Mavila temperament modal harmony: Difference between revisions

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got rid of the horrifically idiosyncratic "patet" stuff and used a more proper mode name system
 
Line 85: Line 85:
|}
|}


=== "Diatonic" Names ===
=== Antidiatonic Names ===


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 105: Line 105:
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">N7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 3|1
| 3|1
Line 114: Line 114:
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">N7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 2|2
| 2|2
Line 120: Line 120:
| Shang
| Shang
| P1
| P1
| <span style="color: #D84F00;">N2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">N7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 1|3
| 1|3
Line 129: Line 129:
| Zhi
| Zhi
| P1
| P1
| <span style="color: #D84F00;">N2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
Line 138: Line 138:
| Gong
| Gong
| P1
| P1
| <span style="color: #D84F00;">N2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
Line 235: Line 235:
! UDP
! UDP
! Imprint
! Imprint
! (Anti)Name
! Name
! 1
! 1
! 2
! 2
Line 246: Line 246:
| 6|0
| 6|0
| LssLsss
| LssLsss
| Locrian
| Antilocrian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">8/7</span>
| <span style="color: #3F5CDB;">8/7</span>
Line 257: Line 257:
| 5|1
| 5|1
| LsssLss
| LsssLss
| Phrygian
| Antiphrygian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">8/7</span>
| <span style="color: #3F5CDB;">8/7</span>
Line 268: Line 268:
| 4|2
| 4|2
| sLssLss
| sLssLss
| Aeolian
| Antiaeolian
| 1/1
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">12/11</span>
Line 279: Line 279:
| 3|3
| 3|3
| sLsssLs
| sLsssLs
| Dorian
| Antidorian
| 1/1
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">12/11</span>
Line 290: Line 290:
| 2|4
| 2|4
| ssLssLs
| ssLssLs
| Mixolydian
| Antimixolydian
| 1/1
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">12/11</span>
Line 301: Line 301:
| 1|5
| 1|5
| ssLsssL
| ssLsssL
| Ionian
| Antiionian
| 1/1
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">12/11</span>
Line 312: Line 312:
| 0|6
| 0|6
| sssLssL
| sssLssL
| Lydian
| Antilydian
| 1/1
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">12/11</span>
Line 322: Line 322:
|}
|}


=== "Diatonic" Names ===
=== Antidiatonic Names ===


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 328: Line 328:
! UDP
! UDP
! Imprint
! Imprint
! (Anti)Name
! Name
! 1
! 1
! 2
! 2
Line 339: Line 339:
| 6|0
| 6|0
| LssLsss
| LssLsss
| Locrian
| Antilocrian
| P1
| P1
| <span style="color: #3F5CDB;">(S)M2</span>
| <span style="color: #3F5CDB;">M2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">sm6, A5</span>
| <span style="color: #3F5CDB;">A5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">N7, M7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 5|1
| 5|1
| LsssLss
| LsssLss
| Phrygian
| Antiphrygian
| P1
| P1
| <span style="color: #3F5CDB;">(S)M2</span>
| <span style="color: #3F5CDB;">M2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">N7, M7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 4|2
| 4|2
| sLssLss
| sLssLss
| Aeolian
| Antiaeolian
| P1
| P1
| <span style="color: #D84F00;">N2, m2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">N7, M7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 3|3
| 3|3
| sLsssLs
| sLsssLs
| Dorian
| Antidorian
| P1
| P1
| <span style="color: #D84F00;">N2, m2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #3F5CDB;">N7, M7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 2|4
| 2|4
| ssLssLs
| ssLssLs
| Mixolydian
| Antimixolydian
| P1
| P1
| <span style="color: #D84F00;">N2, m2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #3F5CDB;">N7, M7</span>
| <span style="color: #3F5CDB;">M7</span>
|-
|-
| 1|5
| 1|5
| ssLsssL
| ssLsssL
| Ionian
| Antiionian
| P1
| P1
| <span style="color: #D84F00;">N2, m2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">(s)m7</span>
| <span style="color: #D84F00;">m7</span>
|-
|-
| 0|6
| 0|6
| sssLssL
| sssLssL
| Lydian
| Antilydian
| P1
| P1
| <span style="color: #D84F00;">N2, m2</span>
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">SM3, d4</span>
| <span style="color: #D84F00;">d4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">(s’m7</span>
| <span style="color: #D84F00;">m7</span>
|}
|}


