Lecturer's aid

Usage examples of notes.

This invariance corresponds to the observation that notes separated by multiples of an octave have a similar subjective quality.

It explains in detail many of the familiar features of music: notes, scales, melody, harmony, chords, home chords, bass, rhythm and repetition.

It is an empirical fact that the listener to music can perceive chords as groups of notes played simultaneously, but can also perceive chords as groups of notes played sequentially.

For example, a musical note at 200Hz will have harmonics at 400Hz and 600Hz, and the ratio between these is 2:3, which corresponds to the harmonic interval that would exist between two notes with fundamental frequencies of 400Hz and 600Hz.

Why are notes separated by multiples of an octave perceived as having a similar quality?

Intervals between notes can be described as vectors and as certain fractional ratios between their frequencies.

The theory about the melody would be an explanation that described the notes in some way that was simpler and shorter than a full listing of the notes.

One form of harmony is chords: groups of notes related by consonant intervals.

It may be that the response to sequential notes is what actually matters and requires explanation in an evolutionary framework, and that the response to simultaneous notes is an accidental side-effect of the ability to respond to notes of a chord sequentially.

Why do melodies consist of notes with constant pitch values taken from scales, where a scale consists of a finite set of possible pitch values?

Why do the more strongly emphasised notes in the melody usually correspond to notes in the current chord?

That is, the differences between two pairs of notes are considered equal if the ratios are equal.

To give an example, the interval between two notes with frequencies 200Hz and 300Hz is perceived to be the same as the interval between 240Hz and 360Hz, since the ratio is 2 to 3 in both cases.

Two notes whose frequencies differ by a power of 2 are psychologically perceived to have a similar quality.

It follows that two notes related by a consonant interval will have some identical harmonics: for example the 3rd harmonic of a 400Hz sound is 1200Hz which is identical to the 2nd harmonic of a 600Hz sound.