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Suggested Reading

1. Rehearsal Rooms

Struggling to improve the acoustics in your band room? Check out how the Medan Band did it.

2. Concerned about playing swing music properly?

Check out my guidelines

3. Ear training exercises for bands

Unlike piano players, ear training is essential for wind band performers. But how many band directors bother to give their bands suitable exercises?

4. Intonation problems

While tuning is simple act of adjusting a length of tubing on a wind instrument (often by reference to a single note), intonation is an ongoing process in which a player strives to match the pitch of others in the ensemble during performance. 

5. “Blowing” a wind instrument

A common misconception among wind players is to believe that the air moves through the instrument in order to produce the sound. This is simply not true. 

6. Conducting – suggestions for home practice

The best way for a conductor to improve is in front of a live ensemble. The unfortunate reality, however, is that this is not always possible. Aspiring conductors therefore have little choice but to find other ways of honing their skills.

 

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Consonance and Dissonance

When two notes are played simultaneously, we hear the resulting sound as consonant or dissonant.  Consonant intervals are considered sweet and smooth, whereas dissonant intervals sound rough and harsh. Generally speaking, different pitches whose frequency multiples tend to reinforce each other are said to be consonant, whereas pitches whose frequency multiples clash are said to be dissonant.  In the case of the latter, the ear senses a regular swelling of sound or beating as the different frequencies go in and out of phase.

Throughout the various periods of musical history there has been a great deal of disagreement about which intervals are consonant and which are dissonant.  This is not particularly surprising since, from a physicist’s point of view, the difference is really one of degree rather than of kind.

 "Perfect" intervals were greatly favoured by Western composers in ancient and medieval times. 
Intervals with very simple mathematical ratios are called “perfect” consonances. The octave in particular sounds consonant because two waves in the upper note correspond exactly with one wave of the lower note, thus giving it a ratio of 2:1 [see the table on this page].  Other “perfect” intervals include the unison (1:1, i.e. the same note), the fifth (3:2 – i.e. three waves in the lower note equaling two waves in the lower note), and the fourth (4:3).  These intervals give the smoothest blend because the frequencies of the upper partials of their respective notes do not clash very noticeably. Such intervals were greatly favoured by Western composers in ancient and medieval times. To modern ears, however, they can sound hollow or even downright boring.

Since around 1250, major and minor thirds (5:4 and 6:5) together with major and minor sixths (5:3 and 8:5) have also been considered consonant.  They sound richer and sweeter than perfect fourths and fifths because there is some beating as well as some agreement between their lower harmonics.

 The twentieth century witnessed a considerable expansion of the range of intervals considered consonant. 
Dissonant intervals include the major second (9:8), the semitone or minor second (16:15), the minor seventh (16:9) and the major seventh (15:8).  The greater the numerator and the denominator of a fraction representing the ratio of vibrations between two sounds, the more acute the resulting dissonance.  This is why, for example, a minor second sounds harsher to the ears than a major second does.  That said, it is also true to say that the twentieth century witnessed a considerable expansion in the range of intervals that were considered consonant.  The fact that the ear can get used to dissonant intervals and treat them as consonant is proved by the way we now accept tonic seventh chords as forming legitimate cadences in jazz music.

Intervals and Frequency Ratios

Interval

Frequency Ratio Cents from staring point
Just intonation Equal Temperament
Unison 1:1 0 0
Semitone 16:15 111.731 100
Minor Second 10:9 182.404 100
Major Second 9:8 203.910 200
Minor Third 6:5 315.641 300
Major Third 5:4 386.314 400
Perfect Fourth 4:3 498..045 500
Augmented Fourth 45:32 590.224 600
Diminished Fifth 64:45 609.777 600
Perfect Fifth 3:2 701.955 700
Minor Sixth 8:5 813.687 800
Major Sixth 5:3 844.359 900
Harmonic Minor Seventh 7:4 968.826 1,000
Minor Seventh 9:5 1,017.597 1,000
Major Seventh 15:8 1,088.269 1,100
Octave 2:1 1,200.000 1,2

When reading this table, remember that "frequency ratio" refers to the number of waves in the upper note compared with the number of waves in the lower note. An octave, for example, has a ratio of 2:1. This means there are two waves in the upper note for every single wave in the lower note. If you are still confused, check out the section on the harmonic series. A "cent" is a convenient measure of the interval between any two notes. By definition, there are 1,200 cents in an octave. In the scale of equal temperament, a semitone therefore equals 100 cents.

The degree of dissonance actually heard can vary not only with the interval but also with the tone quality or timbre of the instruments involved. In some cases, the dissonance does not register very strongly because the clashing harmonics are either absent or of a very low amplitude. A dissonant interval played by two oboes, for example, will actually sound sweeter when played by two flutes. This is because the flute has a relatively "pure" sound with few partials, whereas the oboe produces a rich harmonic spectra.

 Unable to bear the unresolved dissonance, he jumped out of bed and played the appropriate resolution. 
For hundreds of years, audiences have been conditioned to believe that the sounding of a dissonant interval should be “resolved” by playing a consonant one.  In Bach’s time the urge to hear the resolution was particularly strong.  The story is told that one morning the great composer was awakened from his sleep by the sound of his second wife persistently playing a dominant seventh chord on the harpsichord in the music room.  Unable to bear the unresolved dissonance, he jumped out of bed, rushed to the harpsichord and played the appropriate resolution.

Reacting to the traditional rule of harmony that dissonance must be followed by consonance, some twentieth century composers such as Schoenberg went to the other extreme, creating works that glorified in the art of dissonance without using any consonance at all.  Nowadays, this approach has found a legitimate place in the music used for background effects in Hollywood-style movies [for example in creating atmosphere in horror movies]. The resulting cacophony of sound, however, rarely appeals to audiences in the concert hall.  If you do find yourself in charge of an advanced group of musicianswho wish to display their skills in this idiom at their next concert, I suggest you limit yourself to only one or two such pieces.   Asian audiences tend to have fairly conservative musical tastes.

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