAsL
Line 86: Line 158:
|<nowiki>0|6 M5md</nowiki>
|<nowiki>0|6 M5md</nowiki>
|Tied
|Tied
|Locrian ♮6
|-
|-
|LLsAsLs
|LLsAsLs
Line 93: Line 164:
|<nowiki>5|1 A4md</nowiki>
|<nowiki>5|1 A4md</nowiki>
|Tied
|Tied
|Ionian #5 (Ionian augmented)
|-
|-
|LsAsLsL
|LsAsLsL
Line 100: Line 170:
|<nowiki>3|3 A3md</nowiki>
|<nowiki>3|3 A3md</nowiki>
|Tied
|Tied
|Dorian #4
|-
|-
|sAsLsLL
|sAsLsLL
Line 107: Line 176:
|<nowiki>1|5 M2md</nowiki>
|<nowiki>1|5 M2md</nowiki>
|Tied
|Tied
|Phrygian #3 (Phrygian dominant)
|-
|-
|AsLsLLs
|AsLsLLs
Line 114: Line 182:
|<nowiki>6|0 A1md</nowiki>
|<nowiki>6|0 A1md</nowiki>
|Tied
|Tied
|Lydian #2
|-
|-
|sLsLLsA
|sLsLLsA
Line 121: Line 188:
|<nowiki>0|6 d3md d6md</nowiki>
|<nowiki>0|6 d3md d6md</nowiki>
|Tied
|Tied
|Locrian b4 bb7 (Altered diminished)
|-
|-
! colspan="6" |Modes of harmonic major
! colspan="5" |Modes of harmonic major
|-
|-
!Step pattern
!Step pattern
Line 130: Line 196:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|LLsLsAs
|LLsLsAs
Line 137: Line 202:
|<nowiki>5|1 m5md</nowiki>
|<nowiki>5|1 m5md</nowiki>
|Tied
|Tied
|Ionian b6 (Harmonic major)
|-
|-
|LsLsAsL
|LsLsAsL
Line 144: Line 208:
|<nowiki>3|3 d4md</nowiki>
|<nowiki>3|3 d4md</nowiki>
|Tied
|Tied
|Dorian b5
|-
|-
|sLsAsLL
|sLsAsLL
Line 151: Line 214:
|<nowiki>1|5 d3md</nowiki>
|<nowiki>1|5 d3md</nowiki>
|Tied
|Tied
|Phrygian b4
|-
|-
|LsAsLLs
|LsAsLLs
Line 158: Line 220:
|<nowiki>6|0 m2md</nowiki>
|<nowiki>6|0 m2md</nowiki>
|Tied
|Tied
|Lydian b3
|-
|-
|sAsLLsL
|sAsLLsL
Line 165: Line 226:
|<nowiki>4|2 m1md</nowiki>
|<nowiki>4|2 m1md</nowiki>
|Tied
|Tied
|Mixolydian b2
|-
|-
|AsLLsLs
|AsLLsLs
Line 172: Line 232:
|<nowiki>6|0 A1md A4md</nowiki>
|<nowiki>6|0 A1md A4md</nowiki>
|Tied
|Tied
|Lydian #2 #5 (Lydian augmented #2)
|-
|-
|sLLsLsA
|sLLsLsA
Line 179: Line 238:
|<nowiki>0|6 d6md</nowiki>
|<nowiki>0|6 d6md</nowiki>
|Tied
|Tied
|Locrian bb7
|-
|-
! colspan="6" |Modes of harmonic minor
! colspan="5" |Modes of harmonic minor
|-
|-
!Step pattern
!Step pattern
Line 188: Line 246:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|LsLLLLs
|LsLLLLs
Line 195: Line 252:
|<nowiki>3|3 M6md</nowiki>
|<nowiki>3|3 M6md</nowiki>
|Neither
|Neither
|Ionian b3 (Melodic minor)
|-
|-
|sLLLLsL
|sLLLLsL
Line 202: Line 258:
|<nowiki>1|5 M5md</nowiki>
|<nowiki>1|5 M5md</nowiki>
|Brightest-match
|Brightest-match
|Dorian b2
|-
|-
|LLLLsLs
|LLLLsLs
Line 209: Line 264:
|<nowiki>6|0 A4md</nowiki>
|<nowiki>6|0 A4md</nowiki>
|Tied
|Tied
|Lydian #5 (Lydian augmented)
|-
|-
|LLLsLsL
|LLLsLsL
Line 216: Line 270:
|<nowiki>4|2 A3md</nowiki>
|<nowiki>4|2 A3md</nowiki>
|Brightest-match
|Brightest-match
|Lydian b7 (Lydian dominant)
|-
|-
|LLsLsLL
|LLsLsLL
Line 223: Line 276:
|<nowiki>2|4 M2md</nowiki>
|<nowiki>2|4 M2md</nowiki>
|Brightest-match
|Brightest-match
|Mixolydian b6
|-
|-
|LsLsLLL
|LsLsLLL
Line 230: Line 282:
|<nowiki>0|6 M1md</nowiki>
|<nowiki>0|6 M1md</nowiki>
|Darkest-match
|Darkest-match
|Aeolian b5 (Half-diminished)
|-
|-
|sLsLLLL
|sLsLLLL
