53edo: Difference between revisions
→Theory: holdrian comma is a comma in the sense of small interval. Add 212edo, 901edo an mercator family to the multiples list (thereby discarding 17-odd-limit as a threshold) |
→Theory: vulture comma in monzo; big brother (lowercase); note 4096/4095 |
||
| Line 11: | Line 11: | ||
== Theory == | == Theory == | ||
53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) | 53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) and the [[kleisma]] (15625/15552). More complex 5-limit commas tempered out include the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] ({{monzo| 24 -21 4 }}). In the 7-limit it tempers out [[225/224]], [[1728/1715]] and [[3125/3087]], the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[Marvel family #Athene|athene]] temperament. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | ||
53edo has also found a certain dissemination as an edo tuning for [[Arabic, Turkish, Persian]] | 53edo has also found a certain dissemination as an edo tuning for [[Arabic, Turkish, Persian music]]. | ||
53edo's step size is sometimes called the "Holdrian comma", despite not being a rational one. | 53edo's step size is sometimes called the "Holdrian comma", despite not being a rational one. | ||