9/8: Difference between revisions

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| Name = whole tone
| Name = whole tone
| Color name = w2, wa 2nd
| Color name = w2, wa 2nd
| FJS name = M2
| Sound = jid_9_8_pluck_adu_dr220.mp3
| Sound = jid_9_8_pluck_adu_dr220.mp3
}}
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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|Edos]] which tune [[3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well.


== See also ==
== See also ==
* [[Gallery of Just Intervals]]
* [[Gallery of Just Intervals]]
* [[16/9]] its inverse interval
* [[16/9]] its [[octave complement]]
* [https://en.wikipedia.org/wiki/Major_second Major second - Wikipedia]
* [[4/3]] – its [[fifth complement]]
* [[Wikipedia:Major_second|Major second - Wikipedia]]


[[Category:3-limit]]
[[Category:3-limit]]
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