### Approximating the sum of an infinite series (2)

Before we begin, some basic definitions. Suppose is a sequence that converges to a limit . We say that the…

### Approximating the sum of an infinite series

I started thing about this as I was preparing some material on the use of Matlab for teaching engineering mathematics…

### Typesetting music

Recently I’ve been typesetting a little music. My notational needs are simple: mostly single melodic lines, occasional chords or multiple…

### The derivative of sin(x)

We know that we can use the limit definition     to compute the derivative of “from first principles”. And…

### 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 (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…