At 7:34 am -0800 11/14/02, Robert Patterson wrote:
The "American Heritage dictionary of the English Language, Third Edition" ((c) 1992 Houghton Mifflin) defines "order of magnitude" as:On Thu, 14 Nov 2002 07:25:08 -0800 (PST), Andrew Stiller wrote:I hate to be technical, but an order of magnitude means a factor of X, where X is any number you choose (including "real" & "imaginary" numbers). FWIW: I just verified this with my Websters Collegiate, which defines an order of magnitude as a multiple of a "standard unit".An order of magnitude means a factor of 10.
{
order of magnitude n. pl. orders of magnitude 1. An estimate of size or magnitude expressed as a power of ten: Earth's mass is of the order of magnitude of 10^22 tons; that of the sun is 10^27 tons. 2. A range of values between a designated lower value and an upper value ten times as large: The masses of Earth and the sun differ by five orders of magnitude.
}
The "Oxford English Dictionary" (2nd Edition) says:
{
order of magnitude: approximate number or magnitude in a scale in which equal steps correspond to a fixed multiplying factor (usu. taken as 10); a range between one power of 10 and the next; also, the order (order n. 10) of an infinitesimal or an infinite number.
}
and goes on to provide citations (numbering 10 ;-) dating back to (only!) 1875; not all of which support the notion that "an order of magnitude" is "a range between one power of 10 and the next."
I hate to be technical, but an order of magnitude means a factor of X, where X is any number you choose (including "real" & "imaginary" numbers).Anyone in the scientific and technical community can agree that 2^9 is three orders of magnitude greater than 2^6 but, in general parlance, the phrase "order of magnitude" has come to mean "greater (or lesser) by a power of 10."
Ain't it ever. The definitions of English words and (especially) phrases are unavoidably fungible.Anyway, the whole thing is a nitpick.
Here we totally agree; the complexity of a language/symbolism that describes a page of musical notation is much more complicated than that which describes a page of text.Music notation has several additional dimensions of information than text...
Best wishes,
-=-Dennis
_.
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