5/4
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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
| 平均律 | 5/4的步数 | 绝对误差(ie) | 相对误差 |
|---|---|---|---|
| 3 | 1 | +126.4941 | +3.42% |
See also
- 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