Jove: Difference between revisions

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| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.86 | Complexity 2 = ?
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.86 | Complexity 2 = ?
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'''Jove''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the breedsma, [[2401/2400]], in the 7-limit, the rastma, [[243/242]], the werckisma, [[441/440]], and the swetisma, [[540/539]], in the 11-limit.  
'''Jove''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] of the [[breed family]]. Like [[breed (temperament)|breed]], it is generated by a neutral third of [[49/40]][[~]][[60/49]], two of which give a [[3/2|perfect fifth]], and a tritone of [[10/7]], two of which give a generic septimal diesis of [[49/48]]~[[50/49]], such that [[5/4]] and [[7/4]] are found by the septimal diesis plus the neutral third and the tritone plus the neutral third, respectively. Jove further identifies the neutral third as [[11/9]]~[[27/22]], [[tempering out]] [[243/242]], [[441/440]], and [[540/539]], for less accuracy but a compact lattice structure in the [[11-limit]].
 
It can be extended to the [[13-limit]] as jovial (41 & 58 & 72), jovis (31 & 58 & 72), or jofur (31 & 41 & 58).
 
See [[Breed family #Jove]] for technical data.


See [[Breed family #Jove]] for more technical data.
{{Todo|improve synopsis}}
{{Clear}}
== Interval lattice ==
== Interval lattice ==
<gallery>
<gallery>

Latest revision as of 11:50, 11 February 2026

Jove
Subgroups 2.3.5.7.11
Comma basis 243/242, 441/440 (11-limit)
Reduced mapping ⟨1; 2 1 1 5; 0 2 1 0]
ET join 31 & 41 & 58
Generators (CWE) ~11/9 = 350.5 ¢, ~10/7 = 617.9 ¢
MOS scales n/a
Ploidacot n/a
Pergen (P8, P5/2, c^^M7/4)
Color name Bizozoguti
Minimax error 9-odd-limit: 0.18 ¢;
11-limit 21-odd-limit: 2.86 ¢
Target scale size 9-odd-limit: ? notes;
11-limit 21-odd-limit: ? notes

Jove is a rank-3 temperament of the breed family. Like breed, it is generated by a neutral third of 49/40~60/49, two of which give a perfect fifth, and a tritone of 10/7, two of which give a generic septimal diesis of 49/48~50/49, such that 5/4 and 7/4 are found by the septimal diesis plus the neutral third and the tritone plus the neutral third, respectively. Jove further identifies the neutral third as 11/9~27/22, tempering out 243/242, 441/440, and 540/539, for less accuracy but a compact lattice structure in the 11-limit.

It can be extended to the 13-limit as jovial (41 & 58 & 72), jovis (31 & 58 & 72), or jofur (31 & 41 & 58).

See Breed family #Jove for technical data.

Interval lattice

Chords and harmony

Jove enables essentially tempered chords of rastmic, werckismic, swetismic, and jove.

Scales

Tunings

Tuning spectrum

This table assumes the jovis mapping with pure 2 and 11.

Eigenmonzo
(Unchanged-interval)
Major third (¢) Comments
9/7 381.677
10/9 383.458 11-odd-limit minimax
7/6 384.533
6/5 384.886
7/5 385.239
18/13 385.649 13- and 15-odd-limit jovis minimax
15/13 386.157
13/12 386.220
5/4 386.314
14/13 386.642
16/13 386.791
13/10 387.109
8/7 387.388
16/15 387.742
15/14 388.095

Music

Chris Vaisvil