Equal-step tuning: Difference between revisions

Line 5:

The '''equal-step tuning''', '''equal tuning''', or '''equal ~~pitch~~ division''' ('''~~EPD~~''') is the [[tuning system]] where the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. [[88cET|88-cent equal tuning]]) or as a fraction of a larger interval (e.g. [[13edo|13 equal divisions of the 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]].

The '''equal-step tuning''', '''equal tuning''', or '''equal division''' ('''ED''') is the [[tuning system]] where the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. [[88cET|88-cent equal tuning]]) or as a fraction of a larger interval (e.g. [[13edo|13 equal divisions of the 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), 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 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.

@@ Line 5: / Line 5: @@
 {{Wikipedia|Equal temperament}}
-The '''equal-step tuning''', '''equal tuning''', or '''equal pitch division''' ('''EPD''') is the [[tuning system]] where the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. [[88cET|88-cent equal tuning]]) or as a fraction of a larger interval (e.g. [[13edo|13 equal divisions of the 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]].
+The '''equal-step tuning''', '''equal tuning''', or '''equal division''' ('''ED''') is the [[tuning system]] where the distance between adjacent steps is of constant size. The size of this single step is given explicitly (e.g. [[88cET|88-cent equal tuning]]) or as a fraction of a larger interval (e.g. [[13edo|13 equal divisions of the 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), 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 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.