Error in "Stretching the 19-tone Equal"

>>I shall perform a similar operation here for the 19-tone equal.
>
>>The ideal value for the octave itself is of course 1200/19 = 63.16 ;
>>here are the values for the other six consonances.
>>3:2 701.96/11 = 63.82
>>4:3 498.04/8 = 62.26
>>5:4 386.31/6 = 64.39
>>5:3 884.36/14 = 63.17
>>6:5 315.64/5 = 63.13
>>8:5 813.69/13 = 62.59
>
>>If one considers the consonances to be all of equal importance, one can
>>simply take the average of the above seven figures, which is 63.22, to
>>arrive at a figure for the octave of 1201.2.
>
>Gregg, this is not correct. You are not giving equal importance to the
>intervals above. Since whatever compromise is made in taking the average will
>be multiplied 14-fold for the 8:5 but only 5-fold for the 6:5, you are being
>more permissive for tuning errors in the larger intervals. I am certain
>Fokker would not have made this mistake, being a brilliant physicist. I know
>you will probably gloss over this post the way you have dismissed, with total
>lack of understanding, my other comments. But if you are interested, I will
>tell you the other things wrong with your calculations here, and how I
>arrived at an optimal octave of 1202.7 cents for 19-equal.
>
>>However, it seems to me
>>that some weighting in called for, because the smoother a consonance,
>>>the more susceptible it is to mistuning. If one weights the octave at 7,
>>the fifth at 6, the fourth at 5, the major third at 4, the major sixth
>>at 3, the minor third at 2, and the minor sixth at 1, one arrives at a
>>tuning degree of 63.29 cents, giving an octave of 1202.5 cents.
>
>Disregarding the previous error, that's fine, though I would weight things
>differently, and also put some weight on the octave and double octave, etc.


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: RE: 22-tone exhortations
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