Line 419: Line 419:
{| class="wikitable"
{| class="wikitable"
|-
|-
| <nowiki>8|0 - LLLLsLLLs - (Super)Lydian</nowiki>
| <nowiki>8|0 - LLLLsLLLs - Superlydian</nowiki>
|  
|  
|-
|-
| <nowiki>7|1 - LLLsLLLLs - (Super)Ionian</nowiki>
| <nowiki>7|1 - LLLsLLLLs - Adlocrian</nowiki>
|  
|  
|-
|-
| <nowiki>6|2 - LLLsLLLsL - (Super)Mixolydian</nowiki>
| <nowiki>6|2 - LLLsLLLsL - Adphrygian</nowiki>
|  
|  
|-
|-
| <nowiki>5|3 - LLsLLLLsL - (Super)Corinthian</nowiki>
| <nowiki>5|3 - LLsLLLLsL - Adaeolian</nowiki>
|  
|  
|-
|-
| <nowiki>4|4 - LLsLLLsLL - (Super)Olympian</nowiki>
| <nowiki>4|4 - LLsLLLsLL - Addorian</nowiki>
| [[File:MavilaOlympian16edo.mp3]]
| [[File:MavilaOlympian16edo.mp3]]
|-
|-
| <nowiki>3|5 - LsLLLLsLL - (Super)Dorian</nowiki>
| <nowiki>3|5 - LsLLLLsLL - Admixolydian</nowiki>
|  
|  
|-
|-
| <nowiki>2|6 - LsLLLsLLL - (Super)Aeolian</nowiki>
| <nowiki>2|6 - LsLLLsLLL - Adionian</nowiki>
|  
|  
|-
|-
| <nowiki>1|7 - sLLLLsLLL - (Super)Phrygian</nowiki>
| <nowiki>1|7 - sLLLLsLLL - Adlydian</nowiki>
|  
|  
|-
|-
| <nowiki>0|8 - sLLLsLLLL - (Super)Locrian</nowiki>
| <nowiki>0|8 - sLLLsLLLL - Superlocrian</nowiki>
| [[File:MavilaSuperdiatonic16edo.mp3]]
| [[File:MavilaSuperdiatonic16edo.mp3]]
|}
|}


In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian
In cyclic permutational order: Adlocrian - Adaeolian - Admixolydian - Adlydian - Superlydian - Adphrygian - Addorian - Adionian - Superlocrian


