RE: [tuning] Re: Vincentino for Dummies

I wrote,

>> For music with triadic harmony, you only need to augment the usual
>>1/4-comma meantone chain, used for the roots and major thirds, with
>>an
>>exact copy of that chain 1/4 comma higher, used for the fifths and
>>minor thirds. Then all the triads come out in JI within themselves.

>Ok... so this is remedial...

>I thought a 1/3 comma chain is what made the MINOR thirds just. Why
>wouldn't it be a superimposed 1/3 comma chain rather than a 1/4 comma
>chain?? And wouldn't the 1/3 comma chain be BELOW the 1/4 comma
>chain since more of the comma has been subtracted??

Sorry Joseph, I should have been more clear. The first 1/4-comma meantone
chain is used for the roots and for the major third _of a major triad_. The
other chain, 1/4-comma higher, is used for the fifth _of triads_ and for the
minor third _of a minor triad_. We're talking chord degrees rather than
intervals here (gosh, if only music terminology wasn't so darn ambiguous).
The reason this works is that 1/4-comma meantone has major thirds just,
minor thirds 1/4 comma flat, and perfect fifths 1/4 comma flat. So the chain
that's 1/4 comma higher gives you just minor thirds and perfect fifths
against the notes in the lower chain.

If you superimposed a 1/3-comma meantone chain with a 1/4-comma meantone
chain, the two chains would get farther and farther apart from one another
as you moved away from the center along the chain of fifths. With two
1/4-comma meantone chains, always 1/4 comma apart, you get all the just
intervals you need for 5-limit triads anywhere along the chain of fifths.

Try working it out on paper (or better yet, with two keyboards) if you're
still confused.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12773

The first 1/4-comma meantone
> chain is used for the roots and for the major third _of a major
triad_. The other chain, 1/4-comma higher, is used for the fifth _of
triads_ and for the minor third _of a minor triad_. We're talking
chord degrees rather than intervals here (gosh, if only music
terminology wasn't so darn ambiguous).
> The reason this works is that 1/4-comma meantone has major thirds
just,minor thirds 1/4 comma flat, and perfect fifths 1/4 comma flat.
So the chain that's 1/4 comma higher gives you just minor thirds and
perfect fifths against the notes in the lower chain.
>

Got it! Thanks!
________ ____ __ __ _
Joseph Pehrson