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. | ||
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: | ||