#Harmonic series series
The figure shows the harmonic series as a, 2a, 3a, 4a, and 5a produced by vibrational modes of a string. Considering the system, the fundamental frequency ‘a’ at which the nodes are not oscillating while the center with maximum amplitude called the antinode is oscillating. The frequencies that are an integral multiple of the fundamental frequency f 1 f 4 . The frequencies at which the instruments create this pattern are known as harmonics, and the sequence of such frequencies is known as a harmonic series. The lowest among all is known as the fundamental frequency.ĭifferent standing wave patterns or vibrational nodes are produced by different instruments, based on natural frequencies. There may be several such frequencies for any particular object for the occurrence of this phenomenon. It can also be stated that this is the frequency that causes any object to vibrate, resulting in a standing wave pattern. The natural frequency at which any object vibrates is known as its resonant frequency. These waves produce nodes (where the waves cancel each other out) and their antinodes. In such instruments, standing waves travel one from end to another at numerous nodes. Some musical instruments are based on the vibration of the strings and the air column. This is a great opportunity for composers (including yourself!) to get creative.Sound waves are characterized by some parameters, such as frequency, amplitude, and pitch. In general, any combination of triads and seventh chords (in root position or inversion) are possible in a sequence provided that the chords are voiced in a way that does not break part-writing rules. We can also write many of the harmonic sequences to include triads in inversion, 7th chords, and/or 7th chords in inversion! When sequences are comprised of all seventh chords, they are called sequences with INTERLOCKING SEVENTHS and when the sequence alternates between triads (usually odd chords) and seventh chords (usually even chords), they are called sequences with ALTERNATING SEVENTHS. With all of the sequences above, the “even” chords (second chord of the model) are usually serving as a VOICE-LEADING CHORD or helping chord which is a chord that does not serve a strong harmonic function by itself, but rather, supports ease of writing with good voice-leading by avoiding parallel fifths, octaves, and other problems that would arise if the “odd” chords (first chord of the model and copy) were consecutive. (/In parentheses) the direction and distance between the second chord of the model and first chord of the copy + for ascending, - for descending, and a number representing the interval moved in that direction (In parentheses) the direction and distance between the starting chord of the model and the second chord it moves to The direction and distance between the starting chord of the model and each new copyĪ for ascending, D for descending, and a number representing the interval moved in that direction To define an entire sequence, we use three reference points: The original pattern (again, usually two chords) is referred to as the MODEL and the replication of the model pattern starting on a new diatonic chord (on a new scale degree) is called the COPY. Most sequences start with a two chord pattern that is then replicated starting on another chord a certain distance from the opening chord. To save time, it’s faster to refer to a sequence by its chord-relationship function rather than writing out every chord term of the sequence. These progressions are called HARMONIC SEQUENCES. We can also go one step further to create more rigid patterns of chords that are not only predictable but mathematically precise in what chord comes next. To achieve a more “pleasant” harmonic development, we place these chords in their intended areas in each phrase (Tonic, Predominant, Dominant).
If we were to throw random diatonic chords into a piece one after another, there would be a lack of structure and predictability that would sound bewildering. Harmony as Pattern …īy now, you (hopefully) agree that in Western Classical tonal music, chords exist in a hierarchy of strength, color, and tonal areas. Short melodic ideas that recur in musical phrases or across a larger work are also referred to as MELODIC MOTIFS while recurring patterns of scale degrees (including displaced/transposed versions) are called MELODIC SEQUENCES. Most “pleasant,” “comfortable” melodies have some amount of predictability to them and the melody is built on patterns of recurring scale degrees or or intervals. Repetitive rhythms are referred to as RHYTHMIC MOTIFS or OSTINATO patterns.
Rhythms are presented in symmetrical blocks called “measures” or bars with consistent beats defined in the time signature.