5/4：修订间差异
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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". | 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". | ||
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== 另见 == | == 另见 == | ||
* [[5限纯律]] | * [[5限纯律]] | ||
2025年12月2日 (二) 09:56的版本
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。
}}另见
| 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% |