Line 237: Line 288:
|<nowiki>0|6 d3md</nowiki>
|<nowiki>0|6 d3md</nowiki>
|Brightest-match
|Brightest-match
|Locrian b4 (Altered)
|-
|-
! colspan="6" |Modes of Neapolitan minor
! colspan="5" |Modes of Neapolitan minor
|-
|-
!Step pattern
!Step pattern
Line 246: Line 296:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|sLLLsAs
|sLLLsAs
Line 253: Line 302:
|<nowiki>1|5 M6md</nowiki>
|<nowiki>1|5 M6md</nowiki>
|Tied
|Tied
|Phrygian ♮7 (Neapolitan minor)
|-
|-
|LLLsAss
|LLLsAss
Line 260: Line 308:
|<nowiki>6|0 A5md</nowiki>
|<nowiki>6|0 A5md</nowiki>
|Tied
|Tied
|Lydian #6
|-
|-
|LLsAssL
|LLsAssL
Line 267: Line 314:
|<nowiki>4|2 A4md</nowiki>
|<nowiki>4|2 A4md</nowiki>
|Tied
|Tied
|Mixolydian #5 (Mixolydian augmented)
|-
|-
|LsAssLL
|LsAssLL
Line 274: Line 320:
|<nowiki>2|4 A3md</nowiki>
|<nowiki>2|4 A3md</nowiki>
|Tied
|Tied
|Aeolian #4
|-
|-
|sAssLLL
|sAssLLL
Line 281: Line 326:
|<nowiki>0|6 M2md</nowiki>
|<nowiki>0|6 M2md</nowiki>
|Tied
|Tied
|Locrian ♮3 (Locrian dominant)
|-
|-
|AssLLLs
|AssLLLs
Line 288: Line 332:
|<nowiki>5|1 A1md</nowiki>
|<nowiki>5|1 A1md</nowiki>
|Tied
|Tied
|Ionian #2
|-
|-
|ssLLLsA
|ssLLLsA
Line 295: Line 338:
|<nowiki>0|6 d2md d3md d6md</nowiki>
|<nowiki>0|6 d2md d3md d6md</nowiki>
|Tied
|Tied
|Locrian bb3 b4 bb7 (Altered diminished bb3)
|-
|-
! colspan="6" |Modes of Neapolitan major
! colspan="5" |Modes of Neapolitan major
|-
|-
!Step pattern
!Step pattern
Line 304: Line 346:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|sLLLLLs
|sLLLLLs
Line 311: Line 352:
|<nowiki>1|5 M5md M6md</nowiki>
|<nowiki>1|5 M5md M6md</nowiki>
|Brightest-match
|Brightest-match
|Ionian b2 b3 (Neapolitan major)
|-
|-
|LLLLLss
|LLLLLss
Line 318: Line 358:
|<nowiki>6|0 A4md A5md</nowiki>
|<nowiki>6|0 A4md A5md</nowiki>
|Tied
|Tied
|Lydian #5 #6 (Lydian augmented #6)
|-
|-
|LLLLssL
|LLLLssL
Line 325: Line 364:
|<nowiki>4|2 A3md A4md</nowiki>
|<nowiki>4|2 A3md A4md</nowiki>
|Brightest-match
|Brightest-match
|Lydian #5 b7 (Lydian augmented dominant)
|-
|-
|LLLssLL
|LLLssLL
Line 332: Line 370:
|<nowiki>2|4 M2md A3md</nowiki>
|<nowiki>2|4 M2md A3md</nowiki>
|Brightest-match
|Brightest-match
|Lydian b6 b7 (Lydian minor)
|-
|-
|LLssLLL
|LLssLLL
Line 339: Line 376:
|<nowiki>0|6 M1md M2md</nowiki>
|<nowiki>0|6 M1md M2md</nowiki>
|Brightest-match
|Brightest-match
|Mixolydian b5 b6 (Major Locrian)
|-
|-
|LssLLLL
|LssLLLL
Line 346: Line 382:
|<nowiki>0|6 M1md d3md</nowiki>
|<nowiki>0|6 M1md d3md</nowiki>
|Darkest-match
|Darkest-match
|Aeolian b4 b5 (Altered dominant ♮2)
|-
|-
|ssLLLLL
|ssLLLLL
Line 353: Line 388:
|<nowiki>0|6 d2md d3md</nowiki>
|<nowiki>0|6 d2md d3md</nowiki>
|Tied
|Tied
|Locrian bb3 b4 (Altered dominant bb3)
|-
|-
! colspan="6" |Modes of Neapolitan major
! colspan="5" |Modes of double harmonic
|-
|-
!Step pattern
!Step pattern
Line 362: Line 396:
!Darkest match
!Darkest match
!Which is closer?
!Which is closer?
!Default names chosen
|-
|-
|sAsLsAs
|sAsLsAs
|Double harmonic
|Double harmonic
|
|
|
|
|

