Jubilismic–augmented equivalence continuum: Difference between revisions
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The ''' | The '''jubilismic-augmented equivalence continuum''' is a continuum of [[2.5.7 subgroup]] temperaments which equate a number of [[50/49|jubilismas (50/49)]] with the [[128/125|lesser diesis (128/125)]]. | ||
All temperaments in the continuum satisfy (50/49)<sup>''n''</sup> ~ 128/125. Varying ''n'' results in different temperaments listed in the table below. It converges to [[Jubilismic clan#Jubilic|jubilic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.5.7 subgroup temperaments supported by [[6edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is 1.1739…, and temperaments near this tend to be the most accurate ones. | All temperaments in the continuum satisfy (50/49)<sup>''n''</sup> ~ 128/125. Varying ''n'' results in different temperaments listed in the table below. It converges to [[Jubilismic clan#Jubilic|jubilic]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all 2.5.7 subgroup temperaments supported by [[6edo]] (due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them); due to 6edo representing this subgroup modestly well for its size, this continuum is structurally important to 2.5.7. The just value of ''n'' is 1.1739…, and temperaments near this tend to be the most accurate ones. | ||
128/125 is the characteristic 2.5 comma tempered out in [[6edo]]. In each case, we notice that ''n'' equals half the order of harmonic 7 in the corresponding comma (noting that 6edo's ring of [[5/4]]s inherits from [[3edo]]), and equals the number of generators to obtain a harmonic 5 in the MOS scale. | 128/125 is the characteristic 2.5 comma tempered out in [[6edo]]. In each case, we notice that ''n'' equals half the order of harmonic 7 in the corresponding comma (noting that 6edo's ring of [[5/4]]s inherits from [[3edo]]), and equals the number of generators to obtain a harmonic 5 in the MOS scale. | ||