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 (2): Intervals and Pythagorean tuning
In the previous post we looked briefly at intervals, pitches and frequencies, and how to measure them. We also showed…
Tuning and temperaments
When I was tuning my bass viol the other day, I wondered if I was getting the best out of…
The use of commercial software in academic papers
First, consider written language. If you are going to publish an academic paper for an international readership, what language will…
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…
Tanh-sinh quadrature (2)
The working of this quadrature method can be explained in part by the Euler-Maclaurin summation formula, which elegantly relates integral…
Tanh-Sinh quadrature
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…
