### Tuning and Temperament (4): Tempering the cycle of fifths

We have seen that 12 justly tuned fifths will overshoot 7 octaves, so in order for them to match up,…

### Tuning and temperament (3): Just Intonation and Equal Temperament

We have seen in previous posts on this topic that: The perfect fifth corresponds to a frequency ration of 3/2…

### Tuning and temperaments

When I was tuning my bass viol the other day, I wondered if I was getting the best out of…

### Curious results of an incorrect “theorem”

I hope all readers of this blog (all three of you – you know who you are!) have heard of,…

### Chebyshev approximation and Clenshaw-Curtis quadrature

Newton-Cotes integration and Gaussian integration are staples of numerical textbooks. And Gaussian integration is said to be better than Newton-Cotes…

The working of this quadrature method can be explained in part by the Euler-Maclaurin summation formula, which elegantly relates integral…

Tanh-sinh quadrature is one of a sequence of methods known as “double exponential” methods, because the weights used die away…

### Stieltjes polynomials and integration

In a slow and (in my case, uninformed) effort to add some numerical quadrature capabilities to PanAxiom, I’ve been looking…

### Re-discovering Axiom

While preparing my invited talk for a conference: http://atcm.mathandtech.org/ (you can see my name listed as an invited speaker), I started…

### Easy Newton-Raphson method on a calculator

The Newton-Raphson method for solving algebraic equations :     has always presented my students with difficulties.  To solve, for…