3L 4s: Difference between revisions

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'''3L 4s''' or '''mosh''' is the [[MOS scale]] built from a generator that falls between 1\3 (one degree of [[3edo]] – 400 cents) and 2\7 (two degrees of [[7edo]] – 343 cents).

~~It has~~ the ~~form s~~ L s L s L s ~~and its~~ various "modes" (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:

== Notation ==

The notation used in this article is sLsLsLs = JKLMNOPJ 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".)

Thus the 10edo gamut is as follows:

'''J/K@/P&''' '''K/J&''' K&/L@ '''L/M@''' '''M/L&''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P/J@''' '''J'''

== Tuning ranges ==

The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic_family|magic]], where the generator is a 5/4 but five of them make a 3/1.

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo|10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L_3s|7L 3s]] ("unfair mosh"); the other scales make MOS [[3L_7s|3L 7s]] ("fair mosh").

In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.

== Modes ==

The various modes of 3L 4s (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:

{| class="wikitable"

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| | led

|}

The ~~two notable harmonic entropy minima with~~ this ~~pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic_family|magic]], where the generator is a 5/4 but five of them make a 3/1.~~

== Scale tree ==

The spectrum looks like this:

{| class="wikitable"

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Line 646:

| style="text-align:center;" |

|}

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo|10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L_3s|7L 3s]] ("unfair mosh"); the other scales make MOS [[3L_7s|3L 7s]] ("fair mosh").

In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.

[[Category:Scales]]

[[Category:MOS scales]]

[[Category:Abstract MOS patterns]]

@@ Line 12: / Line 12: @@
 '''3L 4s''' or '''mosh''' is the [[MOS scale]] built from a generator that falls between 1\3 (one degree of [[3edo]] – 400 cents) and 2\7 (two degrees of [[7edo]] – 343 cents).
-It has the form s L s L s L s and its various "modes" (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:
+== Notation ==
+The notation used in this article is sLsLsLs = JKLMNOPJ 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".)
+Thus the 10edo gamut is as follows:
+'''J/K@/P&''' '''K/J&''' K&/L@ '''L/M@''' '''M/L&''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P/J@''' '''J'''
+== Tuning ranges ==
+<!-- todo -->
+The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic_family|magic]], where the generator is a 5/4 but five of them make a 3/1.
+\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo|10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L_3s|7L 3s]] ("unfair mosh"); the other scales make MOS [[3L_7s|3L 7s]] ("fair mosh").
+In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".
+In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.
+== Modes ==
+The various modes of 3L 4s (with [[Modal UDP Notation]] and nicknames coined by [[Andrew Heathwaite]]) are:
 {| class="wikitable"
@@ Line 48: / Line 70: @@
 | | led
 |}
-The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic_family|magic]], where the generator is a 5/4 but five of them make a 3/1.
+== Scale tree ==
+The spectrum looks like this:
 {| class="wikitable"
@@ Line 621: / Line 646: @@
 | style="text-align:center;" |
 |}
-\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo_neutral_scale|17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo|10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L_3s|7L 3s]] ("unfair mosh"); the other scales make MOS [[3L_7s|3L 7s]] ("fair mosh").
-In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".
-In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.
 [[Category:Scales]]
 [[Category:MOS scales]]
 [[Category:Abstract MOS patterns]]