Interval
From DNBWiki
An interval is the difference in pitch between two tones. It is frequently expressed in terms of semitones and is defined by the frequency ratio between the two notes.
[edit] Common Interval Names
Below is a list of common interval names and their natural and equal tempered frequency ratios.
| Interval Name | No. of semitones | Natural Frequency Ratio | Equal Tempered Ratio |
|---|---|---|---|
| Semitone | 1 | N/A | 2^(1/12) = 1.059 (4SF) |
| Tone/Whole Tone | 2 | 8/9 = 1.125 | 2^(2/12) = 1.091 (4SF) |
| Minor Third | 3 | 6/5 = 1.2 | 2^(3/12) = 1.189 (4SF) |
| Major Third | 4 | 5/4 = 1.25 | 2^(4/12) = 1.260 (4SF) |
| Perfect Fourth | 5 | 4/3 = 1.33(3SF) | 2^(5/12) = 1.335 (4SF) |
| Augmented Fourth/Diminished Fifth | 6 | N/A | 2^(6/12) = 1.414(4SF) |
| Perfect Fifth | 7 | 3/2 = 1.5 | 2^(7/12) = 1.498 (4SF) |
| Minor Sixth | 8 | 8/5 = 1.6 | 2^(8/12) = 1.587 (4SF) |
| Major Sixth | 9 | 5/3 = 1.667 (4SF) | 2^(9/12) = 1.682 (4SF) |
| Minor Seventh | 10 | 7/4 = 1.75 (4SF) | 2^(10/12) = 1.782 (4SF) |
| Major Seventh | 11 | N/A | 2^(11/12) = 1.888 (4SF) |
| Octave | 12 | 2 | 2 |
The natural intervals can be made using harmonics on a string or similar. They can all be expressed as whole number fractions. The equal tempered intervals are commonly used to tune instruments of fixed pitch particularly keyboard instruments. It should be noted that the equal tempered intervals while quite close, are not identical to the pure harmonic intervals. Consequently, the equal tempered intervals tend to sound impure because they are not perfectly 'in tune' with each other.
The author has decided not to include values of natural intervals for the semitone, augmented fourth/diminished fifth, and major seventh intervals in this table, because he finds it difficult to choose definitive simple ratios for these intervals. The Augmented Fourth/Diminished Fifth could probably be represented by the ratio 7/5. There are several intervals in the harmonic harmonic series that could be considered a semitone, of which the author would probably choose 17/16. Similarly, 15/8 would be a good interval for the major seventh. If a future editor of this page agrees they may like to add these values to the table.
