Tuning a keyboard instrument.
Posted: 14 Apr 2023 16:16
I'm sure that all of us who play keyboards are aware that the notes we play have certain 'frequencies', and the frequencies form the melodies and harmonies of what we hear. When tuning an orchestra, the note the various instruments are tuned to is A = 440Hz, and our keyboards are set to A = 440Hz so we are 'in tune' with everybody else.
An 'octave' (eg. C to top C) is split into 12 'steps up' which gives us our white and black notes. But I wonder how many of us are aware of how these notes are related to each other mathematically, and how we have ended up with these 12 'intervals'? Our keyboard notes are tuned to what is called 'Equal Temperament', but looking back at the history of music and the early composers, the mathematics of how we hear music has been a nightmare for them. Pythagoras was the first person to analyse the relationship between the frequencies of the various notes and work out a 'tuning system' for them. His system sounded fine so long as you played everything in the one basic key, but sounded all 'out of tune' if you tried changing key or playing harmonies that were not the simple harmonies of the key you were playing in.
So put your mathematical hat on, make sure you have half an hour to spare, and take a look at this. It's fascinating!
The Mathematical Problem with Music, and How to Solve It
An 'octave' (eg. C to top C) is split into 12 'steps up' which gives us our white and black notes. But I wonder how many of us are aware of how these notes are related to each other mathematically, and how we have ended up with these 12 'intervals'? Our keyboard notes are tuned to what is called 'Equal Temperament', but looking back at the history of music and the early composers, the mathematics of how we hear music has been a nightmare for them. Pythagoras was the first person to analyse the relationship between the frequencies of the various notes and work out a 'tuning system' for them. His system sounded fine so long as you played everything in the one basic key, but sounded all 'out of tune' if you tried changing key or playing harmonies that were not the simple harmonies of the key you were playing in.
So put your mathematical hat on, make sure you have half an hour to spare, and take a look at this. It's fascinating!
The Mathematical Problem with Music, and How to Solve It