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2L 5s: Difference between revisions

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{{Todo|expand|inline=1|text=Add hard-of-basic tunings, include JI ratio approximations}}
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
Line 23: Line 24:
2L 5s has several rank-2 temperament interpretations, such as:
2L 5s has several rank-2 temperament interpretations, such as:


*[[Chromatic pairs#Score|Score]], with generators around 540.1¢.
* [[Mavila]], with generators around 679.8¢.
*[[Liese]], with generators around 632.4¢.
* [[Casablanca]], with generators around 657.8¢.
*[[Mavila]], with generators around 679.8¢.
* [[Liese]], with generators around 632.4¢.


== Tuning ranges ==
=== Simple tunings ===
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].
{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7}}
=== Soft-of-basic tunings ===
{{Main|Mavila}}
Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].
{{MOS degrees|Step Ratio=3/2; 4/3|Genchain Extend=3}}
==Modes==
==Modes==
Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". [[User:CompactStar|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". [[User:CompactStar|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
{{MOS modes|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian|Table Headers=CompactStar's names|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}
{{MOS modes|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian|Table Headers=CompactStar's names|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}
==Scale tree==
==Scale tree==
Generator ranges:
{{Scale tree|Comments=6/5: [[Gravity]]↑;
* Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
3/2: [[Mavila]];
*Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)
13/8: Golden mavila (527.1497¢);
 
9/5: [[Mabila]]/[[Amavil]];
{| class="wikitable center-all"
2/1: Generators smaller than this are proper;
! colspan="6" |Generator
5/2: Score;
!Cents
13/5: Unnamed golden tuning (541.3837¢);
!L
8/3: [[Casablanca]];
!s
11/3: [[Freivald]]/[[emka]];
!L/s
7/15: [[Thuja]];
!Comments
6/1: [[Liese]]↓, [[triton]]↓}}
|-
|3\7|| || || || || || 514.286||1||1||1.000||
|-
| || || || || ||16\37||518.919||6||5||1.200||[[Gravity]]↑
|-
| || || || || 13\30|| ||520.000||5 || 4||1.250||
|-
| || || || || ||23\53 ||520.755||9||7||1.286||
|-
| || || ||10\23|| || ||521.739||4||3||1.333 ||
|-
| || || || || ||27\62 ||522.581||11||8||1.375||
|-
| || || ||  ||17\39|| ||523.077 ||7 ||5||1.400 ||
|-
| || || || || ||24\55 || 523.636||10 || 7||1.428||
|-
|  ||  ||7\16 ||  ||  ||  || 525.000|| 3|| 2||1.500||[[Mavila]] is in this region
|-
| || || || || ||25\57|| 526.316 ||11||7||1.571||
|-
| || || || ||18\41|| ||526.829 ||8|| 5|| 1.600||
|-
|  ||  || || ||  || 29\66||527.273||13||8 || 1.625 ||Golden mavila (527.1497¢)
|-
|  ||  ||  || 11\25|| || ||528.000||5 || 3|| 1.667 ||
|-
| || || ||  ||  || 26\59||528.814||12||7||1.714 ||
|-
| || || || ||15\34 ||  || 529.412 ||7|| 4||1.750||
|-
| || ||  ||  || ||19\43||530.233||9||5 || 1.800 ||[[Mabila]] / [[Amavil]]
|-
| ||4\9|| || || || ||533.333||2|| 1||2.000 || Basic antidiatonic <br>(Generators smaller than this are proper)
|-
| || || || ||  || 17\38||536.842||9||4||2.250||
|-
| || || || ||13\29|| ||537.931 ||7||3||2.333||
|-
| || || || || ||22\49||538.776||12 || 5||2.400||
|-
| ||  ||  ||9\20|| || ||540.000 || 5|| 2|| 2.500||Score
|-
| || || || || ||23\51||541.176||13||5||2.600 ||Unnamed golden tuning (541.3837¢)
|-
|  || ||  ||  || 14\31|| ||541.935||8||3||2.667 ||[[Casablanca]] is around here
|-
| ||  || || || ||19\42 || 542.857||11|| 4|| 2.750 ||
|-
| || ||5\11|| || || ||545.455||3||1||3.000||
|-
|  || || || || || 16\35||548.571 ||10||3||3.333||
|-
| || || || ||11\24|| ||550.000||7||2||3.500 ||
|-
| ||  ||  || || ||17\37||551.351||11||3||3.667 ||[[Freivald]] / [[emka]]
|-
|  || || ||6\13|| || ||553.846||4||1||4.000||
|-
|  ||  || ||  ||  ||13\28|| 557.143||9||2||4.500 ||
|-
| || || || ||7\15|| ||560.000||5|| 1||5.000 ||[[Thuja]] is around here
|-
| || || || || ||8\17||564.706|| 6|| 1||6.000||[[Liese]]↓, [[triton]]↓
|-
|1\2|| || || || || ||600.000 ||1||0||→ inf||
|}
 
[[Category:7-tone scales]]
[[Category:7-tone scales]]
[[Category:Antidiatonic| ]] <!-- main article -->
[[Category:Antidiatonic| ]] <!-- main article -->
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