9/5: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = just minor seventh, classic(al) minor seventh, ptolemaic minor seventh | |||
| Name = just minor seventh, | |||
| Color name = g7, gu 7th | | Color name = g7, gu 7th | ||
| Sound = jid_9_5_pluck_adu_dr220.mp3 | | Sound = jid_9_5_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Minor seventh}} | {{Wikipedia|Minor seventh}} | ||
'''9/5''' is | '''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. | ||
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. | Coincidentally, the ratio between a common "alternative" tuning frequency (A432) and the most common North American 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.{{dubious}} | ||
== Approximation == | |||
{{Interval edo approximation|9/5}} | |||
== See also == | == See also == | ||
* [[10/9]] – its [[octave complement]] | * [[10/9]] – its [[octave complement]] | ||
* [[5/3]] – its [[twelfth complement]] | |||
* [[Ed9/5]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||
<references/> | |||
[[Category:Seventh]] | [[Category:Seventh]] | ||
[[Category:Minor seventh]] | [[Category:Minor seventh]] | ||
[[Category:Over-5]] | [[Category:Over-5 intervals]] | ||
Latest revision as of 14:15, 7 June 2026
| Interval information |
classic(al) minor seventh,
ptolemaic minor seventh
[sound info]
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 North American 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.[dubious – discuss]
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 6 | 5\6 | 1000.00 | -17.60 | -8.80 |
| 7 | 6\7 | 1028.57 | +10.98 | +6.40 |
| 13 | 11\13 | 1015.38 | -2.21 | -2.40 |
| 20 | 17\20 | 1020.00 | +2.40 | +4.01 |
| 26 | 22\26 | 1015.38 | -2.21 | -4.79 |
| 33 | 28\33 | 1018.18 | +0.59 | +1.61 |
| 39 | 33\39 | 1015.38 | -2.21 | -7.19 |
| 40 | 34\40 | 1020.00 | +2.40 | +8.01 |
| 46 | 39\46 | 1017.39 | -0.20 | -0.79 |
| 52 | 44\52 | 1015.38 | -2.21 | -9.58 |
| 53 | 45\53 | 1018.87 | +1.27 | +5.62 |
| 59 | 50\59 | 1016.95 | -0.65 | -3.18 |
| 66 | 56\66 | 1018.18 | +0.59 | +3.22 |
| 72 | 61\72 | 1016.67 | -0.93 | -5.58 |
| 73 | 62\73 | 1019.18 | +1.58 | +9.62 |
| 79 | 67\79 | 1017.72 | +0.13 | +0.82 |