9/8: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 9/8 | | Ratio = 9/8 | ||
| Monzo = -3 2 | | Monzo = -3 2 | ||
| Cents = 203.91000 | | Cents = 203.91000 | ||
| Name = whole tone | | Name = whole tone, <br>major second | ||
| Color name = w2, wa 2nd | | Color name = w2, wa 2nd | ||
| FJS name = M2 | | FJS name = M2 | ||
| Sound = jid_9_8_pluck_adu_dr220.mp3 | | Sound = jid_9_8_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Major second}} | |||
'''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. | '''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. | ||
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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 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. | 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. | ||
9/8 is well-represented in [[6edo]] and its multiples. [[ | 9/8 is well-represented in [[6edo]] and its multiples. [[Edo]]s which tune [[3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close as well. | ||
== Temperaments == | == Temperaments == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Whole tone]] | [[Category:Whole tone]] | ||
[[Category:Large comma]] | |||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category: | [[Category:Octave-reduced harmonics]] | ||
[[Category:Pages with internal sound examples]] | |||
Revision as of 05:04, 22 January 2022
| Interval information |
major second
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 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.
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.
Temperaments
When this ratio is taken as a comma to be tempered, it produces antitonic temperament. EDOs that temper it out include 2edo and 4edo. If it is instead used as a generator, it produces Baldy.