Latest revision as of 09:30, 24 July 2024

This page is a testing area for the following function from Module:TAMNAMS:

function p.mode_udp(input_mode, input_mos, mos_abbrev)

The function works as follows: given an arbitrary input_mode for an input_mos, find the closest true-mos mode and list the altered scale degrees (alterations) needed to produce that mode. The closest true-mos mode is the mode that requires the fewest alterations to produce the input_mode. If more than one true-mos modes satisfy this condition, then the brightest of those modes is chosen to break the tie.

What's being tested is whether there are any cases in which the tiebreaker of using the brightest mode is not ideal. One notable example of this is melodic minor (step pattern LsLLLLs). This mode is aeolian natural-6 natural-7, but also ionian b3. This is considered a non-issue since ionian b3 is considered an alternate name for melodic minor.

Modmosses shown here are chosen for testing purposes and may not correspond to actual scales used in practice.

Step types
Step Size Value Comments
A Augmented step 2L - s Large step plus a chroma.
L Large step L Large step size.
s Small step s Small step size. If used in conjunction with diminished steps, a capital S can be used instead, to main lexicographic ordering.
c Chroma L - s The difference between a large and small step.

Cannot be used as a step size in the template, but is used to change the size of other steps.

d Diminished step L - 2s Small step minus a chroma.

1L 6s

Scale degrees of the modes of 1L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (ondegree)
0 1 2 3 4 5 6 7
6|0 1 Lssssss Perf. Aug. Maj. Maj. Maj. Maj. Perf. Perf.
5|1 7 sLsssss Perf. Perf. Maj. Maj. Maj. Maj. Perf. Perf.
4|2 6 ssLssss Perf. Perf. Min. Maj. Maj. Maj. Perf. Perf.
3|3 5 sssLsss Perf. Perf. Min. Min. Maj. Maj. Perf. Perf.
2|4 4 ssssLss Perf. Perf. Min. Min. Min. Maj. Perf. Perf.
1|5 3 sssssLs Perf. Perf. Min. Min. Min. Min. Perf. Perf.
0|6 2 ssssssL Perf. Perf. Min. Min. Min. Min. Dim. Perf.

Modmosses chosen:

  • LssssLd - Lssssss, but with a raised 6-degree.
Scale degrees of the modes of 1L 6s (LSSSSLd)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (ondegree)
0 1 2 3 4 5 6 7
6|0 A6md 1 LSSSSLd Perf. Aug. Maj. Maj. Maj. Maj. Aug. Perf.
2|4 d6md
0|6 M5md 		2 SSSSLdL Perf. Perf. Min. Min. Min. Maj. Dim. Perf.
3|3 m5md
1|5 M4md 		3 SSSLdLS Perf. Perf. Min. Min. Maj. Min. Perf. Perf.
4|2 m4md
2|4 M3md 		4 SSLdLSS Perf. Perf. Min. Maj. Min. Maj. Perf. Perf.
5|1 m3md
3|3 M2md 		5 SLdLSSS Perf. Perf. Maj. Min. Maj. Maj. Perf. Perf.
6|0 m2md
4|2 A1md 		6 LdLSSSS Perf. Aug. Min. Maj. Maj. Maj. Perf. Perf.
0|6 d1md 7 dLSSSSL Perf. Dim. Min. Min. Min. Min. Dim. Perf.

