5/4：修订间差异

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{{interwiki
在[[5限纯律]]中，'''5/4''' 是第5泛音与第4泛音之间的频率比，其大小约为386.3¢.
| 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".  
它比[[12ed2]]的4步低约13.7¢；如果用[[3限纯律]]的[[81/64]]逼近，误差则是[[81/80]]≈21.5¢；如果用3限纯律的[[8192/6561]]逼近，误差则是[[32805/32768]]≈1.95¢.


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).
== 平均律逼近 ==
 
== 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。


本表格只包含相对误差的绝对值≤10%且平均律步数与5/4步数没有大于1的公因子的情况。误差的计算方式为平均律音程<math>-</math>纯律音程。
{| class="wikitable"
{| class="wikitable"
|+
|+
第30行： 第15行：
|3
|3
|1
|1
|+126.4941
| +126.4941
|+3.42%
| +3.42%
|-
|-
|22
|22
|7
|7
|-385.101
| -385.101
|-8.24%
| -8.24%
|-
|-
|25
|25
|8
|8
|-748.249
| -748.249
|-4.82%
| -4.82%
|-
|-
|28
|28
|9
|9
|-2888.1427
| -2888.1427
|-1.4%
| -1.4%
|-
|-
|31
|31
|10
|10
|+2210.8565
| +2210.8565
|+2.02%
| +2.02%
|-
|-
|34
|34
|11
|11
|+900.9429
| +900.9429
|+5.44%
| +5.44%
|-
|-
|37
|37
|12
|12
|+602.0688
| +602.0688
|+8.87%
| +8.87%
|-
|-
|53
|53
|17
|17
|-1229.5229
| -1229.5229
|-6.22%
| -6.22%
|-
|-
|59
|59
|19
|19
|+13635.6185
| +13635.6185
|+0.62%
| +0.62%
|-
|-
|65
|65
|21
|21
|+1255.797
| +1255.797
|+7.47%
| +7.47%
|-
|-
|81
|81
|26
|26
|-1534.063
| -1534.063
|-7.62%
| -7.62%
|-
|-
|87
|87
|28
|28
|-16207.4293
| -16207.4293
|-0.77%
| -0.77%
|-
|-
|90
|90
|29
|29
|+4905.0016
| +4905.0016
|+2.65%
| +2.65%
|-
|-
|96
|96
|31
|31
|+1459.3731
| +1459.3731
|+9.49%
| +9.49%
|-
|-
|109
|109
|35
|35
|-1744.1179
| -1744.1179
|-9.02%
| -9.02%
|-
|-
|115
|115
|37
|37
|-7634.743
| -7634.743
|-2.17%
| -2.17%
|-
|-
|121
|121
|39
|39
|+3737.9906
| +3737.9906
|+4.67%
| +4.67%
|-
|-
|143
|143
|46
|46
|-5776.02
| -5776.02
|-3.57%
| -3.57%
|-
|-
|146
|146
|47
|47
|-140249.0112
| -140249.0112
|-0.15%
| -0.15%
|-
|-
|149
|149
|48
|48
|+6570.9626
| +6570.9626
|+3.27%
| +3.27%
|-
|-
|152
|152
|49
|49
|+3276.4236
| +3276.4236
|+6.69%
| +6.69%
|-
|-
|171
|171
|55
|55
|-4963.3778
| -4963.3778
|-4.97%
| -4.97%
|-
|-
|183
|183
|59
|59
|+3029.1111
| +3029.1111
|+8.72%
| +8.72%
|-
|-
|199
|199
|64
|64
|-4507.6517
| -4507.6517
|-6.37%
| -6.37%
|-
|-
|202
|202
|65
|65
|-9887.116
| -9887.116
|-2.95%
| -2.95%
|-
|-
|205
|205
|66
|66
|+62387.8247
| +62387.8247
|+0.47%
| +0.47%
|-
|-
|208
|208
|67
|67
|+7703.0121
| +7703.0121
|+3.9%
| +3.9%
|-
|-
|211
|211
|68
|68
|+4160.1807
| +4160.1807
|+7.32%
| +7.32%
|-
|-
|227
|227
|73
|73
|-4216.0421
| -4216.0421
|-7.77%
| -7.77%
|-
|-
|233
|233
|75
|75
|-36355.6122
| -36355.6122
|-0.92%
| -0.92%
|-
|-
|239
|239
|77
|77
|+5825.8383
| +5825.8383
|+5.92%
| +5.92%
|-
|-
|255
|255
|82
|82
|-4013.4235
| -4013.4235
|-9.17%
| -9.17%
|-
|-
|258
|258
|83
|83
|-6479.1151
| -6479.1151
|-5.74%
| -5.74%
|-
|-
|264
|264
|85
|85
|+34678.4334
| +34678.4334
|+1.1%
| +1.1%
|-
|-
|267
|267
|86
|86
|+8522.3662
| +8522.3662
|+4.52%
| +4.52%
|-}
|}


== See also ==
== 另见 ==
* [[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 ==
* [[5限纯律]]
<references/>


[[Category:Third]]
[[Category:纯律音程]]  
[[Category:Major third]]
[[Category:泛音]]
[[Category:5限纯律]]

2025年12月3日 (三) 18:44的最新版本

在5限纯律中，5/4 是第5泛音与第4泛音之间的频率比，其大小约为386.3¢.

它比12ed2的4步低约13.7¢；如果用3限纯律的81/64逼近，误差则是81/80≈21.5¢；如果用3限纯律的8192/6561逼近，误差则是32805/32768≈1.95¢.

平均律逼近

本表格只包含相对误差的绝对值≤10%且平均律步数与5/4步数没有大于1的公因子的情况。误差的计算方式为平均律音程−纯律音程。

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

检索自“https://tun.wiki/index.php?title=5/4&oldid=64”