User:Inthar/5L 3s: Difference between revisions

Inthar (talk | contribs)
No edit summary
Inthar (talk | contribs)
Standing assumptions: switching to our absolute oneiro notation
Tags: Mobile edit Mobile web edit
Line 2: Line 2:


== Standing assumptions ==
== Standing assumptions ==
The [[TAMNAMS]] system is used in this article to name 5L 3s intervals and step size ratios and step ratio ranges.
The Fox-Raven system is used in this article to name 5L 3s pitches.


The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 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.
The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by # "amp" and b "at".  


The chain of perfect 3-steps becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...
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.
 
The chain of perfect 3-steps becomes: ... Pb Kb Nb Q L O J M P K N Q# L# O# ...


Thus the [[13edo]] gamut is as follows:  
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'''
'''J/Q#''' J#/Kb '''K/Lb''' '''L/K#''' L#/Mb '''M''' M#/Nb '''N/Ob''' '''O/N#''' O#/Pb '''P''' '''Q''' Q#/Jb '''J'''


The [[18edo]] gamut is notated as follows:
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'''
'''J''' Q#/Kb J#/Lb '''K''' '''L''' K#/Mb L# '''M''' Nb M#/Ob '''N''' '''O''' Pb O# '''P''' '''Q''' P#/Jb Qb '''J'''


The [[21edo]] gamut:
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'''
'''J''' J# Kb '''K''' K#/Lb '''L''' L# Mb '''M''' M# Nb '''N''' N#/Ob '''O''' O# Pb '''P''' P#/Qb '''Q''' Q# Jb '''J'''


== Modes ==
== Modes ==