=== Transversal ===
=== Transversal ===
Line 455: Line 455:
! UDP
! UDP
! Imprint
! Imprint
! (Super)Name
! Name
! 1
! 1
! 2
! 2
Line 468: Line 468:
| <nowiki>8|0</nowiki>
| <nowiki>8|0</nowiki>
| LLLLsLLLs
| LLLLsLLLs
| Lydian
| Superlydian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 481: Line 481:
| <nowiki>7|1</nowiki>
| <nowiki>7|1</nowiki>
| LLLsLLLLs
| LLLsLLLLs
| Ionian
| Adlocrian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 494: Line 494:
| <nowiki>6|2</nowiki>
| <nowiki>6|2</nowiki>
| LLLsLLLsL
| LLLsLLLsL
| Mixolydian
| Adphrygian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 507: Line 507:
| <nowiki>5|3</nowiki>
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| LLsLLLLsL
| Corinthian
| Adaeolian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 520: Line 520:
| <nowiki>4|4</nowiki>
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| LLsLLLsLL
| Olympian
| Addorian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 533: Line 533:
| <nowiki>3|5</nowiki>
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| LsLLLLsLL
| Dorian
| Admixolydian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 546: Line 546:
| <nowiki>2|6</nowiki>
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| LsLLLsLLL
| Aeolian
| Adionian
| 1/1
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">12/11</span>
Line 559: Line 559:
| <nowiki>1|7</nowiki>
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| sLLLLsLLL
| Phrygian
| Adlydian
| 1/1
| 1/1
| <span style="color: #D84F00;">22/21</span>
| <span style="color: #D84F00;">22/21</span>
Line 572: Line 572:
| <nowiki>0|8</nowiki>
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| sLLLsLLLL
| Locrian
| Superlocrian
| 1/1
| 1/1
| <span style="color: #D84F00;">22/21</span>
| <span style="color: #D84F00;">22/21</span>
Line 590: Line 590:
! UDP
! UDP
! Imprint
! Imprint
! (Super)Name
! Name
! 1
! 1
! 2
! 2
Line 603: Line 603:
| <nowiki>8|0</nowiki>
| <nowiki>8|0</nowiki>
| LLLLsLLLs
| LLLLsLLLs
| Lydian
| Superlydian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 616: Line 616:
| <nowiki>7|1</nowiki>
| <nowiki>7|1</nowiki>
| LLLsLLLLs
| LLLsLLLLs
| Ionian
| Adlocrian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 629: Line 629:
| <nowiki>6|2</nowiki>
| <nowiki>6|2</nowiki>
| LLLsLLLsL
| LLLsLLLsL
| Mixolydian
| Adphrygian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 642: Line 642:
| <nowiki>5|3</nowiki>
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| LLsLLLLsL
| Corinthian
| Adaeolian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 655: Line 655:
| <nowiki>4|4</nowiki>
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| LLsLLLsLL
| Olympian
| Addorian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 668: Line 668:
| <nowiki>3|5</nowiki>
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| LsLLLLsLL
| Dorian
| Admixolydian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 681: Line 681:
| <nowiki>2|6</nowiki>
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| LsLLLsLLL
| Aeolian
| Adionian
| P1
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">N2</span>
Line 694: Line 694:
| <nowiki>1|7</nowiki>
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| sLLLLsLLL
| Phrygian
| Adlydian
| P1
| P1
| <span style="color: #D84F00;">(s)m2</span>
| <span style="color: #D84F00;">(s)m2</span>
Line 707: Line 707:
| <nowiki>0|8</nowiki>
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| sLLLsLLLL
| Locrian
| Superlocrian
| P1
| P1
| <span style="color: #D84F00;">(s)m2</span>
| <span style="color: #D84F00;">(s)m2</span>
Line 724: Line 724:
! UDP
! UDP
! Imprint
! Imprint
! (Super)Name
! Name
! 1
! 1
! 2
! 2
Line 737: Line 737:
| <nowiki>8|0</nowiki>
| <nowiki>8|0</nowiki>
|  LLLLsLLLs
|  LLLLsLLLs
| Lydian
| Superlydian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 750: Line 750:
| <nowiki>7|1</nowiki>
| <nowiki>7|1</nowiki>
| LLLsLLLLs
| LLLsLLLLs
|  Ionian
|  Adlocrian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 763: Line 763:
| <nowiki>6|2</nowiki>
| <nowiki>6|2</nowiki>
| LLLsLLLsL
| LLLsLLLsL
|  Mixolydian
|  Adphrygian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 776: Line 776:
| <nowiki>5|3</nowiki>
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| LLsLLLLsL
| Corinthian
| Adaeolian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 789: Line 789:
| <nowiki>4|4</nowiki>
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| LLsLLLsLL
| Olympian
| Addorian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 802: Line 802:
| <nowiki>3|5</nowiki>
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| LsLLLLsLL
| Dorian
| Admixolydian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 815: Line 815:
| <nowiki>2|6</nowiki>
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| LsLLLsLLL
| Aeolian
| Adionian
| P
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
Line 828: Line 828:
| <nowiki>1|7</nowiki>
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| sLLLLsLLL
| Phrygian
| Adlydian
| P
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
Line 841: Line 841:
| <nowiki>0|8</nowiki>
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| sLLLsLLLL
| Locrian
| Superlocrian
| P
| P
| <span style="color: #D84F00;">m</span>
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== Notes on Naming ==
== Notes on Naming ==
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.


Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLsLLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Locrian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLsLLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Locrian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.


Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.
 
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.


[[Category:Mavila]]
[[Category:Mavila]]
[[Category:Modes]]
[[Category:Modes]]
[[Category:Essays]]
[[Category:Essays]]

Latest revision as of 06:04, 14 April 2025

Introduction

Mavila is the regular temperament eliminating 135/128. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see 2L 5s) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see 7L 2s) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].

How to read these charts

  • The 6|0, 5|1, 4|2 markings are an instance of Modal UDP Notation.
  • Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.
  • Additionally, "diatonic" names make use of the following abbreviations:
    • SM - Supermajor
    • M - Major
    • N - Neutral
    • m - Minor
    • sm - Subminor

2L 3s Pentatonic MOS: Pentic

4|0 - LsLss - Jue

3|1 - LssLs - Yu

2|2 - sLsLs - Shang

3|1 - sLssL - Zhi

0|4 - ssLsL - Gong

In cyclic permutational order: Gong, Shang, Jue, Zhi, Yu

Transversal

UDP Imprint Name 1 2 3 4 5
0 LsLss Jue 1/1 5/4 4/3 5/3 11/6
1 LssLs Yu 1/1 5/4 4/3 3/2 11/6
2 sLsLs Shang 1/1 12/11 4/3 3/2 11/6
3 sLssL Zhi 1/1 12/11 4/3 3/2 8/5
4 ssLsL Gong 1/1 12/11 6/5 3/2 8/5

Antidiatonic Names

UDP Imprint Name 1 2 3 4 5
0 LsLss Jue P1 M3 P4 M6 M7
1 LssLs Yu P1 M3 P4 P5 M7
2 sLsLs Shang P1 m2 P4 P5 M7
3 sLssL Zhi P1 m2 P4 P5 m6
4 ssLsL Gong P1 m2 m3 P5 m6

Qualities

UDP Imprint Name 1 2 3 4 5
4|0 LsLss Jue P M P A M
3|1 LssLs Yu P M P P M
2|2 sLsLs Shang P m P P M
1|3 sLssL Zhi P m P P m
0|4 ssLsL Gong P m d P m

2L 5s Heptatonic MOS: Antidiatonic

0 - LssLsss - Antilocrian
1 - LsssLss - Antiphrygian ("major")
2 - sLssLss - Antiaeolian
3 - sLsssLs - Antidorian
4 - ssLssLs - Antimixolydian ("minor")
5 - ssLsssL - Antiionian
6 - sssLssL - Antiphrygian

In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian

Transversal

UDP Imprint Name 1 2 3 4 5 6 7
0 LssLsss Antilocrian 1/1 8/7 5/4 4/3 14/9 5/3 11/6
1 LsssLss Antiphrygian 1/1 8/7 5/4 4/3 3/2 5/3 11/6
2 sLssLss Antiaeolian 1/1 12/11 5/4 4/3 3/2 5/3 11/6
3 sLsssLs Antidorian 1/1 12/11 5/4 4/3 3/2 8/5 11/6
4 ssLssLs Antimixolydian 1/1 12/11 6/5 4/3 3/2 8/5 11/6
5 ssLsssL Antiionian 1/1 12/11 6/5 4/3 3/2 8/5 7/4
6 sssLssL Antilydian 1/1 12/11 6/5 9/7 3/2 8/5 7/4

Antidiatonic Names

UDP Imprint Name 1 2 3 4 5 6 7
0 LssLsss Antilocrian P1 M2 M3 P4 A5 M6 M7
1 LsssLss Antiphrygian P1 M2 M3 P4 P5 M6 M7
2 sLssLss Antiaeolian P1 m2 M3 P4 P5 M6 M7
3 sLsssLs Antidorian P1 m2 M3 P4 P5 m6 M7
4 ssLssLs Antimixolydian P1 m2 m3 P4 P5 m6 M7
5 ssLsssL Antiionian P1 m2 m3 P4 P5 m6 m7
6 sssLssL Antilydian P1 m2 m3 d4 P5 m6 m7

7L 2s Nonatonic MOS: Superdiatonic

8|0 - LLLLsLLLs - Superlydian
7|1 - LLLsLLLLs - Adlocrian
6|2 - LLLsLLLsL - Adphrygian
5|3 - LLsLLLLsL - Adaeolian
4|4 - LLsLLLsLL - Addorian
3|5 - LsLLLLsLL - Admixolydian
2|6 - LsLLLsLLL - Adionian
1|7 - sLLLLsLLL - Adlydian
0|8 - sLLLsLLLL - Superlocrian

In cyclic permutational order: Adlocrian - Adaeolian - Admixolydian - Adlydian - Superlydian - Adphrygian - Addorian - Adionian - Superlocrian

Transversal

UDP Imprint Name 1 2 3 4 5 6 7 8 9
8|0 LLLLsLLLs Superlydian 1/1 12/11 6/5 9/7 7/5 3/2 8/5 7/4 21/11
7|1 LLLsLLLLs Adlocrian 1/1 12/11 6/5 9/7 4/3 3/2 8/5 7/4 21/11
6|2 LLLsLLLsL Adphrygian 1/1 12/11 6/5 9/7 4/3 3/2 8/5 7/4 11/6
5|3 LLsLLLLsL Adaeolian 1/1 12/11 6/5 5/4 4/3 3/2 8/5 7/4 11/6
4|4 LLsLLLsLL Addorian 1/1 12/11 6/5 5/4 4/3 3/2 8/5 5/3 11/6
3|5 LsLLLLsLL Admixolydian 1/1 12/11 8/7 5/4 4/3 3/2 8/5 5/3 11/6
2|6 LsLLLsLLL Adionian 1/1 12/11 8/7 5/4 4/3 3/2 14/9 5/3 11/6
1|7 sLLLLsLLL Adlydian 1/1 22/21 8/7 5/4 4/3 3/2 14/9 5/3 11/6
0|8 sLLLsLLLL Superlocrian 1/1 22/21 8/7 5/4 4/3 10/7 14/9 5/3 11/6

"Diatonic" Names

UDP Imprint Name 1 2 3 4 5 6 7 8 9
8|0 LLLLsLLLs Superlydian P1 N2 m3 SM3 A4 P5 m6 (s)m7 (S)M7
7|1 LLLsLLLLs Adlocrian P1 N2 m3 SM3 P4 P5 m6 (s)m7 (S)M7
6|2 LLLsLLLsL Adphrygian P1 N2 m3 SM3 P4 P5 m6 (s)m7 N7
5|3 LLsLLLLsL Adaeolian P1 N2 m3 M3 P4 P5 m6 (s)m7 N7
4|4 LLsLLLsLL Addorian P1 N2 m3 M3 P4 P5 m6 M6 N7
3|5 LsLLLLsLL Admixolydian P1 N2 (S)M2 M3 P4 P5 m6 M6 N7
2|6 LsLLLsLLL Adionian P1 N2 (S)M2 M3 P4 P5 sm6 M6 N7
1|7 sLLLLsLLL Adlydian P1 (s)m2 (S)M2 M3 P4 P5 sm6 M6 N7
0|8 sLLLsLLLL Superlocrian P1 (s)m2 (S)M2 M3 P4 d5 sm6 M6 N7

Superdiatonic Qualities

UDP Imprint Name 1 2 3 4 5 6 7 8 9
8|0 LLLLsLLLs Superlydian P M M M A P M M M
7|1 LLLsLLLLs Adlocrian P M M M P P M M M
6|2 LLLsLLLsL Adphrygian P M M M P P M M m
5|3 LLsLLLLsL Adaeolian P M M m P P M M m
4|4 LLsLLLsLL Addorian P M M m P P M m m
3|5 LsLLLLsLL Admixolydian P M m m P P M m m
2|6 LsLLLsLLL Adionian P M m m P P m m m
1|7 sLLLLsLLL Adlydian P m m m P P m m m
0|8 sLLLsLLLL Superlocrian P m m m P d m m m

Notes on Naming

Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLsLLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Locrian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.

Since there are only seven diatonic modes, two of the superdiatonic modes need additional names. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.

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