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The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third harmonic (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher). An illustration in musical notation of the harmonic series (on C) up to the 20th harmonic.
The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor.
4th harmonic In many musical instruments , it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder ) this has the effect of making the note go up in pitch by an octave , but in more complex cases many other pitch variations are obtained.
To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its top note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals.
Harmonic series, partials 1–5 numbered. In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval.
The harmonic series is the infinite series = = + + + + + in which the terms are all of the positive unit fractions. It is a divergent series : as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
By the fourth octave of the harmonic series, successive harmonics form increasingly small seconds the fifth octave of harmonics (16–32) Tone clusters have generally been thought of as dissonant musical textures, and even defined as such. [5]
Horn notation is a complex subject beyond the scope of this article, but what is written as middle C for the horn is the fourth harmonic of the unlengthened instrument, not the second. Horn music makes greater use of the higher range of the harmonic series than do most other modern brass instruments.