3136/3125: Difference between revisions
→Temperaments: organised temperaments and added orion (an important temperament) |
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'''3136/3125''', the '''hemimean comma''' or '''didacus comma''', is a [[7-limit]] [[small comma]] measuring about 6.1{{cent}}. It is the difference between five classic major thirds ([[5/4]]) and two subminor sevenths ([[7/4]]); it is also the difference between the septimal semicomma ([[126/125]]) and the septimal kleisma ([[225/224]]). | '''3136/3125''', the '''hemimean comma''' or '''didacus comma''', is a [[7-limit]] [[small comma]] measuring about 6.1{{cent}}. It is the difference between five classic major thirds ([[5/4]]) and two subminor sevenths ([[7/4]]); it is also the difference between the septimal semicomma ([[126/125]]) and the septimal kleisma ([[225/224]]). Perhaps most importantly, it is ([[28/25]])<sup>2</sup>/([[5/4]]) and (because [[28/25]] = ([[7/5]])/([[5/4]])) therefore also ([[28/25]])<sup>3</sup>/([[7/5]]) which means that its square is equal to the difference between ([[28/25]])<sup>5</sup> and [[7/4]]. This has the highly favourable property of putting a number of low complexity 2.5.7 subgroup intervals on a short chain of [[28/25]]'s, itself a 2.5.7 subgroup interval. | ||
== Temperaments == | == Temperaments == | ||