9/8: Difference between revisions

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'''9/8''' is the Pythagorean '''whole tone''' or '''major second''', 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.

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 which temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢) ~~include [[19edo]], [[26edo]], [[31edo]], and all~~ [[meantone]] temperaments.

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, such as [[19edo]], [[26edo]], and [[31edo]], which temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢) are called [[meantone]] temperaments.

9/8 is well-represented in [[6edo]] and its multiples. [[EDO|Edos]] which tune [[3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well.

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 '''9/8''' is the Pythagorean '''whole tone''' or '''major second''', 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.
-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 which temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢) include [[19edo]], [[26edo]], [[31edo]], and all [[meantone]] temperaments.
+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, such as [[19edo]], [[26edo]], and [[31edo]], which temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢) are called [[meantone]] temperaments.
 /8 is well-represented in [[6edo]] and its multiples. [[EDO|Edos]] which tune [[3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well.