Origin of 12 TET

Does any body know whether 12 TET was derived from a circle of tempered fifths or derived by simply dividing the octave into 12 equal steps?

It was derived via mean tone as a compromise as far as I know.

http://en.wikipedia.org/wiki/Equal_temperament

Chris

On Sun, Jul 4, 2010 at 2:48 PM, john777music <jfos777@...> wrote:
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>
>
> Does any body know whether 12 TET was derived from a circle of tempered fifths or derived by simply dividing the octave into 12 equal steps?
>

I would think it arose from the evening out of well temperaments. Sort of like pythagorean -> meantone -> well -> equal.

Vincenzo Galilei was recommending an 18:17 semitone for lutes in the sixteenth century, which practically is 12-edo on a stringed instrument (Gibson still uses this ratio for electric guitars).

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
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> Does any body know whether 12 TET was derived from a circle of tempered fifths or derived by simply dividing the octave into 12 equal steps?
>

The reason I ask is that a chapter of my book deals with 12 TET and I want to explain its origins. It seems to me highly likely that 12 TET was developed using a circle of tempered fifths but I wanted to be sure.

John.

--- In tuning@yahoogroups.com, "Tony" <leopold_plumtree@...> wrote:
>
> I would think it arose from the evening out of well temperaments. Sort of like pythagorean -> meantone -> well -> equal.
>
> Vincenzo Galilei was recommending an 18:17 semitone for lutes in the sixteenth century, which practically is 12-edo on a stringed instrument (Gibson still uses this ratio for electric guitars).
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Does any body know whether 12 TET was derived from a circle of tempered fifths or derived by simply dividing the octave into 12 equal steps?
> >
>

> Does any body know whether 12 TET was derived from a circle of tempered fifths
>or derived by simply dividing the octave into 12 equal steps?

Neither...but closer to being a circle of tempered fifths.

I've always thought of it as a modified version of simply a rounding of
mean-tone to TET to obtain the following advantages

A) Every interval is the same amount in/out of key from a pure interval
regardless of transposition (obvious property of any TET tuning).
B) It's very easy to design acoustic instruments based on TET scales
(these are both mentioned in Chris's Wikipedia link)

BUT what explains much of why 12TET was considered over other TET scale is:
C) It's easier to play an instrument with 12 than, say 31 tones per
octave...hence why 12TET was favored over larger TET scales like 31TET and 53TET
that actually maintain more pure intervals on the average.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> The reason I ask is that a chapter of my book deals with 12 TET and I want to explain its origins. It seems to me highly likely that 12 TET was developed using a circle of tempered fifths but I wanted to be sure.

In Europe, in a process taking centuries, Pythagorean (3-limit) tuning lead to meantone, which lead to circulating temperaments, which lead to 12 equal. However lutenists such as Galileo's father were early adopters, as the lute favors the tuning. Meanwhile in China someone proposed the idea as a theory, though I don't know that it lead anywhere in practice.