Comprehensive Notes on Music Theory: Sound, Semiography, Intervals, Chords, and Rhythmic Systems

The Fundamentals of Musical Sound and its Qualities

Musical sound is defined as a sonic phenomenon produced by the regular and periodic vibrations of a sounding body. Unlike noise, which consists of irregular vibrations, musical sound possesses four fundamental qualities that characterize it: pitch, duration, intensity, and timbre.

Pitch represents the degree of acuteness or gravity of a sound. This quality depends entirely on the frequency of the vibrations. A high frequency results in an acute (high-pitched) sound, while a low frequency results in a grave (low-pitched) sound. The second quality, duration, represents the amount of time a sound is heard and is visually represented in musical notation through note values.

Intensity represents the force with which a sound is heard. It depends on the amplitude of the vibrations; a large amplitude creates a strong (loud) sound, while a small amplitude creates a weak (soft) sound. In music, these variations in intensity are called nuances, with common terms being ‘piano’ (soft) and ‘forte’ (strong). Finally, timbre is the color or character of the sound that helps the listener recognize its source. It is the quality that allows us to distinguish between two different instruments or voices even when they emit the same note at the same intensity.

Traditional and Modern Musical Semiography

Musical semiography is the system of signs and symbols through which music is written and read. It is divided into traditional and modern approaches. Traditional semiography includes the standard elements of music theory: the staff (portative), musical clefs, notes, note values, rests, accidentals (alterations), measure and tact (beat), and expression indications.

Modern semiography utilizes non-conventional notation to suggest specific sound effects. This includes the use of lines, dots, geometric figures, arrows, and various graphic symbols. Modern scores often come with a legend to explain these symbols. Key aspects of modern semiography include graphic notation, where music is represented through drawings and symbols giving the performer greater freedom; proportional notation, where duration is indicated by spatial distances rather than fixed symbols; and special symbols for techniques such as noises, instrumental effects, or strikes upon the instrument. A significant concept in modern music is aleatoricism, where certain elements of the music are left to the choice or chance of the performer.

Musical Intervals: Classification and Quality

A musical interval represents the distance between two sounds. Intervals are classified based on several criteria. By execution, an interval can be melodic (sounds played successively) or harmonic (sounds played simultaneously). By the number of steps they span, intervals are divided into simple intervals (prima/first, second, third, fourth/cuanta, fifth/cuinta, sixth, seventh, octave) and compound intervals (ninth/nona, tenth/decima, eleventh/undecima).

Intervals are also classified by quality. Perfect intervals include the Prima ($Do - Do$), Fourth ($Do - Fa$), Fifth ($Do - Sol$), and Octave ($Do - Do_2$). Major and minor intervals include the Second (Major: $Do - Re$ - full tone; minor: $Mi - Fa$ - semitone), the Third (Major: $Do - Mi$ - 2 tones; minor: $Re - Fa$ - 1 tone + 1 semitone), the Sixth (Major: $Do - La$ - 3 tones + 2 semitones; minor: $Mi - Do$), and the Seventh (Major: $Do - Si$; minor: $Re - Do$).

Intervals can also be augmented or diminished by a semitone ($+/-$). Examples include an augmented prima ($Do - Do\#$), a diminished prima ($Do - Do\flat$), an augmented second ($Do - Re\#$), and a diminished second ($Do - Re\flat\flat$). This pattern continues through thirds (Augmented: $Do - Mi\#$, Diminished: $Do - Mi\flat\flat$), fourths (Augmented: $Do - Fa\#$, Diminished: $Do - Fa\flat$), fifths (Augmented: $Do - Sol\#$, Diminished: $Do - Sol\flat$), sixths (Augmented: $Do - La\#$, Diminished: $Do - La\flat\flat$), sevenths (Augmented: $Do - Si\#$, Diminished: $Do - Si\flat\flat$), and octaves (Augmented: $Do - Do\#$, Diminished: $Do - Do\flat$).

Beyond technical classification, intervals are categorized by their sonic effect into consonant intervals (thirds, fifths, sixths, and octaves) and dissonant intervals (seconds and sevenths). A specific dissonant interval is the Triton, which contains exactly three tones; its forms appear as an augmented fourth or a diminished fifth.

Chords of Three and Four Sounds

A chord is a group of at least three different sounds heard simultaneously, typically constructed by stacking thirds. Chords of three sounds are called Triads (Trison), consisting of the fundamental (root), the third, and the fifth. By interval structure, triads are classified as Major ($3M + 3m$, e.g., $Do - Mi - Sol$), minor ($3m + 3M$, e.g., $La - Do - Mi$), Augmented ($3M + 3M$, e.g., $Do - Mi - Sol\#$), or Diminished ($3m + 3m$, e.g., $Si - Re - Fa$).

