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| {{Infobox MOS | | {{Infobox MOS}} |
| | Name = archeotonic
| | {{MOS intro}} |
| | Periods = 1
| | == Names == |
| | nLargeSteps = 6
| | {{TAMNAMS name}} |
| | nSmallSteps = 1
| | |
| | Equalized = 1
| | == Scale properties == |
| | Paucitonic = 1
| | |
| | Pattern = LLLsLLL
| | === Intervals === |
| }} | | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
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| '''1L 6s''' or '''archeotonic''' is the [[MOS scale]] built from a generator between 1\7 (171¢) and 1\6 (200¢). Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
| | === Modes === |
| | {{MOS mode degrees}} |
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| == Notation == | | ==== Proposed names ==== |
| JKLMNOPJ = LLLsLLL (Horthathian mode), &/@ = chroma up/down
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| == Modes ==
| |
| === MOS modes ===
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| [[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]] | | [[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]] |
| === MODMOSes ===
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| == Temperaments == | | == Temperaments == |
| {{main|6L 1s/Temperaments}}
| | There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette|roulette]] and [[Hemimean clan#Mediantone|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit. |
| | |
| | The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds|Bluebirds]], where the generator is identified with [[143/128]]; for example {{nowrap|L {{=}} 7|s {{=}} 4}} (46 edo) is such a scale. |
| | |
| | == Scales == |
| | * [[Tetracot7]] – 34edo, 41edo, and POTE tuning |
| | * [[Bluebirds7]] – 329edo tuning |
| | * [[Glacial7]] – 84edo tuning |
| | * [[Deutone7]] – 44edo tuning |
| | * [[Leantone7]] – 81edo tuning |
| | * [[Roulette7]] – 37edo tuning |
| | |
| == Scale tree == | | == Scale tree == |
| {| class="wikitable center-all" | | {{MOS tuning spectrum |
| ! colspan="6" | Generator
| | | 5/4 = [[Tetracot]] is in this region |
| ! Cents
| | | 9/7 = Tetracot/[[modus]]/[[wollemia]] |
| ! L
| | | 13/8 = Wilson Golden 2 (181.3227{{c}}) |
| ! s
| | | 12/7 = [[Bluebirds]] |
| ! L/s
| | | 13/5 = Golden [[glacial]] (188.0298{{c}}) |
| ! Comments
| | | 3/1 = [[Spell]] |
| |-
| | | 7/2 = [[Isra]]/[[deutone]] |
| | 1\7 || || || || || || 171.429 || 1 || 1 || 1.000 ||
| | | 4/1 = Isra/[[leantone]] |
| |-
| | | 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]] |
| | || || || || || 6\41 || 175.610 || 6 || 5 || 1.200 ||
| | | 6/1 = Didacus/[[roulette]] |
| |-
| | }} |
| | || || || || 5\34 || || 176.471 || 5 || 4 || 1.250 || Tetracot is in this region
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| |-
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| | || || || || || 9\61 || 177.049 || 9 || 7 || 1.286 ||
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| |-
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| | || || || 4\27 || || || 177.778 || 4 || 3 || 1.333 ||
| |
| |-
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| | || || || || || 11\74 || 178.378 || 11 || 8 || 1.375 ||
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| |-
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| | || || || || 7\47 || || 178.723 || 7 || 5 || 1.400 ||
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| |-
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| | || || || || || 10\67 || 179.104 || 10 || 7 || 1.428 ||
| |
| |-
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| | || || 3\20 || || || || 180.000 || 3 || 2 || 1.500 || L/s = 3/2
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| |-
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| | || || || || || 11\73 || 180.822 || 11 || 7 || 1.571 ||
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| |-
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| | || || || || 8\53 || || 181.132 || 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 13\86 || 181.395 || 13 || 8 || 1.625 || Unnamed golden tuning
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| |-
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| | || || || 5\33 || || || 181.818 || 5 || 3 || 1.667 ||
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| |-
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| | || || || || || 12\79 || 182.278 || 12 || 7 || 1.714 || Bluebirds
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| |- | |
| | || || || || 7\46 || || 182.609 || 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 9\59 || 183.051 || 9 || 5 || 1.800 ||
| |
| |-
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| | || 2\13 || || || || || 184.615 || 2 || 1 || 2.000 || Basic archeotonic
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| |-
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| | || || || || || 9\58 || 186.207 || 9 || 4 || 2.250 ||
| |
| |-
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| | || || || || 7\45 || || 186.667 || 7 || 3 || 2.333 ||
| |
| |-
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| | || || || || || 12\77 || 187.013 || 12 || 5 || 2.400 ||
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| |-
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| | || || || 5\32 || || || 187.500 || 5 || 2 || 2.500 ||
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| |-
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| | || || || || || 13\83 || 187.952 || 13 || 5 || 2.600 || Unnamed golden tuning
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| |-
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| | || || || || 8\51 || || 188.235 || 8 || 3 || 2.667 ||
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| |-
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| | || || || || || 11\70 || 188.571 || 11 || 4 || 2.750 ||
| |
| |-
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| | || || 3\19 || || || || 189.474 || 3 || 1 || 3.000 || L/s = 3/1
| |
| |-
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| | || || || || || 10\63 || 190.476 || 10 || 3 || 3.333 ||
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| |-
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| | || || || || 7\44 || || 190.909 || 7 || 2 || 3.500 ||
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| |-
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| | || || || || || 11\69 || 191.304 || 11 || 3 || 3.667 ||
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| |-
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| | || || || 4\25 || || || 192.000 || 4 || 1 || 4.000 ||
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| |-
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| | || || || || || 9\56 || 192.857 || 9 || 2 || 4.500 ||
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| |-
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| | || || || || 5\31 || || 193.548 || 5 || 1 || 5.000 || Didacus, hemithirds, hemiwürschmidt
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| |-
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| | || || || || || 6\37 || 194.595 || 6 || 1 || 6.000 || Roulette
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| |-
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| | 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:Scales]] | | [[Category:Archaeotonic| ]] |
| [[Category:MOS scales]] | | [[Category:7-tone scales]] |
| [[Category:Abstract MOS patterns]]
| | <!-- main article --> |
| [[Category:Archeotonic| ]] <!-- main article -->
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