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


{{Infobox MOS
{{Infobox MOS
Line 15: Line 15:
The [[TAMNAMS]] name for this pattern is '''gramitonic''' (from ''grave minor third'').
The [[TAMNAMS]] name for this pattern is '''gramitonic''' (from ''grave minor third'').


== Notation ==
== Scale properties ==
{{TAMNAMS use}}


The notation used in this article is LsLsLsLss = JKLMNOPQRJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)
=== Intervals ===
{{MOS intervals}}


Thus the 13edo gamut is as follows:
=== Generator chain ===
{{MOS genchain}}


'''J/R&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M/N@''' '''N/M&''' N&/O@ '''O/P@''' '''P/O&''' P&/Q@ '''Q/R@''' '''R/Q&/J@''' '''J'''
=== Modes ===
{{MOS mode degrees}}


== Intervals ==
==== Proposed names ====
Note: In TAMNAMS, a k-step interval class in 4L 5s may be called a "k-step", "k-mosstep", or "k-orstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
[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 $
Steno $
Limni $
Telma $
Krini $
Elos $
Mychos $
Akti $
Dini $
}}
 
== Theory ==
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]].


== Tuning ranges ==
== Tuning ranges ==
=== Parasoft ===
=== 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 tunings of 4L 5s have a step ratio between 4/3 and 3/2, implying a generator sharper than 7\31 = 270.97¢ and flatter than 5\22 = 272.73¢.
Parasoft 4L 5s edos include [[22edo]], [[31edo]], [[53edo]], and [[84edo]].
* [[22edo]] can be used to make large and small steps more distinct (the step ratio is 3/2).
* [[31edo]] can be used for its nearly pure [[5/4]] and having a better approximation of [[13/8]] than 22edo.
* [[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.


In parasoft 4L 5s, the generator (major mosthird) is an approximate [[7/6]], the major mosfifth is an approximate but rather flat [[11/8]], the minor mosfourth is an approximate [[5/4]], and the major mossixth is an approximate [[3/2]].
The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings.


Parasoft 4L 5s EDOs include [[22edo]], [[31edo]], [[53edo]], and [[84edo]].
* [[22edo]] can be used to make large and small steps more distinct (the step ratio is 3/2).
* [[31edo]] can be used for its nearly pure [[5/4]].
* [[53edo]] can be used for its nearly pure [[3/2]] and good [[5/4]].
The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings.
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
|-
|-
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| [[7/6]]
| [[7/6]]
|-
|-
| L (5g - octave)
| L (5g − octave)
| 3\22, 163.64
| 3\22, 163.64
| 4\31, 154.84
| 4\31, 154.84
Line 63: Line 79:
| [[12/11]], [[11/10]]
| [[12/11]], [[11/10]]
|-
|-
| s (octave - 4g)
| s (octave − 4g)
| 2\22, 109.09
| 2\22, 109.09
| 3\31, 116.13
| 3\31, 116.13
Line 71: Line 87:
|}
|}


This set of JI interpretations (g = 7/6, 2g = 11/8, 3g = 8/5, 7g = 3/2) is called 11-limit [[orwell]] temperament in regular temperament theory.
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.


== Modes ==
== Scales ==
The names have been proposed for these Modes of 2/1 by [https://twitter.com/Lilly__Flores/status/1640779893108805632 Lilly Flores].
* [[Guanyintet9]] – [[311edo|70\311]] tuning
 
* [[Orwell9]] – [[84edo|19\84]] tuning
He told us that he assigned the Greek name relating to water because the word Orwell comes from 'a spring situated near a promontory'.
* [[Lovecraft9]] – [[116edo|27\116]] tuning
{{MOS modes|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}}


