Whole Tones and Semitones
a Pythagorean scale
The scale you see above was formed by harmonizing pitches at a 2:3 frequency ratio and then bringing them all within the span of a single ocatve (an octave is the interval between two frequencies at a 1:2 ratio.) Placing the tones in this order creates a new set of ratios between each note. In this scale, there are two.
- The first note (C) has a frequency of 260.740... Hz. The second note (D) has a frequency of 293.333... Hz. The ratio between these notes is 8:9. This relationship is called a whole tone or a whole step.
- The third note (E) has a frequency of 330 Hz. The ratio from the second note (D-293.333...) to the third note (E-330) is also 8:9. This is also a whole tone.
- Likewise when moving from the third note (E-330) to the fourth note (F♯-371.25.) The ratio between 330 and 371.25 is also 8:9, or a whole tone.
- The ratio between the fourth note (F♯-371.25) to the fifth note (G-391.111...), however, is different. The ratio between the frequencies of these notes is actually 243:256, which is called a semitone or half-step.
- If you do the math, you'll find that there is a whole step from the fifth note (G-391.111...) to the sixth note (A-440), and another whole step from there to the seventh note (B-495.) From there to the C-521.481... (an octave above the first note) is another semitone.
If all of that is too confusing, here are the important points:
Important Points
- the frequency of a sound is called its pitch
- the ratio between two frequencies is called an interval
- a 2:1 ratio is called an octave and a 2:3 ratio is called a dominant or fifth
- counting up in fifths and then bringing all the notes within an octave range creates a scale with two different intervals
- the big ones (an 8:9 ratio) are called whole steps or whole tones
- the little ones (a 243:256 ratio) are called half-steps or semitones
Assignment
- semitones and whole tones
- dominants
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