17/13: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 17/13 | | Ratio = 17/13 | ||
| Monzo = 0 0 0 0 0 -1 1 | | Monzo = 0 0 0 0 0 -1 1 | ||
| Cents = 464.42775 | | Cents = 464.42775 | ||
| Name = septendecimal subfourth | | Name = septendecimal subfourth | ||
| Color name = | | Color name = 17o3u4, sothu 4th | ||
| FJS name = P4<sup>17</sup><sub>13</sub> | | FJS name = P4<sup>17</sup><sub>13</sub> | ||
| Sound = jid_17_13_pluck_adu_dr220.mp3 | | Sound = jid_17_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[17-limit]] [[ | In [[17-limit]] [[just intonation]], '''17/13''' is the '''septendecimal subfourth''', measuring about 464.4¢. It differs from the [[4/3]] perfect fourth by the [[comma]] [[52/51]], about 33.6¢. It is the [[mediant]] between [[13/10]] and [[4/3]] and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls [[interseptimal]]. It appears in the [[harmonic series]] between the 13th and 17th harmonics. | ||
It is less than 0.2 cents flat of [[31edo]]'s subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c ([[relative error]] 7.1%). | It is less than 0.2 cents flat of [[31edo]]'s subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c ([[relative error]] 7.1%). | ||
| Line 19: | Line 18: | ||
[[Category:17-limit]] | [[Category:17-limit]] | ||
[[Category:Fourth]] | [[Category:Fourth]] | ||
[[Category:Subfourth]] | [[Category:Subfourth]] | ||
[[Category:Interseptimal]] | [[Category:Interseptimal]] | ||
[[Category:Naiadic]] | [[Category:Naiadic]] | ||
[[Category:Taxicab-2]] | |||
[[Category:Pages with internal sound examples]] | [[Category:Pages with internal sound examples]] | ||
Revision as of 21:04, 12 December 2021
| Interval information |
[sound info]
In 17-limit just intonation, 17/13 is the septendecimal subfourth, measuring about 464.4¢. It differs from the 4/3 perfect fourth by the comma 52/51, about 33.6¢. It is the mediant between 13/10 and 4/3 and falls in the categorically-ambiguous zone between supermajor third and perfect fourth that Margo Schulter calls interseptimal. It appears in the harmonic series between the 13th and 17th harmonics.
It is less than 0.2 cents flat of 31edo's subfourth of 464.52¢ (12\31). In fact, a circle of 31 pure 17/13's closes with an error of only 2.74c (relative error 7.1%).