Dual-fifth tuning: Difference between revisions

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== Dual-fifth scales ==

[[Sixix]][7] can be regarded as the scale which is the most authentic representation of the "dual-fifth" phenomenon via its [[mode]]s, since it features both sharp and flat fifth on different modes, and the interval in this case occupies 5 staff positions. For example, in [[25edo]], sixix can take form of 4 3 4 3 4 3 4, where five staff positions occupy 18\25 (sharp fifth), but if the mode is 3 4 3 4 3 4 4, then five staff positions are equal to 17\25 (flat fifth).

[[Sixix]][7] can be regarded as the scale which is the most authentic representation of the "dual-fifth" phenomenon via its [[mode]]s, since it features both sharp and flat fifth on different modes, and the interval in this case occupies 5 staff positions. For example, in [[25edo]], sixix can take form of 4 3 4 3 4 3 4, where five staff positions occupy 18\25 (sharp fifth), but if the mode is 3 4 3 4 3 4 4, then five staff positions are equal to 17\25 (flat fifth). However, it should be noted that in better tunings of sixix, the flat fifth is Mavila-like in quality while the sharp fifth is a comparatively accurate [[superpyth]] diatonic fifth.

== Dual-fifth edos ==

[[35edo]] is the [[equal temperament]] which can be said to most authentically represent the concept of "dual-fifth", since its fifths of 20\35 and 21\35 correspond to the bounds of the tuning range for the [[diatonic]] scale where the term ''fifth'' in the standard Western practice originates from. 35edo is the largest [[edo]] without a diatonic scale, and it is therefore the smallest whose sharp and flat fifth can be equally treated as being approximants of five staff positions of the diatonic scale.

Although edos like [[18edo]], [[23edo]] and [[25edo]] have been extensively studied as dual-fifth, their corresponding dual-fifth intervals that are also often considered as [[2L 5s|~~mavila~~]] generators or subminor sixths, and not every musical approach treats them as approximants of 3/2 or intervals playing the role of the fifth.

Although edos like [[18edo]], [[23edo]] and [[25edo]] have been extensively studied as dual-fifth, their corresponding dual-fifth intervals that are also often considered as [[2L 5s|antidiatonic]] generators or subminor sixths, and not every musical approach treats them as approximants of 3/2 or intervals playing the role of the fifth.

Perhaps a more familiar dual-fifth system to many is [[18edo]]. It is the first system that has intervals that are close enough to 3/2 that they can be regarded as sharp and flat fifth, but also far enough to sound different. Its sharp fifth and flat fifth are almost equally off from just: it has a 733.3¢ sharp fifth 31.4¢ sharp from pure [[3/2]], and a 666.7¢ flat fifth is 35.3¢ flat.

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 == Dual-fifth scales ==
-[[Sixix]][7] can be regarded as the scale which is the most authentic representation of the "dual-fifth" phenomenon via its [[mode]]s, since it features both sharp and flat fifth on different modes, and the interval in this case occupies 5 staff positions. For example, in [[25edo]], sixix can take form of 4 3 4 3 4 3 4, where five staff positions occupy 18\25 (sharp fifth), but if the mode is 3 4 3 4 3 4 4, then five staff positions are equal to 17\25 (flat fifth).
+[[Sixix]][7] can be regarded as the scale which is the most authentic representation of the "dual-fifth" phenomenon via its [[mode]]s, since it features both sharp and flat fifth on different modes, and the interval in this case occupies 5 staff positions. For example, in [[25edo]], sixix can take form of 4 3 4 3 4 3 4, where five staff positions occupy 18\25 (sharp fifth), but if the mode is 3 4 3 4 3 4 4, then five staff positions are equal to 17\25 (flat fifth). However, it should be noted that in better tunings of sixix, the flat fifth is Mavila-like in quality while the sharp fifth is a comparatively accurate [[superpyth]] diatonic fifth.
 == Dual-fifth edos ==
 [[35edo]] is the [[equal temperament]] which can be said to most authentically represent the concept of "dual-fifth", since its fifths of 20\35 and 21\35 correspond to the bounds of the tuning range for the [[diatonic]] scale where the term ''fifth'' in the standard Western practice originates from. 35edo is the largest [[edo]] without a diatonic scale, and it is therefore the smallest whose sharp and flat fifth can be equally treated as being approximants of five staff positions of the diatonic scale.
-Although edos like [[18edo]], [[23edo]] and [[25edo]] have been extensively studied as dual-fifth, their corresponding dual-fifth intervals that are also often considered as [[2L 5s|mavila]] generators or subminor sixths, and not every musical approach treats them as approximants of 3/2 or intervals playing the role of the fifth.
+Although edos like [[18edo]], [[23edo]] and [[25edo]] have been extensively studied as dual-fifth, their corresponding dual-fifth intervals that are also often considered as [[2L 5s|antidiatonic]] generators or subminor sixths, and not every musical approach treats them as approximants of 3/2 or intervals playing the role of the fifth.
 Perhaps a more familiar dual-fifth system to many is [[18edo]]. It is the first system that has intervals that are close enough to 3/2 that they can be regarded as sharp and flat fifth, but also far enough to sound different. Its sharp fifth and flat fifth are almost equally off from just: it has a 733.3¢ sharp fifth 31.4¢ sharp from pure [[3/2]], and a 666.7¢ flat fifth is 35.3¢ flat.