Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

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:

edo 5ths - pitch-height graph

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
			
. . . . . . . . .
[John Chalmers, Divisions of the Tetrachord]

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

The Diapente in Greek.

. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level