1. Lab 7: Musical Scales The Just Scale The Tempered Scale Transposition
Tuning Triads
Sensitivity to Tuning
The Black Keys of the Keyboard
The Missing Black Keys
Problems With the Just Scale
The Tempered Scale
Transposition
Major Scale
Minor Scale

2. Notation for specific tones: C4 G4 E5 …
Standard frequency of middle A: f (A4) = 440 Hz (or 442 Hz)
Note: the standard frequency to be used in this lab is f (C) = 240 Hz.

3. Musical interval – characterized by the ratio of two frequencies
Name Just Interval
Octave 2
Fifth 3/2
Fourth 4/3
Major Third 5/4
Minor Third 6/5
Name Musical Interval
Second 9/8 (Dissonant)
The simple-number frequency ratios are consonant (“in harmony”) because
“for these special ratios the various partials of the two tones being played together either coincide exactly or are so different as to avoid beats or roughness.” (textbook)
Note: each key on our keyboard generates a pure tone – no higher harmonics.

4. Just Scale – constructed from three major triadsG A B
Just Scale – constructed from three major triads
C-E-G, G-B-D' and F-A-C'
Major Triad – a combination of three tones (chord) with frequency ratio of 4:5:6.
For example, f (C): f (E): f (G) = 4:5:6
If f (C) = 240 Hz,

5. Tempered Scale
Divides each octave into 12 identical semitone intervals. The ratio of frequencies of adjacent keys, x, is the same — equal intervals.
For example, if f (C) = 240 Hz,
The ratio becomes 2 when x is multiplied by itself 12 times or x12 = 2

6. Transposition Large interval = Whole-tone (1) intervalC D E F G A B
Transposition
Large interval = Whole-tone (1) interval
Small interval = Half-tone (½) (or semitone) interval
Major Scale (e.g. C-Major)
C D E F G A B C'
1 1 ½ ½
G-Major
G A B C' D' E' F' G'
F'#
Minor Scale (e.g. A-Minor)
A B C' D' E' F' G' A'
1 ½ ½ 1 1
D-Minor
D E F G A B C' D' Bb
In music, the same letter is used only once as a rule.