Re: Designing a Blackjack guitar (again!)

In-Reply-To: <3.0.6.32.20010606174612.00a7a240@uq.net.au>
Dave Keenan wrote:

> > 116.5-ish sounds okay for a Blackjack fretting. So long as it
> > doesn't have to work as meantone as well.
>
> No. Not meantone as well. It's interesting to consider a keyboard tuning
> that would be a kind of 31 tone well temperament; miracle in one region,
> varying smoothly to meantone in another.

I thought about that last night. Perhaps I don't need to read the List
any more, and ideas will be communicated to me telepathically!

> > I'm trying to find some good ones by ear.
>
> But some will be unavailable to you _because_ of your intial choice of
> open
> string tuning.

Yes, it's that chicken and egg problem again.

> > Guitars being guitars, this
> > often means some added notes creep in to the 11-limit chord.
>
> Please explain. You mean because they have 6 strings and you only have 4
> fingers. This of course is the design challenge.

I could always not strum all the strings, but I find it's better to leave
the "bad" notes in there. It's idiomatic for guitar chords anyway.

> > But different things are likely to sound good with a more accurate
> fretting,
>
> Indeed.

I've also had to throw away chords after finding the guitar was way out of
tune.

> > Another aim is to keep the strings roughly evenly spread in pitch.
> > No pairs in my tuning should be closer than a neutral third, or
> > further >
> apart than a tritone.
>
> Do you mean no further apart than a diminished fifth (approx 7:10) 633
> cents?

Ideally no further apart than the 7:5, but that's hard to pull off and I
see a 7:10 sneaked in there. It's also be convenient if the interval
that's usually G-B doesn't get much bigger, but you get used to that
fairly easily.

> > I thought of putting it around the major third from the nut. Exactly
> > where depends on whether you prefer 5:4 to 9:7.
>
> Please explain.

It's partly to match my meantone fretting, as explained in my reply to
Paul. Oh, and I suppose they should be / instead of :. But with the 5/4,
it'd be like this:

r q r q r q q r q r q r
6/5 5/4 4/3 3/2

r q r q r q r q q r q r
6/5 9/7 4/3 3/2

Either way, you start off with a simple pattern that takes you to a
neutral third, and you have a 4/3. It wouldn't seem right to me for a
guitar not to have a perfect fourth from the nut.

> > How would you define this optimum rotation? Surely it'd depend on
> > how you wanted the "home key" to relate to the open strings.
>
> Yes, but I figure the scale on the top string must be considered as the
> home key (whatever the rotation), because you can't choose to play these
> notes on another string. All other strings only need to give you the
> home
> key as far down the neck as the pitch of the next string (but it's
> better
> if they go further).

Ah, right.

> I think we only need to consider the string with the minimum value, r-3.
> The fretting should be such that the point of symmetry on the reference
> string is the same pitch class as this open string. i.e. POS is (72 -
> 3*7)/72 oct = 51/72 oct = 750 cents from the nut.

I don't think this is correct. You need to consider the strings with the
maximum and minimum values, and make sure they can see each other.

> If the POS is note 4 (decimal) the 21 notes available on the strings
> would
> be: (Missing home-key notes are shown with "*")
>
> r+2 r+5 r-1 r+2 r-3 r

<snip>

> When I set it out like this I see it's tougher than I thought.
>
> Notice that we have a "hole" between the 2nd and 3rd strings where we
> can't
> play 4> or 5> at all.

Looks like your POS is a lot further down than mine. But it should be
possible to place that symmetrically about the tritone. The closer it
gets to the tritone, the more tunings should work by your criterion.
It'll be something to do with the number of generators covered by the open
strings, and the number you can move in either direction from the nut.

Graham