8edf

8EDF (8ED3/2) is the equal division of the fifth into 8 steps of 87.7444 cents each, making it very nearly 88cET. It is related to the octacot temperament. 8EDF corresponds to 13.6761 edo (similar to every third step of 41edo).

Intervals

8EDF can be notated either using sesquitave notation (the notation repeats every period, i.e. just diatonic fifth), or using double sesquitave notation (the notation repeats every two periods, i.e. major diatonic ninth, interpreting it as 16edIX).

The naturals result from a semiwolf generator (~7/6). For sesquitave notation, letters A-E can be used. For double sesquitave notation, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι).

Scale	Cents	Approximate intervals			Uranian	Diatonic	Notation
degree	value	7-limit	11-limit	19-limit	interval	equivalent	Sesquitave	D-Sesquitave
0	0	1			unison	unison	A	Α
1	87.7444	21/20	22/21	20/19, 19/18	min mos2nd	minor second	A#	Α#
2	175.48875	10/9		21/19	maj mos2nd	major second	B	Β
3	263.2331	7/6			perf mos3rd	subminor third	C	Γ
4	350.9775	60/49, 49/40	11/9		aug mos3rd	neutral third	C#	Γ#
5	438.7219	9/7			perf mos4th	supermajor third	D	Δ
6	526.46625	27/20		19/14	min mos5th	wolf fourth	D#	Δ#
7	614.2106	10/7		27/19	maj mos5th	augmented fourth	E	Ε
8	701.955	3/2			sesquitave	just fifth	A	Ϛ/Ϝ
9	789.6994	63/40	11/7	30/19	min mos7th	minor sixth	A#	Ϛ#/Ϝ#
10	877.44375	5/3		63/38	maj mos7th	major sixth	B	Ζ
11	965.1881	7/4			perf mos8th	subminor seventh	C	Η
12	1052.9325	90/49, 35/18	11/6		aug mos8th	neutral seventh	C#	Η#
13	1140.6769	27/14			perf mos9th	supermajor seventh	D	Θ
14	1228.42125	81/40		57/28	min mos10th	acute octave	D#	Θ#
15	1316.1656	15/7		81/38	maj mos10th	minor ninth	E	Ι
16	1403.91	9/4			double sesquitave	major ninth	A	Α

Scale workshop link for a keyboard/MIDI playable 8EDF (with graphical uranian scale, A=220Hz)

Rank 2 temperaments

MOS scales and temperament listed by generator size and period:

Periods per octave	Generator	Scale pattern	Temperaments
1	1\8	1L5s, 1L6s	(pathological)
1	3\8	3L2s (uranian)	Semiwolf
2	3\8	2L 2s	(augmented-like)

Images

8EDF cheat sheet (sesquitave notation) - table only