13/10: Difference between revisions

Line 4:

| Monzo = -1 0 -1 0 0 1

| Cents = 454.21395

| Name = Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third

| Name = Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third

| Color name = 3og4, thogu 4th

| FJS name = d4135

| Sound = jid_13_10_pluck_adu_dr220.mp3

}}

In [[13-limit]] [[Just Intonation]], '''13/10''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[~~OverToneSeries|~~harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.

In [[13-limit]] [[Just Intonation]], '''13/10''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.

== See also ==

* [[20/13]] – its [[octave complement]]

* [[15/13]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of root-3rd-P5 triads in JI]]

* [[~~20/13]] - its [[inverse interval~~]]

* [[The Archipelago]]

[[Category:13-limit]]

~~[[Category:Fourth]]~~

[[Category:Interval]]

[[Category:Just interval]]

[[Category:~~Major third~~]]

[[Category:Ratio]]

[[Category:Fourth]]

[[Category:Subfourth]]

[[Category:Third]]

[[Category:~~Ratio~~]]

[[Category:Supermajor third]]

[[Category:Interseptimal]]

[[Category:Naiadic]]

[[Category:Over-5]]

@@ Line 4: / Line 4: @@
 | Monzo = -1 0 -1 0 0 1
 | Cents = 454.21395
-| Name = Barbados third, <br/> tridecimal 9/4 tone, <br/> tridecimal semidiminished fourth, <br/> tridecimal ultramajor third
+| Name = Barbados third, <br>tridecimal 9/4 tone, <br>tridecimal semidiminished fourth, <br>tridecimal ultramajor third
 | Color name = 3og4, thogu 4th
+| FJS name = d4<sup>13</sup><sub>5</sub>
 | Sound = jid_13_10_pluck_adu_dr220.mp3
 }}
-In [[13-limit]] [[Just Intonation]], '''13/10''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[OverToneSeries|harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.
+In [[13-limit]] [[Just Intonation]], '''13/10''' is an [[interseptimal]] interval measuring about 454.2¢. It falls in an ambiguous zone between a wide major third such as [[9/7]] and a flat perfect fourth such as [[21/16]]. The descriptor "interseptimal" comes from [[Margo Schulter]], and indicates its position between those two septimal (7-based) extremes. 13/10 appears between the 10th and 13th overtones of the [[harmonic series]] and appears in such chords as 8:10:13, a quasi-augmented triad. 13/10 also appears in the relatively-simple 10:13:15 triad, which consists of an interseptimal ultramajor third (13/10) and an interseptimal inframinor third ([[15/13]]) which stack to make a [[3/2]] perfect fifth. It is well-approximated in [[16edo]], [[21edo]], [[24edo]], [[29edo]], [[37edo]], and of course, infinitely many other [[EDO]] systems.
 == See also ==
+* [[20/13]] – its [[octave complement]]
+* [[15/13]] – its [[fifth complement]]
 * [[Gallery of just intervals]]
 * [[List of root-3rd-P5 triads in JI]]
-* [[20/13]] - its [[inverse interval]]
+* [[The Archipelago]]
 [[Category:13-limit]]
-[[Category:Fourth]]
 [[Category:Interval]]
 [[Category:Just interval]]
-[[Category:Major third]]
+[[Category:Ratio]]
+[[Category:Fourth]]
+[[Category:Subfourth]]
 [[Category:Third]]
-[[Category:Ratio]]
+[[Category:Supermajor third]]
 [[Category:Interseptimal]]
 [[Category:Naiadic]]
 [[Category:Over-5]]