1029/1000: Difference between revisions
+ a more significant identity. Cleanup. |
+ factorization into simpler commas |
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'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[10/7]]'s and a perfect twelfth ([[3/1]]), or between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>. | '''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[10/7]]'s and a perfect twelfth ([[3/1]]), or between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>. | ||
It factors into simpler commas as ([[49/48]])⋅([[126/125]]) and ([[81/80]])⋅([[686/675]]). | |||
== Temperaments == | == Temperaments == | ||