## Tuning as an approximation

Previously, we said that the notes written on the staff were approximations of the pitches of the harmonics. But what kind of sense does that make? Intervals and ratios Let’s look at the picture we had indicating harmonics, their frequency … Continue reading

## Overtones and harmonics

We have discussed the circle of fifths as a way in which the various pitches, major keys, and minor keys can all be arranged in a circle. But certainly there must be something else special about the interval of a … Continue reading

## Key signatures

Understanding key signatures Once you have the major keys arranged in the circle of fifths, and you know why they only go around the circle seven steps either way, so they have up to seven flats or seven sharps, it’s … Continue reading

## Notes on the staff

The time has finally come to show some notes on a musical staff. The scheme is rather straightforward. The notes on the staff follow the white keys on the piano keyboard. Each successive white key goes up half of a … Continue reading

## More about the Circle of Fifths

Now we can explain why the circle of fifths looks the way it does. Recall that we had an ambiguous area from 5 o’clock to 7 o’clock: We’re going to examine the circle of fifths in terms of major scales. To … Continue reading

## The Circle of Fifths

A review Previously we discussed a clock in which the numbers going clockwise from the 12 o’clock position went up by sevens. Of course, we want to keep the numbers between 1 and 12, so when the number gets larger … Continue reading

## Half steps and clocks

Up to six hours at a time Suppose I have a clock and it reads 12 o’clock. If I set the clock forward one hour, then it will say 1 o’clock. If I do it again, the clock will say 2 … Continue reading

## Intervals fully named

Previously we named intervals using the numeric portion of their names, and we introduced scientific pitch notation. Now we’re going to finish the job by using the full designation of each interval. To make sense of what follows, you’ll need to know … Continue reading