Re: [tuning] Digest Number 1691

> Subject: Re: New Telemann page - audio files
>
> > Yes, isn't that a strange chord for this time period?
> >
> > But he definitely didn't have 1/4-comma meantone in mind,
> > because the comma- and interval-sizes of 1/4-comma don't
> > match his descriptions.
> >
> I know, but even 1/6-comma meantone is pretty close.
> >
> > The best low-integer approximation to the proportions of
> > the four 55-EDO pitches which I used in the mp3 is
> > 6:16:19:27 -- and this approximation would be an even
> > better fit for 1/6-comma tuning.
>
> I beg to differ, if you're saying 16:19:24:27 fits the chord better
> than 1/6:1/5:1/4:2/7.
>

Paul shows the 31et or 1/4-comma JI interpretation of the first of
these two chords.

> > Eb --> D#
> > A B
> > F# F#
> > C# B
> >
> > where Eb is a comma higher than D#.
>
> That first chord, classically speaking, is an F# minor chord with a
> diminished seventh. I've never heard of a minor chord with a
> diminished seventh being used in classical music -- a minor chord
> with a major sixth would be common but be notated with a D# on top.
> But in 31-tET or 1/4-comma meantone, this chord would approximate
> extremely closely the string lengths 4:5:6:7. Perhaps Telemann knew
> this??? Anyone else have any thoughts about where Telemann would
> have pulled this chord from?

Thoughts I have...

Notice that if the C# were C natural then there would be a
F#dim7 -> B resolution. Not terribly common, but spelled
correctly... This doesn't help at all with a JI
interpretation, since a diminished chord is highly
ambiguous in JI.

However, the voicing in this case would have been the
following stack

diminished fifth -> major third (usual resolution but displaced)
minor third
augmented fourth -> atypical oblique resolution

Telemen may have thought the atypical oblique resolution may have
needed some fixing. Or he may have not found having the two sizes
of 'tritone' so exposed to his tastes.

Or it could just be a melodic consideration, that he was hearing
the diminished chord as tempered (illustration in cents)

1600 -> 1586
1000 -> 1200
700 -> 702
100 -> 0

and felt the endpoints were two 'wiggly' and that a bigger motion
on the bottom voice would make it stronger and balance the A->B
inner voice motion.

1600 -> 1586
1000 -> 1200
700 -> 702
200 -> 0

Another thing that is suggested,, at least in 31, is that one
could start with an Eb aug 6 (septimal seventh)

Eb -> D#
Bb -> B
G -> F#
C# -> B

and then get confused or chicken out or dislike it. Then fixing
the inner voices one would come up with what he did.

The guy was a genius and could have been thinking almost
anything sensible or nonsensical when he came up with this.
(This is another one for the tuning to-do list).

Bob Valentine