8/7: Difference between revisions

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{| class="wikitable"
{{Infobox Interval
|-
| Icon = [[File:glyph_8_7.png|124px]] <small><br/>[[JI glyphs|JI glyph]]</small>
| | [[File:glyph_8_7.png|alt=glyph 8 7.png|122x111px|glyph 8 7.png]]
| Ratio = 8/7
|-
| Monzo = 3 0 0 -1
| | JI glyph for 8/7
| Cents = 231.17409
|}
| Name = septimal supermajor second
| Sound = jid_8_7_pluck_adu_dr220.mp3
| Color name =
}}


'''8/7'''
In [[Just Intonation]], 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of [[12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th overtones in the harmonic series and is thus a [[superparticular]] ratio. In [[7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4]]) and octave. It differs from the Pythagorean major second of [[9/8]] by [[64/63]], a microtone of about 27.3¢.
|3 0 0 -1&gt;


231,17409 cents
== See also ==
* [[Gallery of Just Intervals]]
* [http://en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone - Wikipedia].


[[File:jid_8_7_pluck_adu_dr220.mp3]] [[:File:jid_8_7_pluck_adu_dr220.mp3|sound sample]]
[[Category:7-limit]]
 
In [[Just_intonation|Just Intonation]], 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of [[12edo|12edo]], it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th overtones in the harmonic series and is thus a [[superparticular|superparticular]] ratio. In [[7-limit|7-limit]] JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh ([[7/4|7/4]]) and octave. It differs from the Pythagorean major second of [[9/8|9/8]] by [[64/63|64/63]], a microtone of about 27.3¢.
 
See the Wikipedia article for [http://en.wikipedia.org/wiki/Septimal_whole_tone Septimal whole tone].
 
See also: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:7-limit]]
[[Category:8/7]]
[[Category:8/7]]
[[Category:interval]]
[[Category:interval]]

Revision as of 22:41, 17 October 2018

Interval information
Ratio 8/7
Factorization 23 × 7-1
Monzo [3 0 0 -1⟩
Size in cents 231.1741¢
Name septimal supermajor second
FJS name [math]\displaystyle{ \text{M2}_{7} }[/math]
Special properties superparticular,
reduced,
reduced subharmonic
Tenney norm (log2 nd) 5.80735
Weil norm (log2 max(n, d)) 6
Wilson norm (sopfr(nd)) 13

[sound info]
Open this interval in xen-calc

In Just Intonation, 8/7 is the "septimal supermajor second" of approximately 231.2¢. Although it falls between the familiar major second and minor third of 12edo, it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th overtones in the harmonic series and is thus a superparticular ratio. In 7-limit JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (7/4) and octave. It differs from the Pythagorean major second of 9/8 by 64/63, a microtone of about 27.3¢.

See also

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