2L 5s

Scale degrees of the modes of 2L 5s
UDP Cyclic
order 		Step
pattern 		Scale degree (peldegree)
0 1 2 3 4 5 6 7
6|0 1 LssLsss Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
5|1 4 LsssLss Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 7 sLssLss Perf. Min. Maj. Perf. Perf. Maj. Maj. Perf.
3|3 3 sLsssLs Perf. Min. Maj. Perf. Perf. Min. Maj. Perf.
2|4 6 ssLssLs Perf. Min. Min. Perf. Perf. Min. Maj. Perf.
1|5 2 ssLsssL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 5 sssLssL Perf. Min. Min. Dim. Perf. Min. Min. Perf.

Modmosses chosen

  • sLssLdL - The "sister" of LsLLsAs, a modmos of 5L 2s.
  • ssLsLdL - The "sister" of LLsLsAs, a modmos of 5L 2s.
  • sLssssL - The "sister" of LsLLLLs, a modmos of 5L 2s.
Scale degrees of the modes of 2L 5s (SLSSLdL)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (peldegree)
0 1 2 3 4 5 6 7
4|2 m6md 1 SLSSLdL Perf. Min. Maj. Perf. Perf. Maj. Min. Perf.
6|0 m5md 2 LSSLdLS Perf. Maj. Maj. Perf. Aug. Min. Maj. Perf.
1|5 d4md 3 SSLdLSL Perf. Min. Min. Perf. Dim. Min. Min. Perf.
3|3 d3md 4 SLdLSLS Perf. Min. Maj. Dim. Perf. Min. Maj. Perf.
5|1 m2md 5 LdLSLSS Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
0|6 d1md 6 dLSLSSL Perf. Dim. Min. Dim. Perf. Min. Min. Perf.
6|0 A3md A6md 7 LSLSSLd Perf. Maj. Maj. Aug. Aug. Maj. Aug. Perf.
Scale degrees of the modes of 2L 5s (SSLSLdL)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (peldegree)
0 1 2 3 4 5 6 7
1|5 M5md 1 SSLSLdL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
3|3 A4md 2 SLSLdLS Perf. Min. Maj. Perf. Aug. Min. Maj. Perf.
5|1 A3md 3 LSLdLSS Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 M2md 4 SLdLSSL Perf. Min. Maj. Dim. Perf. Min. Min. Perf.
2|4 M1md 5 LdLSSLS Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 d1md d4md 6 dLSSLSL Perf. Dim. Min. Dim. Dim. Min. Min. Perf.
6|0 A6md 7 LSSLSLd Perf. Maj. Maj. Perf. Aug. Maj. Aug. Perf.
Scale degrees of the modes of 2L 5s (sLssssL)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (peldegree)
0 1 2 3 4 5 6 7
3|3 m6md
1|5 M2md 		1 sLssssL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
5|1 m5md
3|3 M1md 		2 LssssLs Perf. Maj. Maj. Perf. Perf. Min. Maj. Perf.
0|6 d4md 3 ssssLsL Perf. Min. Min. Dim. Dim. Min. Min. Perf.
2|4 d3md
0|6 M6md 		4 sssLsLs Perf. Min. Min. Dim. Perf. Min. Maj. Perf.
4|2 m2md
2|4 M5md 		5 ssLsLss Perf. Min. Min. Perf. Perf. Maj. Maj. Perf.
6|0 m1md
4|2 A4md 		6 sLsLsss Perf. Min. Maj. Perf. Aug. Maj. Maj. Perf.
6|0 A3md 7 LsLssss Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.

3L 4s

Scale degrees of the modes of 3L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (moshdegree)
0 1 2 3 4 5 6 7
6|0 1 LsLsLss Perf. Maj. Perf. Maj. Maj. Aug. Maj. Perf.
5|1 3 LsLssLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 5 LssLsLs Perf. Maj. Perf. Min. Maj. Perf. Maj. Perf.
3|3 7 sLsLsLs Perf. Min. Perf. Min. Maj. Perf. Maj. Perf.
2|4 2 sLsLssL Perf. Min. Perf. Min. Maj. Perf. Min. Perf.
1|5 4 sLssLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 6 ssLsLsL Perf. Min. Dim. Min. Min. Perf. Min. Perf.

