Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


poptimal


    p-optimal. For some p, 2 <= p <= infinity, we have that the generator is optimal for unweighted pth powers of the absolute values of the errors.

    [from Gene Ward Smith, Yahoo Tuning Group message 42429, Tue Feb 18, 2003 9:23 pm]

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    [from Paul Erlich, Yahoo Tuning Group message 42459, Fri Feb 21, 2003 1:51 pm]

    
    after generating the graph, i decided to attempt to localize the 
    minimum, and it appears that it occurs at
    
    p=2.8149
    
    where the optimal generator is
    
    696.1146 cents.
    
    any generator between that and the 1/4-comma meantone generator
    
    696.5784 cents
    
    is therefore poptimal for meantone.
    
    . . . that is, if you weight all the 5-limit consonance equally . . .
    
    


(to download a zip file of the entire Dictionary, click here)

  • For many more diagrams and explanations of historical tunings, see my book.
  • If you don't understand my theory or the terms I've used, start here
  • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.


    return to the Microtonal Dictionary index
    return to my home page
    return to the Sonic Arts home page