6/5: Difference between revisions

(17 intermediate revisions by 8 users not shown)

Line 1:

{{Infobox Interval

~~| Ratio = 6/5~~

| Name = just minor third, classic(al) minor third, ptolemaic minor third

~~| Monzo = 1 1 -1~~

~~| Cents = 315.64129~~

| Name = classic minor third

| Color name = g3, gu 3rd

~~| FJS name = m3<sub>5</sub>~~

| Sound = jid_6_5_pluck_adu_dr220.mp3

}}

In [[5-limit]] [[~~Just Intonation~~]], '''6/5''' is the '''classic minor third''', measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th ~~overtones~~ and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.

In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.

In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.

It is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.

== Approximation ==

6/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.

== See also ==

* [[5/3]] – its [[octave complement]]

* [[5/4]] – its [[fifth complement]]

* [[Gallery of ~~Just Intervals~~]]

* [[10/9]] – its [[fourth complement]]

* [[~~Wikipedia: Minor third~~]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example

~~[[Category:5-limit]]~~

== Notes ==

~~[[Category:Interval]]~~

~~[[Category:Just interval]]~~

[[Category:Third]]

[[Category:Minor third]]

~~[[Category:Ratio]]~~

[[Category:Over-5 intervals]]

~~[[Category:Superparticular]]~~

[[Category:Over-5]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 6/5
+| Name = just minor third, classic(al) minor third, ptolemaic minor third
-| Monzo = 1 1 -1
-| Cents = 315.64129
-| Name = classic minor third
 | Color name = g3, gu 3rd
-| FJS name = m3<sub>5</sub>
 | Sound = jid_6_5_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Minor third}}
-In [[5-limit]] [[Just Intonation]], '''6/5''' is the '''classic minor third''', measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th overtones and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.
+In [[5-limit]] [[just intonation]], '''6/5''' is the '''just minor third''', '''classic(al) minor third''', or '''ptolemaic minor third'''<ref>For reference, see [[5-limit]]. </ref>, measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean]] minor third of [[32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo]], [[12edo]] and all other 4n-[[EDO|edos]]. It arises in the [[harmonic series]] between the 5th and 6th harmonics and appears in the [[5-limit]] otonal triad of 4:5:6. A 5-limit minor triad in just intonation can be written 10:12:15, with 6/5 falling between 10 and 12, [[5/4]] falling between 12 and 15, and [[3/2]] falling between 10 and 15.
 In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit]] is [[7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit]] is [[13/11]] (about 289.2¢), which is [[66/65]] (about 26.4¢) flat of 6/5. Both of these are more complex intervals than 6/5 and have their own character to them.
-It is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
+== Approximation ==
+/5 is very accurately approximated by [[19edo]] (5\19), and hence the [[enneadecal]] temperament.
+{{Interval edo approximation}}
 == See also ==
 * [[5/3]] – its [[octave complement]]
 * [[5/4]] – its [[fifth complement]]
-* [[Gallery of Just Intervals]]
+* [[10/9]] – its [[fourth complement]]
-* [[Wikipedia: Minor third]]
+* [[Gallery of just intervals]]
+* [[List of superparticular intervals]]
 * [[:File:Ji-6-5-csound-foscil-220hz.mp3]] – another sound example
-[[Category:5-limit]]
+== Notes ==
-[[Category:Interval]]
+<references/>
-[[Category:Just interval]]
 [[Category:Third]]
 [[Category:Minor third]]
-[[Category:Ratio]]
+[[Category:Over-5 intervals]]
-[[Category:Superparticular]]
-[[Category:Over-5]]