5/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Wikispaces>FREEZE
No edit summary
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
reworked: simplified links; introduced infobox interval
Line 1: Line 1:
{| class="wikitable"
{{Infobox Interval
|-
| Icon = [[File:glyph_5_3.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| | [[File:glyph_5_3.png|alt=glyph 5 3.png|111x113px|glyph 5 3.png]]
| Ratio = 5/3
|-
| Monzo = 0 -1 1
| | JI Glyph of 5/3
| Cents = 884.35871
|}
| Name = major sixth
| Sound = jid_5_3_pluck_adu_dr220.mp3
| Color name =
}}


'''5/3'''
In [[5-limit]] [[Just Intonation]], 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the [[OverToneSeries|harmonic series]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16]] (about 905.9¢) by the syntonic comma of [[81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo]] and [[meantone]] systems, 5/3 and [[27/16]] are conflated.
|0 -1 1&gt;


884.35871 cents
5/3 has a more mellow sound than 27/16, owing to its relative smallness.
 
[[File:jid_5_3_pluck_adu_dr220.mp3]] [[:File:jid_5_3_pluck_adu_dr220.mp3|sound sample]]
 
In [[5-limit|5-limit]] [[Just_intonation|Just Intonation]], 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the [[OverToneSeries|harmonic series]], and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is [[6/5|6/5]], the 5-limit minor third. It differs from the Pythagorean major sixth of [[27/16|27/16]] (about 905.9¢) by the syntonic comma of [[81/80|81/80]] (about 21.5¢). This means that in systems which temper out the syntonic comma, such as [[12edo|12edo]] and [[Meantone|meantone]] systems, 5/3 and 27/16 are conflated.


5/3 has a more mellow sound than 27/16, owing to its relative smallness.
See: [[Gallery of Just Intervals]]


See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:5-limit]]
[[Category:5-limit]]
[[Category:interval]]
[[Category:interval]]
[[Category:just_interval]]
[[Category:just_interval]]
[[Category:ratio]]
[[Category:ratio]]

Revision as of 22:48, 17 October 2018

Interval information
Ratio 5/3
Factorization 3-1 × 5
Monzo [0 -1 1⟩
Size in cents 884.3587¢
Name major sixth
FJS name [math]\displaystyle{ \text{M6}^{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 3.90689
Weil norm (log2 max(n, d)) 4.64386
Wilson norm (sopfr(nd)) 8

[sound info]
Open this interval in xen-calc

In 5-limit Just Intonation, 5/3 is a major sixth of about 884.4¢. It represents the difference between the 5th and 3rd overtones of the harmonic series, and appears in just chords such as 3:4:5 (a 2nd inversion major triad). Its inversion is 6/5, the 5-limit minor third. It differs from the Pythagorean major sixth of 27/16 (about 905.9¢) by the syntonic comma of 81/80 (about 21.5¢). This means that in systems which temper out the syntonic comma, such as 12edo and meantone systems, 5/3 and 27/16 are conflated.

5/3 has a more mellow sound than 27/16, owing to its relative smallness.

See: Gallery of Just Intervals

Retrieved from "https://en.xen.wiki/index.php?title=5/3&oldid=37358"