Musics and Musical Instruments
Musical Scales
Pythagoras (1200 B.C.) found:
| 2 strings | [1 twice the length of the other] | octave |
|---|---|---|
|
2 strings
|
[length ratio 3/2] | fifth |
|
2 strings
|
[length ratio 4/3] | fourth |
Going up a `fifth' each time he could get a whole musical scale.
One octave : from A --> A --> A
A B C D E F G A B C D E F G A B C D E F G . . . One fifth : C --> G --> D --> A --> ...
Eventually, one comes back to same note.
C . . . . ---> C
This is known of the "circle of fifths" (used in jazz)
Pythagorean Scale
NOTwhat we use today
Example:
| 220 Hz | ||
| = | fundamental | |
| 440 Hz | = | 1 octave |
| 660 Hz | = | a "fifth" above 440 Hz |
| 660 Hz | = | 440 * 3/2 |
a fifth higher than 220 Hz: 220 * 3/2 = 330 Hza third higher than 220 Hz: 220 * 5/4 = 275 Hz
played at once => major chord
Musical Intervals
| Interval | frequency | 1. Pair of matching harmony |
|---|---|---|
| Unison | f 1 ; f 2 = f 1 | f 1 with f 2 |
| Octave | f 1 ; f 2 = 2f 1 | f 2 with 2f 1 |
| Fifth | f 1 ; f 2 = 3/2 f 1 | 2f 2 with 3f 1 |
| Fourth | f 1 ; f 2 = 4/3 f 1 | 3f 2 with 4f 1 |
| Third (major) | f 1 ; f 2 = 5/4 f 1 | 4f 2 with 5f 1 |
| Whole tone | f 1 ; f 2 = 1.123 f 1 | no match |
| Semitone | f 1 ; f 2 = 1.0595 f 1 | no match |
The Just Scale was created to fix this
- make a major chord above
- make a major chord below
- continue until all notes are found
Problem:
has different sizes whole steps
Fix:
Smooth out using the
Equal Tempered Scale
Aug 26 14:27:03 EDT 2019