Diesis: Difference between revisions
m 648/625 fits this definition too so its only unusual property is being larger than 250/243 |
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For someone looking for what sets these (and a few others) apart from other commas in the size range, it might be worth noting be noted that (with the exception of 648/625 being slightly larger than 250/243), almost all just intervals commonly called dieses have a few properties in common that might be used to derive a definition that expands the set of commas called dieses to something closer to the spirit of the term as a whole: | For someone looking for what sets these (and a few others) apart from other commas in the size range, it might be worth noting be noted that (with the exception of 648/625 being slightly larger than 250/243), almost all just intervals commonly called dieses have a few properties in common that might be used to derive a definition that expands the set of commas called dieses to something closer to the spirit of the term as a whole: | ||
* Being an awkward xenmelodic size (as characteristic of intervals of a size between that of the minimal diesis (27.66{{c}}) and maximal diesis (49.17{{c}})). Relatedly: | * Being an awkward xenmelodic size (as characteristic of intervals of a size between that of the minimal diesis (27.66{{c}}) and maximal diesis (49.17{{c}})). Relatedly: | ||
* Equating a ''short'' stack of one LCJI interval with some other LCJI interval (and it appears it's never more than 4 or 5, as suggested by the unusual | * Equating a ''short'' stack of one LCJI interval with some other LCJI interval (and it appears it's never more than 4 or 5, as suggested by the unusual historical diesis of 256/243 = ([[4/3]])<sup>5</sup> / [[4/1|4]] = ([[4/3]])<sup>4</sup> / [[3/1|3]]). Note that due to the minimal and maximal diesis both using a stack of [[~]][[10/9]]'s, one could argue that ''at most'', one is looking at how a short stack of some [[9-odd-limit]] interval relates to some other simple interval of interest. | ||
* Due to the last two constraints, when tempered out and in a tuning that makes the other simple interval of interest pure, all dieses incur a not-unnoticeable amount of damage on the interval being stacked*. This is arguably what truly makes them feel awkward in JI, as they are also small enough to feel like potential commas without being very efficient to temper out. *Notably, some of these are more debatable than others in terms of damage, so one should clarify that the minimum damage logically is that of the minimal diesis (6.9{{c}}), as more than 7 cents of damage is not insignificant for most intervals and is essentially a flexibility afforded by LCJI's temperability. | * Due to the last two constraints, when tempered out and in a tuning that makes the other simple interval of interest pure, all dieses incur a not-unnoticeable amount of damage on the interval being stacked*. This is arguably what truly makes them feel awkward in JI, as they are also small enough to feel like potential commas without being very efficient to temper out. *Notably, some of these are more debatable than others in terms of damage, so one should clarify that the minimum damage logically is that of the minimal diesis (6.9{{c}}), as more than 7 cents of damage is not insignificant for most intervals and is essentially a flexibility afforded by LCJI's temperability. | ||