4L 3s

Scale degrees of the modes of 4L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (smidegree)
0 1 2 3 4 5 6 7
6|0 1 LLsLsLs Perf. Maj. Aug. Maj. Maj. Perf. Maj. Perf.
5|1 6 LsLLsLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 4 LsLsLLs Perf. Maj. Perf. Maj. Min. Perf. Maj. Perf.
3|3 2 LsLsLsL Perf. Maj. Perf. Maj. Min. Perf. Min. Perf.
2|4 7 sLLsLsL Perf. Min. Perf. Maj. Min. Perf. Min. Perf.
1|5 5 sLsLLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 3 sLsLsLL Perf. Min. Perf. Min. Min. Dim. Min. Perf.

Modmosses chosen:

  • LLssLsL - LsLsLsL, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
  • LLssLLs - LsLsLLs, but with the 2nd and 3rd steps rearranged to produce an augmented 2-step.
Scale degrees of the modes of 4L 3s (LLssLsL)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (smidegree)
0 1 2 3 4 5 6 7
3|3 A2md 1 LLssLsL Perf. Maj. Aug. Maj. Min. Perf. Min. Perf.
0|6 M1md 2 LssLsLL Perf. Maj. Perf. Min. Min. Dim. Min. Perf.
0|6 d2md d4md 3 ssLsLLL Perf. Min. Dim. Min. Dim. Dim. Min. Perf.
1|5 M6md 4 sLsLLLs Perf. Min. Perf. Min. Min. Perf. Maj. Perf.
5|1 A5md 5 LsLLLss Perf. Maj. Perf. Maj. Maj. Aug. Maj. Perf.
2|4 M4md 6 sLLLssL Perf. Min. Perf. Maj. Maj. Perf. Min. Perf.
6|0 A3md 7 LLLssLs Perf. Maj. Aug. Aug. Maj. Perf. Maj. Perf.
Scale degrees of the modes of 4L 3s (LLssLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (smidegree)
0 1 2 3 4 5 6 7
6|0 m4md
4|2 A2md 		1 LLssLLs Perf. Maj. Aug. Maj. Min. Perf. Maj. Perf.
3|3 m3md
1|5 M1md 		2 LssLLsL Perf. Maj. Perf. Min. Min. Perf. Min. Perf.
0|6 d2md 3 ssLLsLL Perf. Min. Dim. Min. Min. Dim. Min. Perf.
4|2 m1md
2|4 M6md 		4 sLLsLLs Perf. Min. Perf. Maj. Min. Perf. Maj. Perf.
6|0 A5md 5 LLsLLss Perf. Maj. Aug. Maj. Maj. Aug. Maj. Perf.
5|1 m6md
3|3 M4md 		6 LsLLssL Perf. Maj. Perf. Maj. Maj. Perf. Min. Perf.
2|4 d5md
0|6 M3md 		7 sLLssLL Perf. Min. Perf. Maj. Min. Dim. Min. Perf.

5L 2s

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.

Modmosses chosen

  • Harmonic minor (LsLLsAs); names provided by module
  • Harmonic major (LLsLsAs); names provided by module
  • Melodic minor or ionian b3 (LsLLLLs); names provided by module
  • Neapolitan major (sLLLLLs); attested names added for comparison
  • Neapolitan minor (sLLLsAs); attested names added for comparison

