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-limit tonality diamond. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo#Intervals|31 edo intervals]].

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

In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

In [[~~19edo|~~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.

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.

More complex meantone tunings such as [[31edo]] distinguish all intervals listed on this table.

See also [~~http~~:~~//en.wikipedia.org/wiki/List_of_meantone_intervals Wikipedia's list~~ of meantone intervals]

See also [[Wikipedia: List of meantone intervals]]

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-This table shows all the simple intervals of POTE [[Meantone_family#Septimal meantone|septimal meantone]], which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo#Intervals|31 edo intervals]].
+This table shows all the simple intervals of POTE [[Meantone family #Septimal meantone|septimal meantone]], which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals|31 edo intervals]].
 In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.
-In [[19edo|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.
+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.
 More complex meantone tunings such as [[31edo]] distinguish all intervals listed on this table.
-See also [http://en.wikipedia.org/wiki/List_of_meantone_intervals Wikipedia's list of meantone intervals]
+See also [[Wikipedia: List of meantone intervals]]
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