9/8: Difference between revisions

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'''9/8''', the '''Pythagorean whole tone''' or '''major second''', is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.

'''9/8''', the '''Pythagorean whole tone''' or '''major second,''' is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.

Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.

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 {{Wikipedia|Major second}}
-'''9/8''', the '''Pythagorean whole tone''' or '''major second''', is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.
+'''9/8''', the '''Pythagorean whole tone''' or '''major second,''' is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.
 Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.