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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 == |
| | Collapsed = 1
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| | Pattern = LLLsLLL
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| }}
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| '''6L 1s''' 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.
| | === Intervals === |
| | {{MOS intervals}} |
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| == Names == | | === Generator chain === |
| The [[TAMNAMS]] system uses the name '''archeotonic'''.
| | {{MOS genchain}} |
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| == Notation == | | === Modes === |
| JKLMNOPJ = LLLsLLL (Horthathian mode), &/@ = chroma up/down
| | {{MOS mode degrees}} |
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| == Modes == | | ==== Proposed names ==== |
| === MOS modes === | |
| [[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]] | | [[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]] |
| === MODMOSes ===
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| == Temperaments == | | == Temperaments == |
| There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic pairs#Roulette|roulette]]. (Other temperaments like [[didacus]], [[luna]], [[hemithirds]], and [[hemiwürschmidt]] have very similar 7-note MOSes.) | | 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. |
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| The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale. | | 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. |
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| == Scales == | | == Scales == |
| * [[Roulette7]] | | * [[Tetracot7]] – 34edo, 41edo, and POTE tuning |
| * [[Bluebirds7]] | | * [[Bluebirds7]] – 329edo tuning |
| | * [[Glacial7]] – 84edo tuning |
| | * [[Deutone7]] – 44edo tuning |
| | * [[Leantone7]] – 81edo tuning |
| | * [[Roulette7]] – 37edo tuning |
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| == Scale tree == | | == Scale tree == |
| Generator ranges:
| | {{MOS tuning spectrum |
| * Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
| | | 5/4 = [[Tetracot]] is in this region |
| * Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)
| | | 9/7 = Tetracot/[[modus]]/[[wollemia]] |
| | | | 13/8 = Wilson Golden 2 (181.3227{{c}}) |
| {| class="wikitable center-all" | | | 12/7 = [[Bluebirds]] |
| ! colspan="6" | Generator
| | | 13/5 = Golden [[glacial]] (188.0298{{c}}) |
| ! Cents
| | | 3/1 = [[Spell]] |
| !Remainder
| | | 7/2 = [[Isra]]/[[deutone]] |
| ! L
| | | 4/1 = Isra/[[leantone]] |
| ! s
| | | 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]] |
| ! L/s
| | | 6/1 = Didacus/[[roulette]] |
| ! Comments
| | }} |
| |-
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| | 1\7 || || || || || || 171.429
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| |171.429|| 1 || 1 || 1.000 ||
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| |-
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| | || || || || || 6\41 || 175.610
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| |146.341|| 6 || 5 || 1.200 ||
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| |-
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| | || || || || 5\34 || || 176.471
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| |141.765|| 5 || 4 || 1.250 || [[Tetracot]] is in this region
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| |-
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| | || || || || || 9\61 || 177.049
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| |137.704|| 9 || 7 || 1.286 || Tetracot/[[modus]]/[[wollemia]]
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| |-
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| | || || || 4\27 || || || 177.778
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| |133.333|| 4 || 3 || 1.333 ||
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| |-
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| | || || || || || 11\74 || 178.378
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| |129.730|| 11 || 8 || 1.375 ||
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| |-
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| | || || || || 7\47 || || 178.723
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| |127.660|| 7 || 5 || 1.400 ||
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| |-
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| | || || || || || 10\67 || 179.104
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| |125.373|| 10 || 7 || 1.429 ||
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| |-
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| | || || 3\20 || || || || 180.000
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| |120.000|| 3 || 2 || 1.500 ||
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| |-
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| | || || || || || 11\73 || 180.822
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| |115.068|| 11 || 7 || 1.571 ||
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| |-
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| | || || || || 8\53 || || 181.132
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| |113.208|| 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 13\86 || 181.395
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| |111.628|| 13 || 8 || 1.625 || Wilson Golden 2 (181.3227¢)
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| |-
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| | || || || 5\33 || || || 181.818
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| |109.091|| 5 || 3 || 1.667 ||
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| |-
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| | || || || || || 12\79 || 182.278
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| |106.329|| 12 || 7 || 1.714 || [[Chromatic_pairs#Bluebirds|Bluebirds]]
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| |- | |
| | || || || || 7\46 || || 182.609
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| |104.348|| 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 9\59 || 183.051
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| |101.695|| 9 || 5 || 1.800 ||
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| |-
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| | || 2\13 || || || || || 184.615
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| |92.308|| 2 || 1 || 2.000 || Basic archeotonic
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| |-
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| | || || || || || 9\58 || 186.207
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| |82.759|| 9 || 4 || 2.250 ||
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| |-
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| | || || || || 7\45 || || 186.667
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| |80.000|| 7 || 3 || 2.333 ||
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| |-
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| | || || || || || 12\77 || 187.013
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| |77.922|| 12 || 5 || 2.400 ||
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| |-
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| | || || || 5\32 || || || 187.500
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| |75.000|| 5 || 2 || 2.500 ||
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| |-
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| | || || || || || 13\83 || 187.952
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| |72.289|| 13 || 5 || 2.600 || Golden [[glacial]] (188.0298¢)
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| |-
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| | || || || || 8\51 || || 188.235
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| |70.588|| 8 || 3 || 2.667 ||
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| |-
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| | || || || || || 11\70 || 188.571
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| |68.571|| 11 || 4 || 2.750 ||
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| |-
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| | || || 3\19 || || || || 189.474
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| |63.159|| 3 || 1 || 3.000 || [[Spell]]
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| |-
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| | || || || || || 10\63 || 190.476
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| |57.143|| 10 || 3 || 3.333 ||
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| |-
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| | || || || || 7\44 || || 190.909
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| |54.545|| 7 || 2 || 3.500 || [[Isra]]/[[deutone]]
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| |-
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| | || || || || || 11\69 || 191.304
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| |52.174|| 11 || 3 || 3.667 ||
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| |-
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| | || || || 4\25 || || || 192.000
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| |48.000|| 4 || 1 || 4.000 || Isra/[[leantone]]
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| |-
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| | || || || || || 9\56 || 192.857
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| |42.857|| 9 || 2 || 4.500 ||
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| |-
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| | || || || || 5\31 || || 193.548
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| |38.709|| 5 || 1 || 5.000 || [[Didacus]]/[[hemithirds]]/[[hemiwürschmidt]]
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| |-
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| | || || || || || 6\37 || 194.595
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| |32.432|| 6 || 1 || 6.000 || Didacus/[[roulette]]
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| |-
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| | 1\6 || || || || || || 200.000
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| |0.000|| 1 || 0 || → inf ||
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| |}
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| [[Category:Archeotonic| ]] | | [[Category:Archaeotonic| ]] |
| [[Category:7-tone scales]] | | [[Category:7-tone scales]] |
| <!-- main article --> | | <!-- main article --> |