error on wedge-product page?

Hi Dave [Keenan],

On my Encyclopedia page about "wedge-product"

http://tonalsoft.com/enc/w/wedge-product.aspx

i quoted a tuning-math post from you where you
explain how to do the calculation.

I believe there's an error there, in your first
explanation illustrating the simplest case.

[a1 a2> ^ [b1 b2>

The list of products with their compound indices is:

product index

a1*b1 11
a1*b2 12
a2*b1 21
a2*b2 22

At the end of your explanation of the 3 possibilities of
how to handle the products depending on the indices,
under the third possibility, you wrote:

>> [3.] ... Consider the index 21. There are zero larger
>> digits to the left of the 2 (because there are _no_
>> digits to the left of it), and there is one larger
>> digit to the left of the 1, namely the 2. So the total
>> of the left-and-larger counts is 1, an odd number.
>> So a2*b1 becomes -a2*b1. We now have
>>
>> product index
>>
>> a1*b2 12
>> -a2*b1 21

I believe the index for -a2*b1 at this point should be 12.
Correct? (hard to believe i missed it for over 3 years!)

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "monz" <monz@...> wrote:
> I believe the index for -a2*b1 at this point should be 12.
> Correct? (hard to believe i missed it for over 3 years!)

You're absolutely right Monz. Well spotted.