Ultrapyth

Oceanfront is an alternative extension to superpyth. Like superpyth, it is a temperament generated by a perfect fifth, where stacking two of them reaches the interval of 8/7. The difference is that instead of extending to 2.3.5.7 by mapping 5 to +9 generators, it maps the ultramajor third 13/10 to +4 generators (a supermajor third which is also the diatonic major third). This makes sense because the best tunings of 2.3.7 superpyth (also called archy) are sharp of the optimal tuning for 9/7, making it more ultramajor than supermajor. If intervals of 5 and 13 independently are desired (i.e. 5/4, 13/8), then oceanfront may be extended to ultrapyth by mapping 5 to +14 fifths (a doubly augmented unison) and 13 to +18 fifths (a doubly-augmented third). The best tunings for ultrapyth are between 712 and 714 cents.

If intervals of 11 are desired, 14/11 may be mapped to +9 generators, implying 16/11 is (fittingly) mapped to +11 generators and 11/9 is tempered together with 6/5 (a feature common to many systems with sharp fifths).

The oceanfront MOS scales take the form of 5L (2+5n)s, for n up to 7. Most of these scales are extremely close to 5edo. 37edo makes a good tuning of oceanfront or ultrapyth.

Generator chain

#	Cents	Approximate ratios (Oceanfront)	Approximate ratios (added by Ultrapyth)	Approximate ratios (added in the 11-limit)
0	0	1/1
1	713.4	3/2
2	226.8	8/7, 9/8, 91/80
3	940.2	12/7, 26/15
4	453.6	13/10, 9/7
5	1167	39/20, 27/14
6	680.4	72/49, 52/35
7	193.8	54/49		112/99, 160/143
8	907.2	117/70		56/33
9	420.6			14/11
10	1134		160/81	64/33
11	647.4		40/27	16/11
12	160.8		10/9	12/11
13	874.2		5/3	128/77
14	387.6		5/4	96/77
15	1101		15/8, 52/27	144/77
16	614.4		45/32, 13/9
17	127.8		13/12, 135/128
18	841.2		13/8
19	354.6		39/32
20	1068		117/64