Dual-fifth tuning: Difference between revisions

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[[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.
[[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|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.  


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.  
Although edos like [[18edo]], [[23edo]] and [[25edo]] have been 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.


For a list of edos which could be considered dual-fifth, see:
For a list of edos which could be considered dual-fifth, see: