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…
