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8L 3s (3/1-equivalent): Difference between revisions

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The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges.
The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges.


The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11), #/f = up/down by chroma.
The notation used in this article is GHJKLABCDEFG = LLsLLLsLLLs (Ionian #11), #/f = up/down by chroma (mnemonic f = F molle in Latin).


Thus the [[19edt]] gamut is as follows:
Thus the [[19edt]] gamut is as follows:
Line 1,304: Line 1,304:
| 50/49 81/80 91/90
| 50/49 81/80 91/90
|}
|}
====Intervals====
====Intervals ====
Sortable table of intervals in the Great Mixolydian mode and their Buzzard interpretations:
Sortable table of intervals in the Great Mixolydian mode and their Ultrapyth interpretations:
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
|-
|-
!Degree
!Degree
!Size in [[38edo|~]][[59edt]]
!Size in ~[[59edt]]
!Size in ~[[83edt]]
!Size in ~[[83edt]]
!Size in ~[[91edt]]
!Size in ~[[91edt]]
!Size in ~[[99edt]]
!Size in ~[[99edt]]
!Size in POTE tuning
! Size in POTE tuning
!Note name on D
! Note name on D
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
!#Gens up
!#Gens up
Line 1,329: Line 1,329:
|-
|-
|2
|2
| 7\59, 227.03
|7\59, 227.03
| 10\83, 230.77
|10\83, 230.77
|11\91, 231.58
|11\91, 231.58
|12\99, 232.26
|12\99, 232.26
Line 1,340: Line 1,340:
|3
|3
|14\59, 454.05
|14\59, 454.05
| 20\83, 461.54
|20\83, 461.54
|22\91, 463.16
|22\91, 463.16
|24\99, 464.52
|24\99, 464.52
|461.10
|461.10
|F
|F
|13/10, 9/7
| 13/10, 9/7
| +6
| +6
|-
|-
| 4
|4
|15\59, 486.49
|15\59, 486.49
|21\83, 484.615
|21\83, 484.615
Line 1,354: Line 1,354:
|25\99, 483.87
|25\99, 483.87
|482.06
|482.06
| G
|G
|4/3
|4/3
| -2
| -2
|-
|-
|5
|5
| 22\59, 713.51
|22\59, 713.51
| 31\83, 715.385
|31\83, 715.385
|34\91, 715.79
|34\91, 715.79
|37\99, 716.13
|37\99, 716.13
| 712.61
|712.61
|H
|H
|3/2
|3/2
Line 1,370: Line 1,370:
|6
|6
|29\59, 940.54
|29\59, 940.54
| 41\83, 946.15
|41\83, 946.15
|45\91, 947.36
|45\91, 947.36
|49\99, 948.39
|49\99, 948.39
|943.16
|943.16
|J
|J
| 12/7, 26/15
|12/7, 26/15
| +4
| +4
|-
|-
Line 1,385: Line 1,385:
|964.12
|964.12
|K
|K
| 7/4
|7/4
| -4
| -4
|-
|-
Line 1,396: Line 1,396:
|L
|L
|2/1
|2/1
| -1
| -1
|-
|-
|9
|9
Line 1,415: Line 1,415:
|1655.77
|1655.77
|B
|B
|13/5, 18/7
| 13/5, 18/7
| +5
| +5
|-
|-
Line 1,431: Line 1,431:
|}
|}
==Modes==
==Modes==
Oneirotonic modes are named after cities in the Dreamlands.
Obikhodic modes are named after the Church modes, but with a “Great” prefix.
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,438: Line 1,438:
| style="text-align:center;" |'''Name'''
| style="text-align:center;" |'''Name'''
|-
|-
| |LLsLLsLs
|LLLsLLLsLLs
| style="text-align:center;" |<nowiki>7|0</nowiki>
| style="text-align:center;" |<nowiki>10|0</nowiki>
| |Dylathian (də-LA(H)TH-iən)
|(Great) Lydian #8 (Tanagran)
|-
|LLLsLLsLLLs
| style="text-align:center;" |<nowiki>9|1</nowiki>
|(Great) Lydian
|-
|LLsLLLsLLLs
| style="text-align:center;" |<nowiki>8|2</nowiki>
|(Great) Lydian b4, Ionian #11 (Distomian)
|-
| |LLsLLLsLLsL
| style="text-align:center;" |<nowiki>7|3</nowiki>
| |(Great) Ionian
|-
| |LLsLLsLLLsL
| style="text-align:center;" |<nowiki>6|4</nowiki>
| |(Great) Mixolydian
|-
| |LsLLLsLLLsL
| style="text-align:center;" |<nowiki>5|5</nowiki>
| |(Great) Mixolydian b3, Dorian #10 (Livadeian)
|-
|-
| |LLsLsLLs
| |LsLLLsLLsLL
| style="text-align:center;" |<nowiki>6|1</nowiki>
| style="text-align:center;" |<nowiki>4|6</nowiki>
| |Illarnekian (ill-ar-NEK-iən)
| |(Great) Dorian
|-
|-
| |LsLLsLLs
| |LsLLsLLLsLL
| style="text-align:center;" |<nowiki>5|2</nowiki>
| style="text-align:center;" |<nowiki>3|7</nowiki>
| |Celephaïsian (kel-ə-FAY-zhən)
| |(Great) Aeolian
|-
|-
| |LsLLsLsL
| | sLLLsLLLsLL
| style="text-align:center;" |<nowiki>4|3</nowiki>
| style="text-align:center;" |<nowiki>2|8</nowiki>
| | Ultharian (ul-THA(I)R-iən)
| |(Great) Aeolian b2, Phrygian #9 (Theban)
|-
|-
| |LsLsLLsL
| |sLLLsLLsLLL
| style="text-align:center;" |<nowiki>3|4</nowiki>
| style="text-align:center;" |<nowiki>1|9</nowiki>
| |Mnarian (mə-NA(I)R-iən)
| |(Great) Phrygian
|-
|-
| |sLLsLLsL
| |sLLsLLLsLLL
| style="text-align:center;" |<nowiki>2|5</nowiki>
| style="text-align:center;" |<nowiki>0|10</nowiki>
| | Kadathian (kə-DA(H)TH-iən)
| |(Great) Locrian
|}
 
