8/7: Difference between revisions

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| Name = septimal supermajor second
| Name = septimal supermajor second
| Sound = jid_8_7_pluck_adu_dr220.mp3
| Sound = jid_8_7_pluck_adu_dr220.mp3
| Color name =
| Color name = r2, ru 2nd
}}
}}


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¢.
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¢. It's close in size to one step of 5edo = 240¢.


== See also ==
== See also ==

Revision as of 03:58, 23 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
Color name r2, ru 2nd
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¢. It's close in size to one step of 5edo = 240¢.

See also