The Jam Academy

Math Jams Academy: Jade Zabric Music School

MUSIC

What is sound? Vibrations in the air
What is music? Controlled or Manipulated Vibrations
What is pitch? Measured Vibrations

What is frequency? Number of revolutions per second of the vibration or Hertz (Hz)
Our Human ears can only hear a range of 20Hz – 20,000Hz

By measuring the frequencies and recognizing the patterns, Pythagoras discovered that a one repeats itself an octave higher every time the frequency is doubled.

If A = 220Hz, the next A = 440Hz, 880Hz and on.
Example: hold any string on any instrument at the halfway point and you will always hear one octave higher.

He then used division and fractions to discover the 12 tones between every octave.

There are tones from other cultures that go even further. They are divisions in between the tones that we use. But western music theory is based on these first 12 notes.

NOTES ON THE PIANO

C Left of 2 Black Notes
F Left of 3 Black Notes

Find all the C’s.
Find all the F’s.

Now find all the keys in between

C . D . E F . G . A . B C

Find D, A, E, B.

What are the Black keys?

To the Right (Up) of a Black Key is Sharp (#)
To the Left (down) of a Black Key is Flat (b)

C#/Db D#/Eb F#/Gb G#/Ab A#/Bb
C . D . E F . G . A . B C

The space between the notes is called a STEP
Half Step = 1 step
Whole Step = 2 steps

*notice there is only 1 step between the E and F notes and the B and C notes
C can also be called B# and B can also be called Cb
F can also be called E# and E can also be called Fb

There are 12 notes total that cycle over and over.
Each cycle is called an Octave.

NOTES ON THE GUITAR

From the Bottom/Low end, the notes on the strings are E A D G B E

Notes on the first 5 frets: (Each fret is one half step)
0pen | 1 | 2 | 3 | 4 | 5 |
1 E | F | F#/Gb | G | G#/Ab | A |
2 B | C | C#/Db | D | D#/Eb | E |
3 G | G#/Ab | A | A#/Bb | B | C |
4 D | D#/Eb | E | F | F#/Gb | G |
5 A | A#/Bb | B | C | C#/Db | D |
6 E | F | F#/Gb | G | G#/Ab | A |

Notes without sharps or flats
0pen | 1 | 2 | 3 | 4 | 5 |
1 E | F | | G | | A |
2 B | C | | D | | E |
3 G | | A | | B | C |
4 D | | E | F | G |
5 A | | B | C | | D |
6 E | F | | G | | A |

*notice that the 5th Fret notes is the same as the open note on the next string up
This is true for all strings except the G to B String. Instead, the 4th Fret on the G String is B which is the next string.

This is how you tune the guitar! Listen to the notes very closely as you play them together and you will hear the revolutions out of tune. If the revolutions sound fast, that is bad. You want them to slow down all the way to playing in sync with each.
Hearing this will come in time. You should still use a tuner to help you tune your guitar.

To start, go string by string and memorize the natural notes on the first 3 frets:
0pen | 1 | 2 | 3 |
1 E | F | | G |

2 B | C | | D |

Songs to play on the first two strings:
Ode to Joy
Mary had a Little Lamb

Add the 3rd string
3 G | | A | |

Songs to play on the first 3 strings:
Happy Birthday

4 D | | E | F |

5 A | | B | C |
6 E | F | | G |

SCALES

What is a scale? A pattern of whole steps and half steps

The Pattern of the Major Scale is:
W W H W W W H

You can apply this pattern starting on any note and it will sound like a major scale.
The notes are the same as the Solfedge tones: Do Re Mi Fa Sol La Ti Do

If you start the pattern on C, you will get all the natural notes, (white keys)

W W H W W W H
Do RE Mi Fa Sol La Ti Do
C . D . E F . G . A . B C

If you start the pattern a different note, you will get a mix of black and white keys:

W W H W W W H
G . A . B C . D . E . F# G
F . G . A Bb . C . D . E F

We’ll just focus on C Major for now.

W W H W W W H
C . D . E F . G . A . B C
1 2 3 4 5 6 7 8/1

The numbers underneath the notes are the Degree of the scale.
So, if I say play the 1st note in the C maj scale, you play C.
The 2nd note of the C Major Scale is D.
What is the 3rd note? What is the 5th note? 6th, 7th, 4th, 8th?

INTERVALS

An interval is the amount of space between two notes by the degree.
To find the space, count the number of letter names between the notes

m2 = minor 2nd C Db 1 half-step
M2 = major 2nd C D 2 half-steps
m3 = minor 3rd C Eb 3 half-steps
M3 = Major 3rd C E 4 half-steps
P4 = Perfect 4th C F 5 half-steps
A4 = Augmented 4th C F# 6 half-steps
D5 = Diminished 5th C Gb 6 half-steps
P5 =

CHORDS

What is a chord? 2 or more notes played together
The most common chords are triads (3 notes: 1 3 5)
So to make up the C Major Chord = C E G

Here are the triads in the C Major Scale:

C . D . E F . G . A . B C . D . E F . G . A . B C
1 2 3 4 5 6 7 1 2 3 4 5 6 7 1

C . . . E . . G

D . . F . . . A

E . . G . . . B

F . . . A . . C

G . . . B . . D

A . . C . . . E

B . . D . . F

Here are the Triads spaced out by step:

C . . . E . . G
D . . F . . . A
E . . G . . . B
F . . . A . . C
G . . . B . . D
A . . C . . . E
B . . D . . F

Just like the scales, chords can be thought of as a pattern of steps.

2W 1 ½W = 4HS 3HS
C . . . E . . G C . . . E . . G

Which other chords in C Major Scale have the 4 half step/3 half-step combo?

2W 1 ½W
C . . . E . . G
F . . . A . . C
G . . . B . . D

C F and G are the 1 4 and 5 chords and they are Major.

What about the other triads in the C Major Scale?