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4L 5s: Difference between revisions

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: ''For the tritave-equivalent 4L 5s pattern, see [[4L 5s (3/1-equivalent)]].''


{{Infobox MOS
{{Infobox MOS
| Name =  
| Name = gramitonic
| Periods = 1
| Periods = 1
| nLargeSteps = 4
| nLargeSteps = 4
| nSmallSteps = 5
| nSmallSteps = 5
| Equalized = 2
| Equalized = 2
| Paucitonic = 1
| Collapsed = 1
| Pattern = LsLsLsLss
| Pattern = LsLsLsLss
}}
}}
'''4L 5s''' refers to the structure of [[MOS scales]] whose generator falls between 2\9 (two degrees of [[9edo|9edo]] = approx. 266.667¢) and 1\4 (one degree of [[4edo|4edo]] = 300¢). In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:
{{MOS intro}}


{| class="wikitable"
== Names ==
|-
The [[TAMNAMS]] name for this pattern is '''gramitonic''' (from ''grave minor third'').
! colspan="5" | Generator
 
! | Scale
== Scale properties ==
! | Generator in cents
{{TAMNAMS use}}
! | Comments
 
|-
=== Intervals ===
| | 2\9
{{MOS intervals}}
| |
 
| |
=== Generator chain ===
| |
{{MOS genchain}}
| |
 
| style="text-align:center;" | 1 1 1 1 1 1 1 1 1
=== Modes ===
| | 266.667
{{MOS mode degrees}}
| style="text-align:center;" |
 
|-
==== Proposed names ====
| |
[http://twitter.com/Lilly__Flores/status/1640779893108805632 Lilly Flores] proposed using the Greek name relating to water as mode names. The names are in reference to the scale's former name ''orwelloid'' because the word Orwell comes from 'a spring situated near a promontory'.
| |
{{MOS modes
| |
| Mode Names=
| |
Roi $
| | 9\40
Steno $
| style="text-align:center;" | 4 5 4 5 4 5 4 5 4
Limni $
| | 270
Telma $
| |
Krini $
|-
Elos $
| |
Mychos $
| |
Akti $
| |
Dini $
| | 7\31
}}
| |
 
| style="text-align:center;" | 3 4 3 4 3 4 3 4 3
== Theory ==
| | 270.968
The only low harmonic entropy minimum corresponds to [[orwell]] temperament, where 1 generator approximates [[7/6]], 2 generators approximate [[11/8]], and 3 generators approximate [[8/5]].
| style="text-align:center;" |
 
|-
== Tuning ranges ==
| |
=== Parasoft ===
| |
Parasoft tunings of 4L 5s have a step ratio between 4/3 and 3/2, implying a generator sharper than {{nowrap|7\31 {{=}} 270.97{{c}}}} and flatter than {{nowrap|5\22 {{=}} 272.73{{c}}}}.
| |
 
| |
Parasoft 4L 5s edos include [[22edo]], [[31edo]], [[53edo]], and [[84edo]].
| | 12\53
* [[22edo]] can be used to make large and small steps more distinct (the step ratio is 3/2).
| style="text-align:center;" | 5 7 5 7 5 7 5 7 5
* [[31edo]] can be used for its nearly pure [[5/4]] and having a better approximation of [[13/8]] than 22edo.
| | 271.698
* [[53edo]] can be used for its nearly pure [[3/2]] and [[5/4]] and having much more accurate approximations of 13-limit intervals than 22edo or 31edo.
| style="text-align:center;" | Orwell is around here
 
