# perfect 5th, perfect fifth, p5

[Joe Monzo]

The interval which encompasses 5 degrees of a diatonic scale. It is usually close in size to the frequency ratio 3:2, which is approximately 702 cents.

In the usual 12-edo tuning, the perfect 5th encompasses 7 semitones, and is thus exactly 700 cents.

Below is a graph of the size of the best approximation to the 3:2 "5th" in cents, for all the EDOs from 10 to 72:

Below is a table showing the sizes of "perfect-5th" for various tunings of the historically important meantone family:

```  tuning    ~cents of generator

12-edo       700.000000
1/11-comma    699.9998836
103-edo       699.029126
91-edo       698.901099
79-edo       698.734177
67-edo       698.507463
1/6-comma     698.3706193
55-edo       698.181818
98-edo       697.959184
43-edo       697.674419
1/5-comma     697.6537429
3/14-comma    697.3465102
74-edo       697.297297
2/9-comma     697.1758254
105-edo       697.142857
31-edo       696.774194
1/4-comma     696.5784285
112-edo       696.428571
81-edo       696.296296
7/26-comma    696.164846
50-edo       696.000000
5/18-comma    695.9810315
2/7-comma     695.8103467
69-edo       695.652174
88-edo       695.454545
107-edo       695.327103
1/3-comma     694.7862377
19-edo       694.736842
```
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[John Chalmers, Divisions of the Tetrachord]

The interval 3/2 in Just Intonation or the closest approximation to 702 cents (Â¢) in an equal temperament.

The Diapente in Greek.

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