查看“︁5/4”︁的源代码

{{interwiki
| de = Naturterz
| en = 5/4
| es = 
| ja = 
| ro = 5/4 (ro)
}}
{{Infobox Interval
| Name = just major third, classic(al) major third, ptolemaic major third
| Color name = y3, yo 3rd
| Sound = jid_5_4_pluck_adu_dr220.mp3
}}
{{Wikipedia|Major third}}

In [[5-limit]] [[just intonation]], '''5/4''' is the [[frequency ratio]] between the 5th and 4th [[harmonic]]s. It has been called the '''just major third''', '''classic(al) major third''', or '''ptolemaic major third'''<ref>For reference, see [[5-limit]].</ref> to distinguish it from other intervals in that neighborhood. Measuring about 386.3 [[cent|¢]], it is about 13.7{{c}} away from [[12edo]]'s major third of 400{{c}}. It has a distinctive "sweet" sound, and has been described as more "laid back" than its 12edo counterpart. Providing a novel consonance after 3, it is the basis for [[5-limit]] harmony. It is distinguished from the [[Pythagorean]] major third of [[81/64]] by the syntonic comma of [[81/80]], which measures about 21.5{{c}}, and from the Pythagorean diminished fourth of [[8192/6561]] by the [[schisma]], which measures about 1.95{{c}}. 81/64 and 5/4 are both just intonation "major thirds", 81/64 having a more active and discordant quality, 5/4 sounding more "restful". 

In the context of the harmonic series, 5/4 can be heard between the 4th and 5th member of the series, demonstrated in [[:File: 5-4.mp3]] melodically in singing into a resonant [[udderbot]] (from the fundamental up to 5 and then noodling between 5 and 4).

== Approximations by edos ==

本表格只包含相对误差≤10%且平均律步数与5/4步数没有大于1的公因子的情况。

{| class="wikitable"
|+
!平均律步数
!5/4的步数
!绝对误差(ie)
!相对误差
|-
|3
|1
|+126.4941
|+3.42%
|-
|22
|7
|-385.101
|-8.24%
|-
|25
|8
|-748.249
|-4.82%
|-
|28
|9
|-2888.1427
|-1.4%
|-
|31
|10
|+2210.8565
|+2.02%
|-
|34
|11
|+900.9429
|+5.44%
|-
|37
|12
|+602.0688
|+8.87%
|-
|53
|17
|-1229.5229
|-6.22%
|-
|59
|19
|+13635.6185
|+0.62%
|-
|65
|21
|+1255.797
|+7.47%
|-
|81
|26
|-1534.063
|-7.62%
|-
|87
|28
|-16207.4293
|-0.77%
|-
|90
|29
|+4905.0016
|+2.65%
|-
|96
|31
|+1459.3731
|+9.49%
|-
|109
|35
|-1744.1179
|-9.02%
|-
|115
|37
|-7634.743
|-2.17%
|-
|121
|39
|+3737.9906
|+4.67%
|-
|143
|46
|-5776.02
|-3.57%
|-
|146
|47
|-140249.0112
|-0.15%
|-
|149
|48
|+6570.9626
|+3.27%
|-
|152
|49
|+3276.4236
|+6.69%
|-
|171
|55
|-4963.3778
|-4.97%
|-
|183
|59
|+3029.1111
|+8.72%
|-
|199
|64
|-4507.6517
|-6.37%
|-
|202
|65
|-9887.116
|-2.95%
|-
|205
|66
|+62387.8247
|+0.47%
|-
|208
|67
|+7703.0121
|+3.9%
|-
|211
|68
|+4160.1807
|+7.32%
|-
|227
|73
|-4216.0421
|-7.77%
|-
|233
|75
|-36355.6122
|-0.92%
|-
|239
|77
|+5825.8383
|+5.92%
|-
|255
|82
|-4013.4235
|-9.17%
|-
|258
|83
|-6479.1151
|-5.74%
|-
|264
|85
|+34678.4334
|+1.1%
|-
|267
|86
|+8522.3662
|+4.52%
|-}

== See also ==
* [[8/5]] – its [[octave complement]]
* [[6/5]] – its [[fifth complement]]
* [[16/15]] – its [[fourth complement]]
* [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]
* [[Ed5/4]]
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]

== Notes ==
<references/>

[[Category:Third]]
[[Category:Major third]]