Modmos properties

5L 2s modmosses
Step pattern Common name Brightest mode Darkest mode Is chiral? (Reverses to what modmos?)
LsLLsAs Harmonic minor AsLsLLs sLsLLsA Yes (Harmonic major)
LLsLsAs Harmonic major AsLLsLs sLLsLsA Yes (Harmonic minor)
LsLLLLs Melodic minor LLLLsLs sLsLLLL No (reverses to itself)
sLLLLLs Neapolitan major LLLLLss ssLLLLL No (reverses to itself)
sLLLsAs Neapolitan minor LLLsAss ssLLLsA Yes (AsLLLss, ssAsLLL)
sAsLsAs Double harmonic AsLsAss ssAsLsA No (reverses to itself)
Scale degrees of the modes of 5L 2s (AssLAss)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 A1md A5md 1 AssLAss Perf. Aug. Maj. Perf. Perf. Aug. Maj. Perf.
1|5 d2md d3md d6md 2 ssLAssA Perf. Min. Dim. Dim. Perf. Min. Dim. Perf.
1|5 A3md M6md 3 sLAssAs Perf. Min. Min. Aug. Perf. Min. Maj. Perf.
6|0 A2md A5md 4 LAssAss Perf. Maj. Aug. Aug. Perf. Aug. Maj. Perf.
4|2 A1md A4md 5 AssAssL Perf. Aug. Maj. Perf. Aug. Maj. Min. Perf.
0|6 d2md d5md d6md 6 ssAssLA Perf. Min. Dim. Perf. Dim. Dim. Dim. Perf.
0|6 M2md M6md 7 sAssLAs Perf. Min. Maj. Perf. Dim. Min. Maj. Perf.
Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.


Scale degrees of the modes of 5L 2s (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 (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 (sLLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m1md m2md
1|5 M5md M6md 		1 sLLLLLs Perf. Min. Min. Perf. Perf. Maj. Maj. Perf.
6|0 A4md A5md 2 LLLLLss Perf. Maj. Maj. Aug. Aug. Aug. Maj. Perf.
6|0 A4md m6md
4|2 A3md A4md 		3 LLLLssL Perf. Maj. Maj. Aug. Aug. Maj. Min. Perf.
6|0 m5md m6md
2|4 M2md A3md 		4 LLLssLL Perf. Maj. Maj. Aug. Perf. Min. Min. Perf.
4|2 d4md m5md
0|6 M1md M2md 		5 LLssLLL Perf. Maj. Maj. Perf. Dim. Min. Min. Perf.
2|4 d3md d4md
0|6 M1md d3md 		6 LssLLLL Perf. Maj. Min. Dim. Dim. Min. Min. Perf.
0|6 d2md d3md 7 ssLLLLL Perf. Min. Dim. Dim. Dim. Min. Min. Perf.


Scale degrees of the modes of 5L 2s (sLLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
1|5 M6md 1 sLLLsAs Perf. Min. Min. Perf. Perf. Min. Maj. Perf.
6|0 A5md 2 LLLsAss Perf. Maj. Maj. Aug. Perf. Aug. Maj. Perf.
4|2 A4md 3 LLsAssL Perf. Maj. Maj. Perf. Aug. Maj. Min. Perf.
2|4 A3md 4 LsAssLL Perf. Maj. Min. Aug. Perf. Min. Min. Perf.
0|6 M2md 5 sAssLLL Perf. Min. Maj. Perf. Dim. Min. Min. Perf.
5|1 A1md 6 AssLLLs Perf. Aug. Maj. Perf. Perf. Maj. Maj. Perf.
0|6 d2md d3md d6md 7 ssLLLsA Perf. Min. Dim. Dim. Dim. Min. Dim. Perf.
Scale degrees of the modes of 5L 2s (sAsLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m1md m5md
1|5 M2md M6md 		1 sAsLsAs Perf. Min. Maj. Perf. Perf. Min. Maj. Perf.
6|0 A1md A5md 2 AsLsAss Perf. Aug. Maj. Aug. Perf. Aug. Maj. Perf.
1|5 d3md d6md 3 sLsAssA Perf. Min. Min. Dim. Perf. Min. Dim. Perf.
6|0 m2md m5md
2|4 A3md M6md 		4 LsAssAs Perf. Maj. Min. Aug. Perf. Min. Maj. Perf.
4|2 m1md d4md
0|6 M2md M5md 		5 sAssAsL Perf. Min. Maj. Perf. Dim. Maj. Min. Perf.
5|1 A1md A4md 6 AssAsLs Perf. Aug. Maj. Perf. Aug. Maj. Maj. Perf.
0|6 d2md d6md 7 ssAsLsA Perf. Min. Dim. Perf. Dim. Min. Dim. Perf.

Default names chosen for 5L 2s modmosses

The criteria for closeness is whichever reported UDP (ignoring alterations) matches the common name. In most cases, the brightest closest mode is either closest or exact.

