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.