Tuning Question

[Mike and Jane Spalding]

HI Richard,

There's probably a more direct proof, but try walking through this one, and
tell me if it makes sense?

1.  Minor third = inverted Major sixth for pure 6:3 octave, let's assume
this is your target octave size from the temperament octave down to the
bottom.  Using your example notes, C2-D#2 = D#2-C3.

2.  The Major sixth having a common bottom note would be C2-A2.  If your
3rds and 6ths are progressing properly, C2-A2 should beat slower than
D#2-C3, by not quite a 4:5 ratio (It IS slower than E2-C#2 by a 4:5 ratio).

3.  Therefore, C2-A2 should beat slower than C2-D#2 by not quite 4:5.
Unless you are doing a funny stretch, or have some weird inharmonicity
(probably wouldn't have one without the other) I would expect this
relationship to hold throughout the scale.  Or another way to say it, I
would expect this relationship to hold as well as your 3rds progression.

Mike




----- Original Message -----
From: Richard Brekne <rbrekne@operamail.com>
To: <pianotech@ptg.org>
Sent: Wednesday, August 22, 2001 2:17 PM
Subject: Re: Tuning Question


> 22.08.2001 01:27:37, Newton Hunt <nhunt@optonline.net> wrote:
>
> >Hi Richard,
> >
> >The minor third inverted into a major sixth is a valid test of an octave
at and
> >below the temperament because it reflects the 6:3 octave.  But, the minor
sixth
> >should be slower than the sixth.
> >
> >Example: C2-Eb2 minor third and Eb2- C3 major sixth the minor third
should be
> >faster to expand the octave at the 6:3.
>
>
> Not exactly what I was talking about Newton. By way of example take C2-Eb2
minor third and C2-A3 major sixth. In this comparison the minor third should
be faster then
> the major sixth... or what ?. And my question was ....is every such
comparision of a minor third / major sixth taken from the same note the
same... (m3rd faster then
> M6th) ?
>
> I have fooled around a bit with this today too.... seems to work really
neat.. and easy to hear. Just pull up the note til the minor third above it
beats just a tad faster then
> its major 6th above. Run this quickly chromatically to the bottom and go
back and check Major 3rds and 10ths and other test intervals. Each time so
far its put me really
> nicely in range.. Just wondered if this could be treated sort of
universally true in the sense we do contiguous 3rds..
>
> >Bear in mind, the minor third is a contract interval the sixth an
expanded one.
> >
> > Newton
>
>
>
>