back to list

Haluska commas

🔗Gene Ward Smith <gwsmith@svpal.org>

3/29/2004 12:06:42 PM

Haluska defines a (p-limit) comma as an interval such that any
smaller p-limit interval has a greater height. He uses the numerator
as a height function, but nothing essential is changed by taking
Tenney height instead, and I think that will actually make it easier
to compute a comma list.

I propose we call a p-limit interval m/n>1 a "Haluska comma" if
for any p-limit interval a/b>1, a/b<m/n ==> m*n<a*b. The first
Haluska comma for any odd p will be 2, followed always by 3/2 and 4/3.
If p>3 we then get 5/4 and 6/5, etc.