4L 5s: Difference between revisions

Line 15:

The [[TAMNAMS]] name for this pattern is '''gramitonic''' (from ''grave minor third'').

== ~~Notation~~ ==

== Scale properties ==

~~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 ===

~~Thus the 13edo gamut is as follows:~~

=== Modes ===

~~'''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'''

==== Proposed Names ====

[https://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|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}}

== ~~Intervals~~ ==

== Theory ==

~~Note: In TAMNAMS~~, ~~a k-step interval class in 4L 5s may be called a "k-step"~~, ~~"k-mosstep"~~, ~~or "k-gramstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses~~.

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 ==

Line 31:

Line 36:

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¢.

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]].

Parasoft 4L 5s EDOs include [[22edo]], [[31edo]], [[53edo]], and [[84edo]].

Line 72:

Line 75:

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.

~~== Modes ==~~

~~{{MOS mode degrees}}~~

~~===Proposed Names===~~

[https://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|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}}~~

== Scale tree ==

{{Scale tree|Comments=6/5: Lower range of [[orwell]];

~~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:~~

5/3: Upper range of orwell;

13/8: Unnamed golden tuning;

{| ~~class="wikitable center-all"~~

12/5: [[Lovecraft]];

~~! colspan~~="6~~" | Generator~~

13/5: Golden lovecraft}}

~~! Cents~~

~~! L~~

~~! 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 11\49 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 depending on the EDO.

[[Category:Gramitonic]]

@@ Line 15: / Line 15: @@
 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:
+=== Modes ===
+{{MOS mode degrees}}
-'''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'''
+==== Proposed Names ====
+[https://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|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}}
-== Intervals ==
+== Theory ==
-Note: In TAMNAMS, a k-step interval class in 4L 5s may be called a "k-step", "k-mosstep", or "k-gramstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
+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 ==
@@ Line 31: / Line 36: @@
 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¢.
-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]].
 Parasoft 4L 5s EDOs include [[22edo]], [[31edo]], [[53edo]], and [[84edo]].
@@ Line 72: / Line 75: @@
 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.
-== Modes ==
-{{MOS mode degrees}}
-===Proposed Names===
-[https://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|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}}
 == Scale tree ==
+{{Scale tree|Comments=6/5: Lower range of [[orwell]];
-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:
+/3: Upper range of orwell;
+/8: Unnamed golden tuning;
-{| class="wikitable center-all"
+/5: [[Lovecraft]];
-! colspan="6" | Generator
+/5: Golden lovecraft}}
-! Cents
-! L
-! 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 11\49 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 depending on the EDO.
 [[Category:Gramitonic]] <!-- main article -->