5/4：修订间差异

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== Approximations by edos ==
== 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"
{| class="wikitable"
|+
|+
!平均律
!平均律步数
!5/4的步数
!5/4的步数
!绝对误差(ie)
!绝对误差(ie)
第27行： 第30行：
|3
|3
|1
|1
| +126.4941
|+126.4941
| +3.42%
|+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 ==
== See also ==

2025年12月2日 (二) 09:52的版本

模板:Interwiki 模板:Infobox Interval 模板:Wikipedia

In 5-limit just intonation, 5/4 is the frequency ratio between the 5th and 4th harmonics. It has been called the just major third, classic(al) major third, or ptolemaic major third[1] to distinguish it from other intervals in that neighborhood. Measuring about 386.3 ¢, it is about 13.7模板:C away from 12edo's major third of 400模板: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模板:C, and from the Pythagorean diminished fourth of 8192/6561 by the schisma, which measures about 1.95模板: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。

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
25 8
28 9
31 10
2210.8565 2.02%
34 11
900.9429 5.44%
37 12
602.0688 8.87%
53 17
59 19
13635.6185 0.62%
65 21
1255.797 7.47%
81 26
87 28
90 29
4905.0016 2.65%
96 31
1459.3731 9.49%
109 35
115 37
121 39
3737.9906 4.67%
143 46
146 47
149 48
6570.9626 3.27%
152 49
3276.4236 6.69%
171 55
183 59
3029.1111 8.72%
199 64
202 65
205 66
62387.8247 0.47%
208 67
7703.0121 3.9%
211 68
4160.1807 7.32%
227 73
233 75
239 77
5825.8383 5.92%
255 82
258 83
264 85
34678.4334 1.1%
267 86
8522.3662 4.52%}

See also

Notes

  1. ↑ For reference, see 5-limit.
检索自“https://tun.wiki/index.php?title=5/4&oldid=10”