A clarification: Suppose you want to place the frets on a lute so that:
1) All unisons are pure. That means the f on the second course has the same frequency as the open 1. course, the g on the second string has the same pitch as the b on the 1. course, ... over all courses. 2) All octaves are pure. The c on the fourth course has half the frequency of the first course, .... Then you have no choice left except equal temperament. The reason is that lutes cannot be tuned in any meantone temperament. You always have to accept false unisons or octaves. Rainer PS I use 1/6 comma meantone. However, I have no Baroque lutes nor have I ever tried accord nouveaux... On 13.05.2018 21:04, Ralf Mattes wrote:
Am Sonntag, 13. Mai 2018 20:43 CEST, Ron Andrico <praelu...@hotmail.com> schrieb:Ralf and Rainer, I believe you are in agreement. Octaves, fourths and fifths are pure and other intervals are an approximation.No, that's not what I (or Rainer) said. And it's wrong: Octaves are alway pure in all (western) tuning systems. Fifth/forth can be pure but then will be incomensurable with octaves (i.e. you can't stack fifth/forth and ever end up with pure octaves. As a matter of fact no pure intervals are comensurable. That IS a mathematic fact). Cheers, RalfD
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