Harmonics 30–60

Harmonics 30–60

Prime factorization	2 × 3 × 5
Fifth	45/30 (701.955c)

The harmonic segment 30::60 (also harmonics 30–60) consists of harmonics 30 through 60 (30:31:…:60) and spans one octave above the root. Used as a scale, it is also called mode 30 of the harmonic series. Since 30 factors into primes as 2 × 3 × 5, this scale contains many common 5-limit intervals above its root and is extremely useful for common tonal harmony.

Intervals

#	Cents	Ratio	Decimal	Interval name	Audio
0	0	1/1	1.000	perfect unison
1	56.2	31/30	1.0333	large tricesimoprimal quartertone
2	111.7	16/15	1.0667	classic diatonic semitone
3	165.0	11/10	1.1000	undecimal submajor second
4	216.7	17/15	1.1333	septendecimal whole tone
5	266.9	7/6	1.1667	subminor third
6	315.6	6/5	1.2000	just minor third
7	363.1	37/30	1.2333	trigintaseptimal submajor third
8	409.2	19/15	1.2667	Eratosthenes' major third
9	454.2	13/10	1.3000	tridecimal semisixth
10	498.0	4/3	1.3333	just perfect fourth
11	540.8	41/30	1.3667	quadragesimaunal superfourth
12	582.5	7/5	1.4000	small septimal tritone
13	623.25	43/30	1.4333	large quadragintatertial tritone
14	663.05	22/15	1.4667	undecimal diminished fifth
15	702.0	3/2	1.5000	just perfect fifth
16	740.0	23/15	1.5333	vicesimotertial ultraminor sixth	File:Jid 23 15 pluck adu dr220.mp3
17	777.2	47/30	1.5667	quadragintaseptimal subminor sixth
18	813.7	8/5	1.6000	just minor sixth
19	849.4	49/30	1.6333	septimal neutral sixth
20	884.5	5/3	1.6667	just major sixth
21	918.6	17/10	1.7000	septendecimal major sixth
22	952.3	26/15	1.7333	tridecimal semitwelfth
23	985.2	53/30	1.7667	quinquagintatertial minor seventh
24	1017.6	9/5	1.8000	just minor seventh
25	1049.4	11/6	1.8333	undecimal neutral seventh
26	1080.6	28/15	1.8667	septimal grave major seventh
27	1111.2	19/10	1.9000	Eratosthenes' major seventh
28	1141.3	29/15	1.9333	undetricesimal supermajor seventh
29	1170.9	59/30	1.9667	undexsexagesimal suboctave
30	1200.0	2/1	2.0000	perfect octave

Scales

• 30:36:40:45:50:55:60 Baobab^{[idiosyncratic term]}
• 30:35:40:45:47:60 Mushroom^{[idiosyncratic term]}
• 30:33:36:40:45:50:55:60 Neutral Melodic Minor^{[idiosyncratic term]}
• 30:32:35:40:44:47:54:60 James Wyness' "Kai Udan Arum pelog"
• 30:32:34:36:37:40:41:45:48:50:52:54:56:60 loose approximation of fluid just intonation