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'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. It uses the [[5/1|pentave]] (5/1) as its equivalence instead of the more common [[2/1|octave]] or even [[3/1|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.
'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out [[125/121]]. Its subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1|pentave]] (5/1) as its equivalence instead of the more common [[2/1|octave]] or even [[3/1|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 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. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 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 has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625.
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 has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.
   
   
Juggernaut contains multi-[[MOS scale]]s of the families [[4L 2s (5/1-equivalent)|4L 2s]], [[4L 6s (5/1-equivalent)|4L 6s]],  [[10L 4s (5/1-equivalent)|10L 4s]], [[14L 10s (5/1-equivalent)|14L 10s]], and [[24L 14s (5/1-equivalent)|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.
Juggernaut contains multi-[[MOS scale]]s of the families [[4L 2s (5/1-equivalent)|4L 2s]], [[4L 6s (5/1-equivalent)|4L 6s]],  [[10L 4s (5/1-equivalent)|10L 4s]], [[14L 10s (5/1-equivalent)|14L 10s]], and [[24L 14s (5/1-equivalent)|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.
Technical data: [[No-twos subgroup temperaments#Juggernaut]].


== Intervals ==
== Intervals ==
TBA
{|class="wikitable"
|-
! Generator
! Cents*
! Ratios
! Ratios<br>(tridecimal juggernaut)
|-
| -5
| 1266.911
|
| 715/343
|-
| -4
| 456.266
| 3025/2401
| 65/49
|-
| -3
| 1038.778
| 605/343, 625/343
| [[13/7]], 1625/847
|-
| -2
| 228.133
| [[55/49]], 625/539
| [[13/11]], 143/125
|-
| -1
| 810.645
| [[11/7]], 125/77
| 91/55, 1001/625
|-
| 0
| 0.000
| [[1/1]]
|
|-
| 1
| 582.512
| [[7/5]], 847/625
| 121/91, 125/91
|-
| 2
| 1165.024
| [[49/25]], 5929/3125
| [[25/13]], 121/65
|-
| 3
| 354.379
| 343/275, 3773/3125
| 77/65, 9317/8125
|-
| 4
| 936.891
| 2401/1375
| 539/325
|-
| 5
| 126.246
|
| 343/325
|}
<nowiki>*</nowiki>In no-twos-or-threes 11-limit CTE tuning
 
== Tuning spectrum ==
== Tuning spectrum ==
This assume tridecimal juggernaut mapping for no-twos-or-threes 13-limit intervals.
This assume tridecimal juggernaut mapping for no-twos-or-threes 13-limit intervals.
{|class="wikitable"
{|class="wikitable"
|-
|-
!ED5 generator
! ED5 generator
![[Eigenmonzo]] (unchanged-interval)
! [[Eigenmonzo]] (unchanged interval)
!Cents
! Cents
|-
|-
|
|  
|91/25
| 91/25
|549.588
| 549.588
|-
|-
|
|  
|[[13/11]]
| [[13/11]]
|551.974
| 551.974
|-
|-
|
|  
|77/25
| 77/25
|554.360
| 554.360
|-
|-
|2\[[10ed5]]
| 2\[[10ed5]]
|
|  
|557.263
| 557.263
|-
|-
|
|  
|[[13/5]]
| [[13/5]]
|566.050
| 566.050
|-
|-
|
|  
|539/125
| 539/125
|568.436
| 568.436
|-
|-
|
|  
|[[13/7]]
| [[13/7]]
|571.538
| 571.538
|-
|-
|7\[[34ed5]]
| 7\[[34ed5]]
|
|  
|573.653
| 573.653
|-
|-
|
|  
|49/13
| 49/13
|574.281
| 574.281
|-
|-
|5\[[24ed5]]
| 5\[[24ed5]]
|
|  
|580.482
| 580.482
|-
|-
|
|  
|143/125
| 143/125
|580.126
| 580.126
|-
|-
|
|  
|[[7/5]]
| [[7/5]]
|582.512
| 582.512
|-
|-
|8\[[38ed5]]
| 8\[[38ed5]]
|
|  
|586.592
| 586.592
|-
|-
|11\[[52ed5]]
| 11\[[52ed5]]
|
|  
|589.413
| 589.413
|-
|-
|
|  
|49/11
| 49/11
|596.589
| 596.589
|-
|-
|3\[[14ed5]]
| 3\[[14ed5]]
|
|  
|597.067
| 597.067
|-
|-
|
|  
|343/121
| 343/121
|601.281
| 601.281
|-
|-
|10\[[46ed5]]
| 10\[[46ed5]]
|
|  
|605.720
| 605.720
|-
|-
|7\[[32ed5]]
| 7\[[32ed5]]
|
|  
|609.506
| 609.506
|-
|-
|
|  
|[[11/7]]
| [[11/7]]
|610.665
| 610.665
|-
|-
|4\[[18ed5]]
| 4\[[18ed5]]
|
|  
|619.181
| 619.181
|-
|-
|5\[[22ed5]]
| 5\[[22ed5]]
|
|  
|633.253
| 633.253
|-
|-
|
|  
|121/35
| 121/35
|638.818
| 638.818
|}
|}


[[Category:Temperaments]]
[[Category:Juggernaut| ]] <!-- main article -->
[[Category:Nonoctave]]
[[Category:Rank-2 temperaments]]
[[Category:Pentave]]
[[Category:Non-octave temperaments]]
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