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| | 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¢. |
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| | ro = 5/4 (ro)
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| {{Infobox Interval
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| | Name = just major third, classic(al) major third, ptolemaic major third
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| | Color name = y3, yo 3rd
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| | Sound = jid_5_4_pluck_adu_dr220.mp3
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| {{Wikipedia|Major third}}
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| 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¢. |
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| 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 == |
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| == Approximations by edos == | |
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| 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。
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| | 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。 |
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| | +8522.3662 | | | +8522.3662 |
| | +4.52% | | | +4.52% |
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| == See also == | | == 另见 == |
| * [[8/5]] – its [[octave complement]]
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| * [[6/5]] – its [[fifth complement]]
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| * [[16/15]] – its [[fourth complement]]
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| * [[5/2]] – the interval up one [[octave]] which sounds even more [[consonant]]
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| * [[Ed5/4]]
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| * [[Gallery of just intervals]]
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| * [[List of superparticular intervals]]
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| == Notes ==
| | * [[5限纯律]] |
| <references/>
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| [[Category:Third]] | | [[Category:纯律音程]] |
| [[Category:Major third]] | | [[Category:泛音]] |
| | [[Category:5限纯律]] |
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