5L 3s: Difference between revisions

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In the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.

== Notation==

The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch J = 180 Hz, 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".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.

Thus the [[13edo]] gamut is as follows:

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

The [[18edo]] gamut is notated as follows:

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

The [[21edo]] gamut:

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

Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.

== Scale tree ==

{| class="wikitable" style="text-align:center;"

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| 55/54 81/80 91/90

|}

~~== Notation==~~

The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch J = 180 Hz, 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".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.

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

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

~~The [[18edo]] gamut is notated as follows:~~

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

~~The [[21edo]] gamut:~~

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

~~Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.~~

== Intervals ==

@@ Line 30: / Line 30: @@
 In the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament [[father]]. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.
+== Notation==
+The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch J = 180 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L &minus; s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.
+Thus the [[13edo]] gamut is as follows:
+'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P''' '''Q''' Q&/J@ '''J'''
+The [[18edo]] gamut is notated as follows:
+'''J''' Q&/K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' P@ O& '''P''' '''Q''' P&/J@ Q@ '''J'''
+The [[21edo]] gamut:
+'''J''' J& K@ '''K''' K&/L@ '''L''' L& M@ '''M''' M& N@ '''N''' N&/O@ '''O''' O& P@ '''P''' P&/Q@ '''Q''' Q& J@ '''J'''
+Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.
 == Scale tree ==
 {| class="wikitable" style="text-align:center;"
@@ Line 616: / Line 632: @@
 | 55/54 81/80 91/90
 |}
-== Notation==
-The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch J = 180 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L &minus; s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.
-Thus the [[13edo]] gamut is as follows:
-'''J/Q&''' J&/K@ '''K/L@''' '''L/K&''' L&/M@ '''M''' M&/N@ '''N/O@''' '''O/N&''' O&/P@ '''P''' '''Q''' Q&/J@ '''J'''
-The [[18edo]] gamut is notated as follows:
-'''J''' Q&/K@ J&/L@ '''K''' '''L''' K&/M@ L& '''M''' N@ M&/O@ '''N''' '''O''' P@ O& '''P''' '''Q''' P&/J@ Q@ '''J'''
-The [[21edo]] gamut:
-'''J''' J& K@ '''K''' K&/L@ '''L''' L& M@ '''M''' M& N@ '''N''' N&/O@ '''O''' O& P@ '''P''' P&/Q@ '''Q''' Q& J@ '''J'''
-Note: N is close to standard C, since the reference pitch 180 Hz for J was chosen to be nearly a pure 16/11 below standard 12edo C.
 == Intervals ==