Is there an analogue to the "Delta" symbol for ratios?

A capital delta ($\Delta$) is commonly used to indicate a difference (especially an incremental difference). For example, $\Delta x = x_1 - x_0$

My question is: is there an analogue of this notation for ratios?

In other words, what's the best symbol to use for $[?]$ in $[?]x = \dfrac{x_1}{x_0}$?

Not entirely standard, but in Peter Henrici's discussion of the (justly famous) quotient-difference (QD) algorithm in the books Elements of Numerical Analysis (see p. 163) and Essentials of Numerical Analysis (see p. 155), he defines the quotient operator as

$$Q\,x_n=\frac{x_{n+1}}{x_n}$$

in complete analogy with the (forward) difference operator $\Delta$.

Henrici's a pretty sharp mathematician, so I wouldn't mind borrowing notation from him if I were in your shoes...

Here's a screenshot of the relevant page of the first book (sorry, I don't have a digital copy of the other book):

The best symbol to use is $\exp\Delta\log$: $$\exp\Delta\log x = \exp(\log x_1-\log x_0) = \frac{x_1}{x_0}.$$ The point is that this operation isn't "qualitatively different" from $\Delta$, so it may be reduced to $\Delta$. So far, I haven't used any new symbols but if you want some multiplicative new creative symbols, see e-percentages and units of evidence:

http://motls.blogspot.com/2010/01/exponential-percentages-useful-proposed.html
http://motls.blogspot.com/2010/08/units-of-evidence.html

There is no compact symbol for $\exp\Delta\log$. If you want an ally who would endorse the idea to introduce such a symbol, you may count on me. What about $\Delta^\times$?

The greek letter $\Delta$ stands for Difference So the symbol for the multiplicative increase of variable should be related to letter $Q$ in greek which is the ancient Qoppa letter and stands for Quotient