19/17: Difference between revisions
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Wikispaces>spt3125 **Imported revision 513547160 - Original comment: ** |
Hotcrystal0 (talk | contribs) use octave complement instead |
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{{Infobox Interval | |||
| Name = quasi-meantone | |||
| Color name = 19o17u2, nosu 2nd | |||
| Sound = jid_19_17_pluck_adu_dr220.mp3 | |||
}} | |||
'''19/17''' is a [[19-limit]] [[just intonation]] 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. | |||
== Approximation == | |||
[[ | {{Interval edo approximation|19/17}} | ||
== See also == | |||
* [[15/14]] – its coordinated semi-meantone ((19/17)<sup>5</sup> × (15/14)<sup>2</sup> = (2/1) / ([[mercurial comma]])) | |||
* [[34/19]] – its [[octave complement]] | |||
* [[Gallery of just intervals]] | |||
[[Category:Second]] | |||
[[Category:Whole tone]] | |||
[[Category:Meantone]] | |||
[[Category:Mercurial]] | |||
[[Category:Taxicab-2 intervals]] | |||
Latest revision as of 16:35, 27 January 2026
| Interval information |
[sound info]
19/17 is a 19-limit just intonation 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.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 6 | 1\6 | 200.00 | +7.44 | +3.72 |
| 12 | 2\12 | 200.00 | +7.44 | +7.44 |
| 13 | 2\13 | 184.62 | -7.94 | -8.60 |
| 19 | 3\19 | 189.47 | -3.08 | -4.88 |
| 25 | 4\25 | 192.00 | -0.56 | -1.16 |
| 31 | 5\31 | 193.55 | +0.99 | +2.56 |
| 37 | 6\37 | 194.59 | +2.04 | +6.28 |
| 38 | 6\38 | 189.47 | -3.08 | -9.77 |
| 44 | 7\44 | 190.91 | -1.65 | -6.04 |
| 50 | 8\50 | 192.00 | -0.56 | -2.32 |
| 56 | 9\56 | 192.86 | +0.30 | +1.40 |
| 62 | 10\62 | 193.55 | +0.99 | +5.12 |
| 68 | 11\68 | 194.12 | +1.56 | +8.84 |
| 69 | 11\69 | 191.30 | -1.25 | -7.21 |
| 75 | 12\75 | 192.00 | -0.56 | -3.49 |
See also
- 15/14 – its coordinated semi-meantone ((19/17)5 × (15/14)2 = (2/1) / (mercurial comma))
- 34/19 – its octave complement
- Gallery of just intervals