Tuning Methods

Prime Limit Otonal Tunings

3-limit

3-prime-limit tuning is very ancient, and has been widespread at various times in many world cultures, including the West. It is known most widely now as Pythagorean tuning, after the Greek philosopher Pythagorus, who is often credited with promoting its use.

Scale DegreeGen-
era-
tion
3^gen-
eration
:2^x divisorQuotientCentsCents devia-
tion from 12 EDO
Tun-
ing Table
Round-
ed Tuning Table
Note Name
111:110.000.00-10.75-11C
282187:20481.067871094113.6913.692.933C#
339:81.125203.913.91-6.84-7D
41019683:163841.20135498317.6017.606.847D#
5581:641.265625407.827.82-2.93-3E
612177147:1310721.351524353521.5121.5110.7511F
77729:5121.423828125611.7311.730.981F#
823:21.5701.961.96-8.80-9G
996561:40961.601806641815.6415.644.895G#
10427:161.6875905.875.87-4.89-5A
111159049:327681.8020324711019.5519.558.809A#
126243:1281.89843751109.789.78-0.98-1B

Play Tuning bar chart

Largest step size:113.69 c (2187:2048)
Smallest step size:90.22 c (256:243)
Number of step sizes:2 

Very high odd limit: 177,147.

HC = 12.1


2004 by David J. Finnamore
tuning@elvenminstrel.com