Equal-step tuning: Difference between revisions

Line 5:

In an '''equal-step tuning''', the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). Any interval, rational, Just, or irrational, may be used as the basis for an equal tuning, although divisions of the octave are most common leading to [[EDO]] systems. When a just interval is equally divided, it is assumed none of the resulting intervals are just, because if the interval has a rational root it is seen as a division of that [[root]].

When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET ~~(for n-{{PAGENAME}})~~), this usually means "n divisions of 2/1, the octave, or some approximation thereof" but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify.

When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET), this usually means "n divisions of 2/1, the octave, or some approximation thereof" but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify.

There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term ''EDO'' (occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [http://www.tonalsoft.com/enc/encyclopedia.aspx Tonalsoft Encyclopedia]. More generally, the term ''EDn'' can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).

@@ Line 5: / Line 5: @@
 In an '''equal-step tuning''', the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. 88 cent equal temperament) or as a fraction of a larger interval (e.g. 13 equal tones per octave). Any interval, rational, Just, or irrational, may be used as the basis for an equal tuning, although divisions of the octave are most common leading to [[EDO]] systems. When a just interval is equally divided, it is assumed none of the resulting intervals are just, because if the interval has a rational root it is seen as a division of that [[root]].
-When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET (for n-{{PAGENAME}})), this usually means "n divisions of 2/1, the octave, or some approximation thereof" but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify.
+When a tuning is called "n-tone equal temperament" (abbreviated n-tET or n-ET), this usually means "n divisions of 2/1, the octave, or some approximation thereof" but it also implies a mindset of [[Regular Temperaments|temperament]]—that is, of a harmony-centric, JI-approximation-based understanding of the scale. If you are wondering how equal divisions of the octave can become associated with temperaments, the page [[EDOs to ETs]] may help clarify.
 There are many reasons why one might choose to not consider JI approximations when dealing with equal tunings, and thus not treat equal tunings as temperaments. In such case, the less theory-laden term ''EDO'' (occasionally written ED2), meaning "equal divisions of the octave" (or "equal divisions of 2/1"), leaves comparison to JI out of the picture, aside from the octave itself (which is assumed to be Just). There are other less standard terms, many in the [http://www.tonalsoft.com/enc/encyclopedia.aspx Tonalsoft Encyclopedia]. More generally, the term ''EDn'' can be used, where n is any harmonic of the harmonic series. For example, the equal-tempered Bohlen-Pierce scale may also be referred to as 13-ED3, for 13 equal divisions of 3/1 (the 3rd harmonic).