===Cyclic Permutation order===
{| class="wikitable"
|+
!Spelling
!'''Mode'''
![[Modal UDP Notation|'''UDP''']]
!'''Name'''
|-
|-
| |sLLsLsLL
|GHJKLABCDEFG
| style="text-align:center;" |<nowiki>1|6</nowiki>
|LLsLLLsLLLs
| |Hlanithian (lə-NITH-iən)
| style="text-align:center;" |<nowiki>8|2</nowiki>
|(Great) Distomian
|-
|-
| |sLsLLsLL
|HJKLABCDEFGH
| style="text-align:center;" |<nowiki>0|7</nowiki>
|LsLLLsLLLsL
| |Sarnathian (sar-NA(H)TH-iən), can be shortened to "Sarn"
| style="text-align:center;" |<nowiki>5|5</nowiki>
|}<references />
|(Great) Livadeian
|-
|JKLABCDEFGHJ
|sLLLsLLLsLL
| style="text-align:center;" |<nowiki>2|8</nowiki>
|(Great) Theban
|-
|KLABCDEFGHJK
|LLLsLLLsLLs
| style="text-align:center;" |<nowiki>10|0</nowiki>
|(Great) Tanagran
|-
|LABCDEFGHJKL
|LLsLLLsLLsL
| style="text-align:center;" |<nowiki>7|3</nowiki>
|(Great) Ionian
|-
|ABCDEFGHJKLA
|LsLLLsLLsLL
| style="text-align:center;" |<nowiki>4|6</nowiki>
|(Great) Dorian
|-
|BCDEFGHJKLAB
|sLLLsLLsLLL
| style="text-align:center;" |<nowiki>1|9</nowiki>
|(Great) Phrygian
|-
|CDEFGHJKLABC
|LLLsLLsLLLs
| style="text-align:center;" |<nowiki>9|1</nowiki>
|(Great) Lydian
|-
|DEFGHJKLABCD
|LLsLLsLLLsL
| style="text-align:center;" |<nowiki>6|4</nowiki>
|(Great) Mixolydian
|-
|EFGHJKLABCDE
|LsLLsLLLsLL
| style="text-align:center;" |<nowiki>3|7</nowiki>
|(Great) Aeolian
|-
|FGHJKLABCDEF
|sLLsLLLsLLL
| style="text-align:center;" |<nowiki>0|10</nowiki>
|(Great) Locrian
|}
===Notes on Naming===
The modes of the Obikhodic scale are  named after the existing modes, but contain the "Great" prefix (e.g. Great Ionian, Great Aeolian, etc.). The "Great" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
 
Each Obikhodic mode contains its corresponding mode in the diatonic scale. This leads to a pattern: LLsLLLsLLLs and LLsLLLsLLsL both contain the meantone LLsLLLs Ionian mode. Additionally, sLLsLLLsLLL contains the diatonic sLLsLLL Locrian mode.
 
Since there are only seven diatonic modes, four of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These four modes present themselves as "altered" modes, which have an accidental the mode below them lacks, or vice versa. These are the only four modes to exhibit this behavior. They're interspersed on the ranking above and below Lydian, between Dorian and Mixolydian and between Aeolian and Phrygian and on the rotational continuum between Locrian and Ionian.
 
As were the original modes named after regions of ancient Greece, so are these new Obikhodic extensions. They are called after regions of Boeotia, set up so that the Locrian -> Distomian -> Livadeian -&gt; Theban -&gt; Tanagran -&gt; Ionian cyclic sequence will resemble the geography of ancient Greece.
 
== Scale tree ==
{| class="wikitable"
|+
! colspan="2" |Generator
!Normalized
!''ed19\12''
|-
|3\8
|
|<u>720</u>
|''712.5''
|-
|19\51
|
|<u>712.5</u>
|''707.843''
|-
|
|35\94
|<u>711.864</u>
|''707.447''
|-
|16\43
|
|<u>711.111</u>
|''706.977''
|-
|
|29\78
|<u>710.204</u>
|''706.41''
|-
|13\35
|
|<u>709.091</u>
|''705.714''
|-
|
|23\62
|<u>707.692</u>
|''704.839''
|-
|10\27
|
|<u>705.882</u>
|''703.704''
|-
|
|17\46
|<u>703.448</u>
|''702.174''
|-
|7\19
|
|<u>700</u>
|''700''
|-
|
|18\49
|<u>696.77</u>
|''697.959''
|-
|11\30
|
|<u>694.737</u>
|''696.667''
|-
|
|26\71
|<u>693.333</u>
|''695.775''
|-
|15\41
|
|<u>692.308</u>
|''695.122''
|-
|
|34\93
|<u>691.525</u>
|''694.623''
|-
|19\52
|
|<u>690.909</u>
|''694.231''
|-
|
|42\115
|<u>690.411</u>
|''693.913''
|-
|23\63
|
|<u>690</u>
|''693.651''
|-
|4\11
|
|<u>685.714</u>
|''690.909''
|}
<references />


<references />
<references />
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