6/5: Difference between revisions

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reworked: simplified links; introduced infobox interval
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{| class="wikitable"
{{Infobox Interval
|-
| Icon = [[File:glyph_6_5.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| | [[File:glyph_6_5.png|alt=glyph 6 5.png|112x114px|glyph 6 5.png]]
| Ratio = 6/5
|-
| Monzo = 1 1 -1
| | JI Glyph of 6/5
| Cents = 315.64129
|}
| Name = minor third
| Sound = jid_6_5_pluck_adu_dr220.mp3
| Color name =
}}


'''6/5'''
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|edo]]s. It arises in the [[OverToneSeries|harmonic series]] between the 5th and 6th overtones and appears in the [[5-limit|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.
|1 1 -1&gt;


315.64129 cents
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.


[[File:jid_6_5_pluck_adu_dr220.mp3]] [[:File:jid_6_5_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[Gallery of Just Intervals]]
* [[List of root-3rd-P5 triads in JI]]


In [[5-limit|5-limit]] [[Just_intonation|Just Intonation]], '''6/5''' is the classic minor third, measuring about 315.6[[cent|¢]]. It is sharp of the [[Pythagorean|Pythagorean]] minor third of [[32/27|32/27]] (about 294.1¢) as well as the 300¢ minor third of [[4edo|4edo]], [[12edo|12edo]] and all other 4n-[[EDO|edo]]s. It arises in the [[OverToneSeries|harmonic series]] between the 5th and 6th overtones and appears in the [[5-limit|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|5/4]] falling between 12 and 15, and [[3/2|3/2]] falling between 10 and 15.
[[Category:5-limit]]
 
In higher-limit JI, 6/5 is only one of many minor thirds. A popular one in the [[7-limit|7-limit]] is [[7/6|7/6]] (about 266.9¢), the septimal subminor third, which is [[36/35|36/35]] (about 48.8¢) flat of 6/5. Another in the [[13-limit|13-limit]] is [[13/11|13/11]] (about 289.2¢), which is [[66/65|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.
 
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_root-3rd-P5_triads_in_JI|List of root-3rd-P5 triads in JI]]      [[Category:5-limit]]
[[Category:interval]]
[[Category:interval]]
[[Category:just_interval]]
[[Category:just_interval]]

Revision as of 22:45, 17 October 2018

Interval information
Ratio 6/5
Factorization 2 × 3 × 5-1
Monzo [1 1 -1
Size in cents 315.6413¢
Name minor third
FJS name [math]\displaystyle{ \text{m3}_{5} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 4.90689
Weil norm (log2 max(n, d)) 5.16993
Wilson norm (sopfr(nd)) 10

[sound info]
Open this interval in xen-calc

In 5-limit Just Intonation, 6/5 is the classic minor third, measuring about 315.6¢. 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-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 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.

See also