5-LIMIT JUST TUNINGS

Non-octave odd-prime 5-limit tuning: 3, 5

This tuning dispenses with octave-equivalency. Symmetry is based instead on the larger interval of the twelfth.

Western fifths, fourths, thirds, and seconds are omitted. The familiar chords of close Western harmony are omitted.

Based on only odd harmonics, this tuning may lend itself to single-reed instruments such as clarinets, that produce terraced rather than sawtoothed sound waves.

**3, 5**
Interval name	Numerator	/	Denominator	Decimal	Diapasons	Cents
Perfect 12th	3	/	1	3.000	1.585	1902
?	3,486,784,401	/	1,220,703,125	2.856	1.514	1817
?	25	/	9	2.778	1.474	1769
?	129,140,163	/	48,828,125	2.645	1.403	1684
?	625	/	243	2.572	1.363	1635
?	4,782,969	/	1,953,125	2.449	1.292	1551
min 10th	15,625	/	6,561	2.381	1.252	1502
Maj 9th	177,147	/	78,125	2.267	1.181	1417
?	390,625	/	177,147	2.205	1.141	1369
?	6,561	/	3,125	2.100	1.070	1284
?	9,765,625	/	4,782,969	2.042	1.030	1236
?	243	/	125	1.944	0.959	1151
Maj 7th	244,140,625	/	129,140,163	1.891	0.919	1103
min 7th	9	/	5	1.800	0.848	1018
?	6,103,515,625	/	3,486,784,401	1.750	0.808	969
Maj 6th	5	/	3	1.667	0.737	884
min 6th	387,420,489	/	244,140,625	1.587	0.666	799
?	125	/	81	1.543	0.626	751
?	14,348,907	/	9,765,625	1.469	0.555	666
?	3,125	/	2,187	1.429	0.515	618
?	531,441	/	390,625	1.360	0.444	533
?	78,125	/	59,049	1.323	0.404	485
Maj 3rd	19,683	/	15,625	1.260	0.333	400
?	1,953,125	/	1,594,323	1.225	0.293	351
Aug 2nd	729	/	625	1.166	0.222	266
Maj 2nd	48,828,125	/	43,046,721	1.134	0.182	218
dim 2nd	27	/	25	1.080	0.111	133
?	1,220,703,125	/	1,162,261,467	1.050	0.071	85
Unison	1	/	1	1.000	0.000	0

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Last revised: 16 August 2008
visitors since 28 June 1999