Meantone intervals: Difference between revisions

Line 1:

This table shows all the simple intervals of [[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|~~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|~~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 [[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.

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

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]

Line 12:

|-

! | Name

! | Size*

! | Size

! | Ratios

|-

Line 147:

| | 25/12~21/10

|}

* In POTE septimal meantone

@@ Line 1: / Line 1: @@
-This table shows all the simple intervals of [[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|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|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 [[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.
-More complex meantone edos such as [[31edo|31edo]] distinguish all intervals listed on this table.
+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]
@@ Line 12: / Line 12: @@
 |-
 ! | Name
-! | Size*
+! | Size
 ! | Ratios
 |-
@@ Line 147: / Line 147: @@
 | | 25/12~21/10
 |}
-* In POTE septimal meantone