|-
The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings.
| |
| |
| | 5\22
| |
| |
| style="text-align:center;" | 2 3 2 3 2 3 2 3 2
| | 272.727
| style="text-align:center;" | Optimum rank range (L/s=3/2) orwell
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">2 pi 2 pi 2 pi 2 pi 2</span>
| | 273.412
| |
|-
| |
| |
| |
| |
| | 13\57
| style="text-align:center;" | 5 8 5 8 5 8 5 8 5
| | 273.684
| style="text-align:center;" | Golden orwell (bad tuning)
|-
| |
| |
| |
| | 8\35
| |
| style="text-align:center;" | 3 5 3 5 3 5 3 5 3
| | 274.286
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="background-color: #ffffff;">1 √3 1 √3 1 √3 1 √3 1</span>
| | 274.85
| |
|-
| |
| |
| |
| |
| | 11\48
| style="text-align:center;" | 4 7 4 7 4 7 4 7 4
| | 275
| |
|-
| |
| | 3\13
| |
| |
| |
| style="text-align:center;" | 1 2 1 2 1 2 1 2 1
| | 276.923
| style="text-align:center;" | Boundary of propriety:


generators smaller than this are proper
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
|-
| |
| |
| |
| |
| | 10\43
| style="text-align:center;" | 3 7 3 7 3 7 3 7 3
| | 279.07
| |
|-
| |
| |
| |
| | 7\30
| |
| style="text-align:center;" | 2 5 2 5 2 5 2 5 2
| | 280.000
| style="text-align:center;" |
|-
| |
| |
| |
| |
| | 11\47
| style="text-align:center;" | 3 8 3 8 3 8 3 8 3
| | 280.851
| |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 1 e 1 e 1 e 1 e 1
| | 281.100
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| | 4\17
| |
| |
| style="text-align:center;" | 1 3 1 3 1 3 1 3 1
| | 282.353
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | 1 pi 1 pi 1 pi 1 pi 1
| | 282.922
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
|-
| |
!
| |
! [[22edo]]
| |
! [[31edo]]
| |
! [[53edo]]
| | 9\38
! [[84edo]]
| style="text-align:center;" | 2 7 2 <span style="font-size: 12.8000001907349px; line-height: 1.5;">7 </span><span style="font-size: 13px; line-height: 1.5;">2 7 2 7 2 </span>
! JI intervals represented
| | 284.2105
| |
|-
|-
| |
| generator (g)
| |
| 5\22, 272.73
| |
| 7\31, 270.97
| | 5\21
| 12\53, 271.70
| |
| 19\84, 271.43
| style="text-align:center;" | 1 4 1 4 1 4 1 4 1
| [[7/6]]
| | 285.714
| style="text-align:center;" | L/s = 4
|-
|-
| |
| L (5g − octave)
| |
| 3\22, 163.64
| |
| 4\31, 154.84
| |
| 7\53, 158.49
| | 6\25
| 11\84, 157.14
| style="text-align:center;" | 1 5 1 5 1 5 1 5 1
| [[12/11]], [[11/10]]
| | 288
| |
|-
|-
| | 1\4
| s (octave − 4g)
| |
| 2\22, 109.09
| |
| 3\31, 116.13
| |
| 5\53, 113.21
| |
| 8\84, 114.29
| style="text-align:center;" | 0 1 0 1 0 1 0 1 0
| [[16/15]], [[15/14]]
| | 300.000
| style="text-align:center;" |
|}
|}


Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.
This set of JI interpretations ({{nowrap|g → 7/6|2g → 11/8|3g → 8/5|7g → 3/2}}) is called 11-limit [[Orwell]] temperament in regular temperament theory.
[[Category:Abstract MOS patterns]]
 
[[Category:scales]]
== Scales ==
* [[Guanyintet9]] – [[311edo|70\311]] tuning
* [[Orwell9]] – [[84edo|19\84]] tuning
* [[Lovecraft9]] – [[116edo|27\116]] tuning
 
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = Lower range of [[Orwell]]
| 5/3 = Upper range of Orwell
| 13/8 = Unnamed golden tuning
| 12/5 = [[Lovecraft]]
| 13/5 = Golden lovecraft
| 6/1 = [[Gariberttet]]/[[Quasitemp]]/[[Kleiboh]]&nbsp;↓
}}
 
[[Category:Gramitonic]] <!-- main article -->
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