Modes of harmonic minor
Step pattern Common name(s) Brightest match Darkest match Which is closer?
LsLLsAs Harmonic minor 2|4 M6md 2|4 M6md Tied
sLLsAsL Locrian ♮6 0|6 M5md 0|6 M5md Tied
LLsAsLs Ionian augmented 5|1 A4md 5|1 A4md Tied
LsAsLsL Dorian #4 3|3 A3md 3|3 A3md Tied
sAsLsLL Phrygian dominant 1|5 M2md 1|5 M2md Tied
AsLsLLs Lydian #2 6|0 A1md 6|0 A1md Tied
sLsLLsA Altered diminished 0|6 d3md d6md 0|6 d3md d6md Tied
Modes of harmonic major
Step pattern Common name(s) Brightest match Darkest match Which is closer?
LLsLsAs Harmonic major 5|1 m5md 5|1 m5md Tied
LsLsAsL Dorian b5 3|3 d4md 3|3 d4md Tied
sLsAsLL Phrygian b4 1|5 d3md 1|5 d3md Tied
LsAsLLs Lydian b3 6|0 m2md 6|0 m2md Tied
sAsLLsL Mixolydian b2 4|2 m1md 4|2 m1md Tied
AsLLsLs Lydian augmented #2 6|0 A1md A4md 6|0 A1md A4md Tied
sLLsLsA Locrian bb7 0|6 d6md 0|6 d6md Tied
Modes of harmonic minor
Step pattern Common name(s) Brightest match Darkest match Which is closer?
LsLLLLs Melodic minor 5|1 m2md 3|3 M6md Neither
sLLLLsL Dorian b2 3|3 m1md 1|5 M5md Brightest-match
LLLLsLs Lydian augmented 6|0 A4md 6|0 A4md Tied
LLLsLsL Lydian dominant 6|0 m6md 4|2 A3md Brightest-match
LLsLsLL Mixolydian b6 4|2 m5md 2|4 M2md Brightest-match
LsLsLLL Locrian ♮2 2|4 d4md 0|6 M1md Darkest-match
sLsLLLL Altered 0|6 d3md 0|6 d3md Brightest-match
Modes of Neapolitan minor
Step pattern Common name(s) Brightest match Darkest match Which is closer?
sLLLsAs Neapolitan minor 1|5 M6md 1|5 M6md Tied
LLLsAss Lydian #6 6|0 A5md 6|0 A5md Tied
LLsAssL Mixolydian augmented 4|2 A4md 4|2 A4md Tied
LsAssLL Aeolian #4 2|4 A3md 2|4 A3md Tied
sAssLLL Locrian dominant 0|6 M2md 0|6 M2md Tied
AssLLLs Ionian #2 5|1 A1md 5|1 A1md Tied
ssLLLsA Altered diminished bb3 0|6 d2md d3md d6md 0|6 d2md d3md d6md Tied
Modes of Neapolitan major
Step pattern Common name(s) Brightest match Darkest match Which is closer?
sLLLLLs Neapolitan major 5|1 m1md m2md 1|5 M5md M6md Brightest-match
LLLLLss Lydian augmented #6 6|0 A4md A5md 6|0 A4md A5md Tied
LLLLssL Lydian augmented dominant 6|0 A4md m6md 4|2 A3md A4md Brightest-match
LLLssLL Lydian dominant b6 6|0 m5md m6md 2|4 M2md A3md Brightest-match
LLssLLL Major locrian 4|2 d4md m5md 0|6 M1md M2md Brightest-match
LssLLLL Altered dominant #2 2|4 d3md d4md 0|6 M1md d3md Darkest-match
ssLLLLL Altered dominant bb3 0|6 d2md d3md 0|6 d2md d3md Tied
Modes of double harmonic
Step pattern Common name(s) Brightest match Darkest match Which is closer?
sAsLsAs Double harmonic

6L 1s

Scale degrees of the modes of 6L 1s
UDP Cyclic
order 		Step
pattern 		Scale degree (archdegree)
0 1 2 3 4 5 6 7
6|0 1 LLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Aug. Perf.
5|1 2 LLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Perf. Perf.
4|2 3 LLLLsLL Perf. Perf. Maj. Maj. Maj. Min. Perf. Perf.
3|3 4 LLLsLLL Perf. Perf. Maj. Maj. Min. Min. Perf. Perf.
2|4 5 LLsLLLL Perf. Perf. Maj. Min. Min. Min. Perf. Perf.
1|5 6 LsLLLLL Perf. Perf. Min. Min. Min. Min. Perf. Perf.
0|6 7 sLLLLLL Perf. Dim. Min. Min. Min. Min. Perf. Perf.
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