9/5: Difference between revisions

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'''9/5'''
{{Infobox Interval
|0 2 -1>
| Name = just minor seventh, classic(al) minor seventh, ptolemaic minor seventh
| Color name = g7, gu 7th
| Sound = jid_9_5_pluck_adu_dr220.mp3
}}
{{Wikipedia|Minor seventh}}


1017.5963 cents
'''9/5''', the '''just''', '''classic(al)''', or '''ptolemaic minor seventh'''<ref>For reference, see [[5-limit]]. </ref> is often treated as a consonance in [[5-limit]] [[just intonation]], forming a part of such chords such as the 1-6/5-3/2-9/5 minor seventh chord, and the supermajor tetrad, 1-9/7-3/2-9/5 in the 7-limit.


[[File:jid_9_5_pluck_adu_dr220.mp3]] [[:File:jid_9_5_pluck_adu_dr220.mp3|sound sample]]
Coincidentally, the ratio between a common "alternative" tuning frequency (A432) and the most common AC electrical frequency (60hz) is exactly 36/5, two octaves above 9/5. This is notably a more consonant interval than the 11/6 formed by the more common tuning frequency of A440, which may lead to a noticeable improvement in consonance when electrically powered instruments or amplifiers are interfered with by AC power.


'''9/5''' is a treated as a consonance in [[5-limit|5-limit]] just intonation, forming a part of such chords such as the 1-6/5-3/2-9/5 minor seventh chord, and the supermajor tetrad, 1-9/7-3/2-9/5 in the 7-limit.
== See also ==
* [[10/9]] – its [[octave complement]]
* [[5/3]] – its [[twelfth complement]]
* [[Ed9/5]]
* [[Gallery of just intervals]]


Coincidentally, the ratio between a common "alternative" tuning frequency (A432) and the most common AC electrical frequency (60hz) is exactly 36/5, two octaves above 9/5. This is notably a more consonant interval than the 11/6 formed by the more common tuning frequency of A440, which may lead to a noticeable improvement in consonance when electrically powered instruments or amplifiers are interfered with by AC power.
== Notes ==
[[Category:ji]]
<references/>
[[Category:ratio]]
 
[[Category:todo:expand]]
[[Category:Seventh]]
[[Category:Minor seventh]]
[[Category:Over-5 intervals]]

Latest revision as of 00:00, 27 October 2024

Interval information
Ratio 9/5
Factorization 32 × 5-1
Monzo [0 2 -1⟩
Size in cents 1017.596¢
Names just minor seventh,
classic(al) minor seventh,
ptolemaic minor seventh
Color name g7, gu 7th
FJS name [math]\displaystyle{ \text{m7}_{5} }[/math]
Special properties reduced
Tenney height (log2 nd) 5.49185
Weil height (log2 max(n, d)) 6.33985
Wilson height (sopfr(nd)) 11

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

9/5, the just, classic(al), or ptolemaic minor seventh[1] is often treated as a consonance in 5-limit just intonation, forming a part of such chords such as the 1-6/5-3/2-9/5 minor seventh chord, and the supermajor tetrad, 1-9/7-3/2-9/5 in the 7-limit.

Coincidentally, the ratio between a common "alternative" tuning frequency (A432) and the most common AC electrical frequency (60hz) is exactly 36/5, two octaves above 9/5. This is notably a more consonant interval than the 11/6 formed by the more common tuning frequency of A440, which may lead to a noticeable improvement in consonance when electrically powered instruments or amplifiers are interfered with by AC power.

See also

Notes

  1. ↑ For reference, see 5-limit.
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