18/13: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tridecimal augmented fourth, low tritone | |||
| Name = tridecimal augmented fourth, | |||
| Color name = 3u4, thu 4th | | Color name = 3u4, thu 4th | ||
| Sound = jid_18_13_pluck_adu_dr220.mp3 | | Sound = jid_18_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
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The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢. | The low tritone in [[17edo]] approximates 18/13 quite well, while 17edo's approximations of [[13/8]] and [[9/8]] are both a little sharp. The inversion of 18/13 is [[13/9]], a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is [[169/162]], approximately 73.2¢. | ||
== Approximation == | |||
{{Interval edo approximation|18/13}} | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Tritone]] | [[Category:Tritone]] | ||
Latest revision as of 13:11, 3 November 2025
| Interval information |
low tritone
[sound info]
In 13-limit just intonation, 18/13, the tridecimal augmented fourth is a low tritone measuring about 563.4¢. It represents the interval between the 13th and 18th harmonics of the harmonic series.
The low tritone in 17edo approximates 18/13 quite well, while 17edo's approximations of 13/8 and 9/8 are both a little sharp. The inversion of 18/13 is 13/9, a high tritone measuring about 636.6¢; the interval between these two tridecimal (13-based) tritones is 169/162, approximately 73.2¢.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 1\2 | 600.00 | +36.62 | +6.10 |
| 15 | 7\15 | 560.00 | -3.38 | -4.23 |
| 17 | 8\17 | 564.71 | +1.32 | +1.88 |
| 19 | 9\19 | 568.42 | +5.04 | +7.98 |
| 30 | 14\30 | 560.00 | -3.38 | -8.46 |
| 32 | 15\32 | 562.50 | -0.88 | -2.35 |
| 34 | 16\34 | 564.71 | +1.32 | +3.75 |
| 36 | 17\36 | 566.67 | +3.28 | +9.85 |
| 47 | 22\47 | 561.70 | -1.68 | -6.58 |
| 49 | 23\49 | 563.27 | -0.12 | -0.48 |
| 51 | 24\51 | 564.71 | +1.32 | +5.63 |
| 64 | 30\64 | 562.50 | -0.88 | -4.71 |
| 66 | 31\66 | 563.64 | +0.25 | +1.40 |
| 68 | 32\68 | 564.71 | +1.32 | +7.50 |
| 79 | 37\79 | 562.03 | -1.36 | -8.93 |