On a Scale of One

[Ron Nossaman]

Tuning a Cable Nelson (Lyon & Healy) yesterday, I noticed something
interesting about the tenor/treble bridge. Periodically, the speaking
length progressions would change at every four or six unisons, so that at
the change, the note above was nearly as long as the one below. This is the
first one of these I have noticed out there in the world, but I recognized
the pattern because I had played with it on my scaling spreadsheet a couple
of years ago. It was a genuine equal tension scale, at least through the
treble. The idea is that you sweep a "regular" log scale, determine wire
size breaks, and adjust individual unison speaking lengths up or down from
the center of each wire size section, to make the tension changes between
wire sizes as smooth as possible. Of course, it screws up the corresponding
inharmonicity curve, but what the heck.

I've heard a lot of talk about equal tension scaling through the years, but
this is the first production example where I've seen it done through the
treble. In the bass, it's not necessary to change speaking lengths, and
some truly strange scales are possible without looking like anything unusual. 

Now for the big question. Why would anyone particularly care if string
tensions were the same through any particular section when it's done at the
expense of the inharmonicity curve? Yea, OK, they probably didn't have the
inharmonicity information we have today and were playing the cards they
had, but it still seems like a strange approach.

Ron N