The Greek Pythagoras (570-495 BC), and his followers, were mathematicians and philosophers. The OCTAVE was so pleasing to hear they sought to find out why.

Any steady sound you hear is actually a collection of waves.

You hear a particular pitch because it is the FUNDAMENTAL. The ones you don’t hear are still there, but much less noticeable. A guitar player can pluck a string, then softly dampen it at some place along the fretboard and a HARMONIC note will be sounded. That’s because it was always there to begin with. The dampening had the effect of removing the lower pitches.

The faster the wave the higher the pitch.

The OCTAVE interval has one pitch that is twice as fast as the first, or 2:1.That is it’s RATIO.

All the INTERVALS in the DIATONIC scale have easy to understand ratios.

When you turn the tuning peg of a guitar, or violin, the string is tightened, or loosened. The tighter the string the higher the pitch. The looser the string, the lower the pitch.

People are able to sense when a series of notes are in tune. Much of that ability is due to a natural phenomena called the OVERTONE SERIES.

They sound almost the same.

Pleasing sounds are CONSONANT.

Harsh sounds are DISSONANT.

Another consonant sound is the INTERVAL of a Fifth.

Above you see F is 1, or the Tonic. The 5th above F is C. Together they sound an INTERVAL called a PERFECT FIFTH. Along with the OCTAVE, it is a very pleasing consonant sound and an important element of all Western Music.

The sound of INTERVALS are always the same- relative to the TONIC.

Learn the sounds of each interval.

For these examples we are using the intervals in relation to C as the Tonic, or 1.

C + C Unison sounds the same like 1 note

C-Db (C#) Minor 2nd

C-D Major 2nd

C-Eb (D#) Minor 3rd

C-E Major 3rd

C-F Perfect 4th

C-F# Diminished 5th (Tritone)

C-G Perfect 5th

C-Ab (G#) Minor 6th

C-A Major 6th

C-Bb Minor 7th

C-B Major 7th

C-C‘ Octave

The octave blends so well you may think it's only 1 note. That's because the ratio of the vibrations are 2-1.

When 2 notes have the same pitch they are ENHARMONIC.

The correct name of the note depends on the KEY that the note is in.

The KEY is the particular scale being used named after the first note of the scale.

If the KEY is one with sharps, then raise the note using a sharp. If the KEY is a flat key, then use a flat to lower the note.

The DIATONIC scale starting on C has no sharps, or flats. On paper, starting from Middle C, it’s line, space, line, space, line, space, line.

The Overtone Series

Any steady sound you hear is actually a collection of waves.

Nature has a truth it reveals to us in a collection of sounds that occur naturally whenever a pitch is created. It’s called the OVERTONE SERIES. It’s important for us to state this fact as it has much to do with the two important scales we will learn about.

You hear a particular pitch because it is the FUNDAMENTAL of the OVERTONE SERIES, i.e., the first pitch. The ones you don’t hear are still there, but much less noticeable. A guitar player can pluck a string, then softly dampen it at some place along the fretboard and a HARMONIC note will be sounded. That’s because it was always there to begin with. The dampening had the effect of removing the lower pitches.

Let’s say you play an F note on the piano and leave your finger down on it. The sound is a collection of pitches (vibrations) all at once! The most prominent pitch is the F that was struck, but within that there are these notes in ascending order: the next F above, the C following that F, the next F, the A above that, the F above that A.

There are several more, even ones you can’t hear. The assortment of different vibrations create the particular sound you hear. This is why an F on a trumpet will not sound like an F on a guitar- even though it’s the same pitch. The tone quality is called the TIMBRE (pronounced tam-ber).