== Scale tree ==
== Scale tree ==
 
{{MOS tuning spectrum
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:
| 6/5 = Lower range of [[Orwell]]
 
| 5/3 = Upper range of Orwell
{| class="wikitable center-all"
| 13/8 = Unnamed golden tuning
! colspan="6" | Generator
| 12/5 = [[Lovecraft]]
! Cents
| 13/5 = Golden lovecraft
! L
| 6/1 = [[Gariberttet]]/[[Quasitemp]]/[[Kleiboh]] ↓
! s
}}
! L/s
! Comments
|-
| 2\9 || || || || || || 266.667 || 1 || 1 || 1.000 ||
|-
| || || || || || 11\49 || 269.388 || 6 || 5 || 1.200 ||
|-
| || || || || 9\40 || || 270.000 || 5 || 4 || 1.250 ||
|-
| || || || || || 16\71 || 270.423 || 9 || 7 || 1.286 ||
|-
| || || || 7\31 || || || 270.968 || 4 || 3 || 1.333 ||
|-
| || || || || || 19\84 || 271.429 || 11 || 8 || 1.375 || Orwell is in this region
|-
| || || || || 12\53 || || 271.698 || 7 || 5 || 1.400 ||
|-
| || || || || || 17\75 || 272.000 || 10 || 7 || 1.428 ||
|-
| || || 5\22 || || || || 272.727 || 3 || 2 || 1.500 || L/s = 3/2
|-
| || || || || || 18\79 || 273.418 || 11 || 7 || 1.571 ||
|-
| || || || || 13\57 || || 273.684 || 8 || 5 || 1.600 ||
|-
| || || || || || 21\92 || 273.913 || 13 || 8 || 1.625 || Unnamed golden tuning
|-
| || || || 8\35 || || || 274.286 || 5 || 3 || 1.667 ||
|-
| || || || || || 19\83 || 274.699 || 12 || 7 || 1.714 ||
|-
| || || || || 11\48 || || 275.000 || 7 || 4 || 1.750 ||
|-
| || || || || || 14\61 || 275.410 || 9 || 5 || 1.800 ||
|-
| || 3\13 || || || || || 276.923 || 2 || 1 || 2.000 || Basic gramitonic<br>(Generators smaller than this are proper)
|-
| || || || || || 13\56 || 278.571 || 9 || 4 || 2.250 ||
|-
| || || || || 10\43 || || 279.070 || 7 || 3 || 2.333 ||
|-
| || || || || || 17\73 || 279.452 || 12 || 5 || 2.400 || [https://en.xen.wiki/w/Chromatic_pairs#Lovecraft Lovecraft] is around here
|-
| || || || 7\30 || || || 280.000 || 5 || 2 || 2.500 ||
|-
| || || || || || 18\77 || 280.519 || 13 || 5 || 2.600 || Golden Lovecraft
|-
| || || || || 11\47 || || 280.851 || 8 || 3 || 2.667 ||
|-
| || || || || || 15\64 || 281.250 || 11 || 4 || 2.750 ||
|-
| || || 4\17 || || || || 282.353 || 3 || 1 || 3.000 || L/s = 3/1
|-
| || || || || || 13\55 || 283.636 || 10 || 3 || 3.333 ||
|-
| || || || || 9\38 || || 284.211 || 7 || 2 || 3.500 ||
|-
| || || || || || 14\59 || 284.746 || 11 || 3 || 3.667 ||
|-
| || || || 5\21 || || || 285.714 || 4 || 1 || 4.000 ||
|-
| || || || || || 11\46 || 286.957 || 9 || 2 || 4.500 ||
|-
| || || || || 6\25 || || 288.000 || 5 || 1 || 5.000 ||
|-
| || || || || || 7\29 || 289.655 || 6 || 1 || 6.000 || Gariberttet
|-
| 1\4 || || || || || || 300.000 || 1 || 0 || → inf ||
|}
Note that between 9\40 and 8\35, 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, altough they may still technically support it.


[[Category:Gramitonic]] <!-- main article -->
[[Category:Gramitonic]] <!-- main article -->
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