9/8: Difference between revisions
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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 which temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢) include [[19edo]], [[26edo]], [[31edo]], and all [[meantone]] temperaments. | ||
9/8 is well-represented in [[6edo]] and its multiples. [[EDO|Edo]]s which tune [[3_2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well. | 9/8 is well-represented in [[6edo]] and its multiples. [[EDO|Edo]]s which tune [[3_2|3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well. | ||
== See also == | == See also == | ||
Revision as of 16:44, 30 October 2019
| Interval information |
reduced,
reduced harmonic
[sound info]
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.
9/8 is well-represented in 6edo and its multiples. Edos which tune 3/2 close to just (29edo, 41edo, 53edo, to name three) will tune 9/8 close as well.
See also
- Gallery of Just Intervals
- 16/9 its inverse interval
- Major second - Wikipedia