19/17: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 19/17 | | Ratio = 19/17 | ||
| Monzo = 0 0 0 0 0 0 -1 1 | | Monzo = 0 0 0 0 0 0 -1 1 | ||
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'''19/17''' is a JI interval intermediate in size to [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, for which 19/17 is often a good rational approximation, depending on the exact meantone tuning. It is a particularly good rational approximation to the whole tone of quarter comma meantone, as two of them fall short of a perfect [[5/4]] by [[1445/1444]], or 1.1985 cents. 19/17 is also very close to the size of the whole tone in golden meantone, being only about a tenth of a cent off. | '''19/17''' is a JI interval intermediate in size to [[9/8]] and [[10/9]], two common sizes of whole tone. In [[meantone]] systems, the two are conflated into one interval, for which 19/17 is often a good rational approximation, depending on the exact meantone tuning. It is a particularly good rational approximation to the whole tone of quarter comma meantone, as two of them fall short of a perfect [[5/4]] by [[1445/1444]], or 1.1985 cents. 19/17 is also very close to the size of the whole tone in golden meantone, being only about a tenth of a cent off. | ||
19/17 is the [[mediant]] of 9/8 and 10/9: (9+10)/(8+9)=19/17. | 19/17 is the [[mediant]] of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17. | ||
== See also == | == See also == | ||
* [[15/14]] – its coordinated semi-meantone ((19/17)<sup>5</sup> × (15/14)<sup>2</sup> = (2/1) / ([[mercurial comma]])) | |||
* [[15/14]] – its coordinated semi-meantone ((19/17) | |||
* [[34/19]] – its [[inverse interval]] | * [[34/19]] – its [[inverse interval]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:19-limit]] | [[Category:19-limit]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Whole tone]] | [[Category:Whole tone]] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Mercurial]] | [[Category:Mercurial]] | ||
[[Category:Pages with internal sound examples]] | |||
[[Category: | |||
Revision as of 17:30, 13 December 2021
| Interval information |
[sound info]
19/17 is a JI interval intermediate in size to 9/8 and 10/9, two common sizes of whole tone. In meantone systems, the two are conflated into one interval, for which 19/17 is often a good rational approximation, depending on the exact meantone tuning. It is a particularly good rational approximation to the whole tone of quarter comma meantone, as two of them fall short of a perfect 5/4 by 1445/1444, or 1.1985 cents. 19/17 is also very close to the size of the whole tone in golden meantone, being only about a tenth of a cent off.
19/17 is the mediant of 9/8 and 10/9: (9 + 10)/(8 + 9) = 19/17.
See also
- 15/14 – its coordinated semi-meantone ((19/17)5 × (15/14)2 = (2/1) / (mercurial comma))
- 34/19 – its inverse interval
- Gallery of just intervals