### Tuning and temperament (5): Meantone and the syntonic comma

The Pythagorean comma may be considered as the difference in two ways of tuning 84 semitones: either as 12 fifths,…

### 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…