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 next best extension named as "tridecimal juggernaut" 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

TBA

Tuning spectrum

This assume tridecimal juggernaut mapping for 13-limit intervals.

ED5 generator	Eigenmonzo (unchanged-interval)	Cents
	91/25	549.588
	13/11	551.974
	77/25	554.360
2\10ed5		557.263
	13/5	566.050
	539/125	568.436
	13/7	571.538
7\34ed5		573.653
	49/13	574.281
5\24ed5		580.482
	143/125	580.126
	7/5	582.512
8\38ed5		586.592
11\52ed5		589.413
	49/11	596.589
3\14ed5		597.067
	343/121	601.281
10\46ed5		605.720
7\32ed5		609.506
	11/7	610.665
4\18ed5		619.181
5\22ed5		633.253
	121/35	638.818