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I.8

I.8

## Intervalla

intervals

From inter (between) and vallum (wall/rampart); intervallum = the open space between the walls.

The interval refers to the space or distance between notes.

If we sound A=220 and then A=440, the interval between the two notes is an octave.

If we sound A = 220 and then E = 330, the interval between the two notes is a fifth.

A - B - C - D - E

1  - 2  - 3  - 4  - 5

Intervals:

Unison

Second

Third

Fourth

Fifth

Sixth

Seventh

Octave

I.8

## Series Harmonica

harmonic series

The principal note sounded is called the fundamental note; it is also the lowest note of the series.

Within that principal note, the frequencies of the harmonic series are also vibrated.; i.e. more than one frequency is sounded by just one string.

While the string in this video vibrates at the fundamental frequency, it also produces the additional frequencies of the harmonic series. The initial notes of the series are the loudest as the amplitude (energy) diminishes with each additional step along the harmonic series.

These frequencies are SO SUBTLE that they sound like one note, the principal note. The "timbre" or richness of the note is actually the additional "overtone" frequencies of the harmonic series sounding along with the fundamental.

The first four steps or  "nodes" along the harmonic series are:

Octave

Fifth

Fourth

Harmonic Series A=55

Fourth (4:3)

3: A = 440

Fifth  (3:2)

2: E = 330

Double Octave (2:1)

1: A = 220

Fundamental

0: A= 55

I.8

## Intervalla Perfecta

Perfect Intervals

## ​

The first three intervals of the Harmonic Series are called the perfect intervals from their "cold" and "tight-fit" sound as compared to the "warm" sound of 3rds and 6ths,  and the "dissonant" sound of 2nds and 7ths.

The strongest principal overtones of a fundamental are the octave, fourth, and fifth.

## ​

The octave is created with a ratio of 2:1.

A = 220 | A = 110

The fourth is created with a frequency ratio of 4:3.

A = 440 | E = 330

The fifth is created with the frequency ration 3:2.

E = 330 | A = 220

To play a fifth above any pitch, the frequency of the fifth must be 3:2 of the original pitch's frequency.

To play a fifth above A=220, we must sound the frequency 330.

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## ​

5 note music created from perfect intervals; found by tuning in fifths.

C - G - D - A - E

and then transferring to the correct octave:

A C D E G A

Early scales are believed to only use five notes instead of seven or twelve.

This is not reflected in the harmonic series but rather derived from measuring perfect fifths from a given note.

Add a fifth above and below, than transfer to the correct octave.

F - C - G ~ C - F - G

continue

Bb - F - C - G - D

Pentatonic Scale :

Bb - C - D - F - G

two more fifths and we have:

Eb - Bb - F - C - G - D - A

Major Scale:

Bb - C - D - Eb - F - G - A bottom of page