Meantone intervals: Difference between revisions

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This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals|31edo intervals]]. Intervals in limits higher than 7 are in brackets.

In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.

In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except arguably for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.

In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.

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 This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals|31edo intervals]]. Intervals in limits higher than 7 are in brackets.
-In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.
+In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except arguably for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.
 In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.