查看“︁5/4”︁的源代码

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 thir'''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。
[[Category:三度]]
[[Category:大三度]]
{| 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%
|}

== 另见 ==

* [[5限纯律]]  


[[Category:三度]]
[[Category:大三度]]