Triads change based on the position of the sounds. In direct state (root position), the fundamental is in the bass ($Do - Mi - Sol$). In the 1st inversion (sexta-chord), the third becomes the lowest sound ($Mi - Sol - Do$). In the 2nd inversion (cuant-sextacord), the fifth becomes the lowest sound ($Sol - Do - Mi$).

Chords of four sounds are called Sevenths (Septacord), consisting of a fundamental, third, fifth, and seventh. They are classified by structure: Diminished seventh ($3m + 3m + 3m$; e.g., $Si - Re - Fa - La\flat$), Half-diminished seventh ($3m + 3m + 3M$; e.g., $Si - Re - Fa - La$), Major-Major seventh ($3M + 3m + 3M$; e.g., $Do - Mi - Sol - Si$), Dominant/Major-minor seventh ($3M + 3m + 3m$; e.g., $Sol - Si - Re - Fa$), minor-Major seventh ($3m + 3M + 3M$; e.g., $La - Do - Mi - Sol\#$), and minor-minor seventh ($3m + 3M + 3m$; e.g., $La - Do - Mi - Sol$).

Seventh chords also have inversions: direct state ($Sol - Si - Re - Fa$), 1st inversion/quint-sextacord ($Si - Re - Fa - Sol$), 2nd inversion/terti-cuantacord ($Re - Fa - Sol - Si$), and 3rd inversion/secund-acord ($Fa - Sol - Si - Re$).

Rhythm and Meter in Music

Rhythm is the organization of sounds and rests in time, providing movement and order to music. Its elements include duration (how long a sound lasts), accent (highlighting one sound over others), rest (moments of silence), and tempo (the speed of the music). Meter, on the other hand, is the regular organization of accented and unaccented beats into equal groups called measures. Elements of meter include the pulse (regular beat felt in music), the beat (the basic unit of the measure), the metric accent (appearing periodically), and the measure (the grouping of beats between two bar lines, such as $\frac{2}{4}$, $\frac{3}{4}$, or $\frac{4}{4}$).

Meters are classified by the number of beats. Binary meter ($\frac{2}{4}$, $\frac{2}{2}$) follows a ‘strong - weak’ accent pattern, found in marches and polkas. Ternary meter ($\frac{3}{4}$, $\frac{3}{8}$) follows a ‘strong - weak - weak’ pattern, common in waltzes. Quaternary meter ($\frac{4}{4}$) follows a ‘strong - weak - strong - weak’ pattern. Internally, meters are classified as simple ($\frac{2}{4}, \frac{3}{4}, \frac{4}{4}$) or compound ($\frac{6}{8}, \frac{9}{8}, \frac{12}{8}$).

Rhythmic Systems and Cultural Variations

Rhythmic systems represent ways of organizing sound durations and rests. Five major types are noted: 1) The Proportional System, where values are divided mathematically; 2) The Giusto-syllabic System, characterized by a regular pulse, constant tempo, and one rhythmic value per syllable (found in Romanian colinde and hore); 3) The Parlando-rubato System, which features a free rhythm close to speech, a flexible tempo, and no strict pulse (found in doina and funeral laments/bocet); 4) Th e Aksak System, which is an asymmetric rhythm alternating binary and ternary groups (common in Romanian folklore); and 5) The Polyrhythmic System, involving the superposition of multiple different rhythms (common in jazz).

Different musical cultures exhibit distinct metro-rhythmic systems. The European system uses regular rhythms, fixed measures, stable accents, and precise mathematical organization (e.g., Strauss's ‘Blue Danube’ or Beethoven's ‘Ode to Joy’). The Byzantine system, used in religious music, features a free rhythm without strict measures, following the text and breath (e.g., ‘Prohodul Domnului’). The Romanian Folk system uses asymmetric rhythms and irregular combinations like $\frac{5}{8}, \frac{7}{8},$ or $\frac{9}{8}$ (found in Enescu's ‘Romanian Rhapsody No. 1’). Oriental systems (Indian, Arabic, Turkish) utilize very complex rhythmic formulas. In Indian music, this includes the ‘Tala’ (repetitive cyclic rhythm, such as Teental with 16 beats or Jhaptal with 10 beats), while Arabic/Turkish systems use ‘maul,’ based on regular successions of accents like Semai (6 beats) or Sofyan (4 beats). African systems are characterized by deep polyrhythms, while Jazz is defined by syncopation, swing, and rhythmic freedom.