string length and wavelength

hi group. I was reading (Grove's article on Harmony) that Zarlino
considered string lengths, such that the major triad was 15:12:10, and
the minor triad 6:5:4, but that later, Rameau used frequencies, such
that the major triad was 4:5:6, and the minor triad triad 10:12:15.

Does this "reversal" occur because wavelength and frequency are in
inverse proportion?

...trying to understand the fundamentals...hee hee....

thanks, Kelly

--- In tuning@yahoogroups.com, "traktus5" <kj4321@...> wrote:
>
> hi group. I was reading (Grove's article on Harmony) that Zarlino
> considered string lengths, such that the major triad was 15:12:10, and
> the minor triad 6:5:4, but that later, Rameau used frequencies, such
> that the major triad was 4:5:6, and the minor triad triad 10:12:15.
>
> Does this "reversal" occur because wavelength and frequency are in
> inverse proportion?
>
> ...trying to understand the fundamentals...hee hee....
>
> thanks, Kelly
>
Hi Kelly

I haven't read the articles but this reversal sounds more like a
reversal of opinion on what ratios to assign to these triads, nothing
to do with fact that period/string lengths are inversely proportional
to frequency. After all, the ratios b/w string lengths and frequencies
are the same i.e. to halve string is to halve period but double freq.
Both are 1:2.

Rick

--- In tuning@yahoogroups.com, "traktus5" <kj4321@...> wrote:
>
> hi group. I was reading (Grove's article on Harmony) that Zarlino
> considered string lengths, such that the major triad was 15:12:10,
and
> the minor triad 6:5:4, but that later, Rameau used frequencies,
such
> that the major triad was 4:5:6, and the minor triad triad 10:12:15.
>
> Does this "reversal" occur because wavelength and frequency are in
> inverse proportion?
>
> ...trying to understand the fundamentals...hee hee....
>
> thanks, Kelly
>

Hi Kelly,
I assume you have noticed that 4*15 = 5*12 = 6*10.
I think it is rather that "length of string" and "frequency" are in
inverse proportion - for a given string at a given tension that is.
The wavelength of the sound will in turn be in inverse proportion to
the frequency (for a given speed of sound) but I think that is beside
the point.

Note that the ratios have been reduced to lowest terms; in order to
sound the major triad followed by the minor triad on the same root at
the same octave, you would have to use e.g. 30:24:20 then 30:25:20.

Regards,
Steve M.