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6L 1s: Difference between revisions

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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 = LLLLLLs
=== Intervals ===
}}
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
==== Proposed names ====
[[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]]
 
== 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.


There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot_family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7|roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic_pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)
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.


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.
== Scales ==
* [[Tetracot7]] – 34edo, 41edo, and POTE tuning
* [[Bluebirds7]] – 329edo tuning
* [[Glacial7]] – 84edo tuning
* [[Deutone7]] – 44edo tuning
* [[Leantone7]] – 81edo tuning
* [[Roulette7]] – 37edo tuning


Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
== Scale tree ==
{{MOS tuning spectrum
| 5/4 = [[Tetracot]] is in this region
| 9/7 = Tetracot/[[modus]]/[[wollemia]]
| 13/8 = Wilson Golden 2 (181.3227{{c}})
| 12/7 = [[Bluebirds]]
| 13/5 = Golden [[glacial]] (188.0298{{c}})
| 3/1 = [[Spell]]
| 7/2 = [[Isra]]/[[deutone]]
| 4/1 = Isra/[[leantone]]
| 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]]
| 6/1 = Didacus/[[roulette]]
}}


{| class="wikitable"
[[Category:Archaeotonic| ]]
|-
[[Category:7-tone scales]]
! colspan="6" | Generator
<!-- main article -->
! | Cents
! | Comments
|-
| | 1\7
| |
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" |  
|-
| |
| |
| |
| |
| |
| | 6\41
| | 175.61
| style="text-align:center;" | Enipucrop is between here and 1\7
|-
| |
| |
| |
| |
| | 5\34
| |
| | 176.47
| style="text-align:center;" | Tetracot is around here
|-
| |
| |
| |
| | 4\27
| |
| |
| | 177.78
| style="text-align:center;" |
|-
| |
| |
| | 3\20
| |
| |
| |
| | 180
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 180.815
| |
|-
| |
| |
| |
| |
| | 8\53
| |
| | 181.13
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 1200/(5+phi)
| style="text-align:center;" | Unnamed golden temperament (discussed in [http://launch.groups.yahoo.com/group/tuning/message/100254 this thread])
|-
| |
| |
| |
| | 5\33
| |
| |
| | 181.82
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 182.44
| |
|-
| |
| |
| |
| |
| | 7\46
| |
| | 182.61
| |
|-
| |
| | 2\13
| |
| |
| |
| |
| | 184.62
| style="text-align:center;" | Optimum rank range glacial (L/s=2/1)
|-
| |
| |
| |
| | 5\32
| |
| |
| | 187.5
| |
|-
| |
| |
| |
| |
| |
| |
| | 188.03
| |
|-
| |
| |
| |
| |
| | 8\51
| |
| | 188.235
| |
|-
| |
| |
| |
| |
| |
| |
| | 188.45
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| | 3\19
| |
| |
| |
| | 189.47
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| | 189.92
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| |
| | 4\25
| |
| |
| | 192
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| | 5\31
| |
| | 193.55
| style="text-align:center;" | Luna/hemithird/roulette is around here
|-
|
|
|
|
|
|6\37
|194.595
|
|-
| | 1\6
| |
| |
| |
| |
| |
| | 200
| style="text-align:center;" |
|}
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