Juggernaut

Juggernaut is a 5.7.11 nonoctave regular temperament, first documented by User:CompactStar, tempering out 125/121. It uses the pentave (5/1) as its equivalence instead of the more common octave or even tritave. It has a period of 1\2ed5 (1393 cents) representing 11/5, and a generator representing 7/5. This gives juggernaut an extremely low complexity with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-badness 5/1-equivalent or "no-twos-or-threes" temperaments, similar to meantone and BPS/lambda in their respective spheres. 24ed5 is the first ed5 offering a workable tuning of juggernaut with the generator as 5\24ed5.

The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two 13/11 by tempering out 847/845. The "tridecimal juggernaut" extension preserves the original 7/5 generator, and maps to 13/5 to -2 generators by tempering out 637/625.

Juggernaut contains multi-MOS scales of the families 4L 2s, 4L 6s, 10L 4s, 14L 10s, and 24L 14s. The 6-note MOS is rendered unusable because it has very large melodic steps (it corresponds to to 6*log(2)/log(5) ≈ 2.6 note octave-repeating scale) and contains too little 5:7:11 chords for the usage in no-twos-or-threes harmony.

Intervals

# gens	Period 0		Period 1
	Cents*	Approximate Ratios	Cents	Approximate Ratios
0	0.000	1/1	600.000	7/5, 10/7
1	230.966	8/7	830.966	8/5, 13/8
2	461.932	21/16, 13/10	1061.932	11/6, 15/8, 24/13
3	692.898	3/2	92.898	15/14
4	923.864	12/7, 22/13	323.864	6/5, 39/32
5	1154.830	48/25, 63/32, 96/48	554.830	11/8
6	185.796	9/8	785.796	11/7
7	416.762	9/7	1016.762	9/5
8	647.728	36/25	47.728	33/32, 36/35

* In 13-limit POTE tuning. This tuning is very close to 26edo.

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