Introduction to Music Theory: Pitch, Scales, Chords, and Notation

Pitch, Frequencies, and Sound Wave Dynamics

• Frequency: Measured in Hertz ($\text{Hz}$), frequency represents the number of cycles per second generated by a sound wave. It directly determines the pitch of a sound.

• Pitch Dynamics and Octave Relationships:

  • Doubling a frequency raises the resulting pitch by exactly one octave.

  • Halving a frequency lowers the resulting pitch by exactly one octave.

  • Sequential halving of frequency demonstrates octave drops:

  • $440\,\text{Hz}$

  • $220\,\text{Hz}$

  • $110\,\text{Hz}$

  • $55\,\text{Hz}$

  • $22.5\,\text{Hz}$ (or $22\frac{1}{2}\,\text{cycles per second}$)

  • Extremely low frequencies, such as $22.5\,\text{Hz}$, produce slow sound waves where the physical pulsations ("womp, womp, womp") become distinctly perceptible.

• Physical Bottle Analogy for Pitch and Frequency:

  • Blowing air across the top of a bottle filled with water illustrates how frequency creates pitch.

  • Adding more water decreases the volume of air remaining in the bottle.

  • Blowing into a bottle with less air space creates faster cycles per second ($\text{Hz}$), which results in a higher pitch.

Musical Intervals, Solfege, and Pitch Naming

• Musical Intervals:

  • An interval is defined as the exact distance between two musical notes.

  • Counting Rule for Intervals: The bottom (starting) note must always be counted as $1$. Failing to count the bottom note as $1$ results in calculation errors off by one step.

  • Interval designations measured upward from the note C:

  • C to D: Interval of a second ($2^{\text{nd}}$).

  • C to E: Interval of a third ($3^{\text{rd}}$).

  • C to G: Interval of a fifth ($5^{\text{th}}$).

  • C to A: Interval of a sixth ($6^{\text{th}}$).

  • C to B: Interval of a seventh ($7^{\text{th}}$).

  • C to C (higher octave): An octave ($8^{\text{th}}$).

• Unison vs. Octave:

  • Unison: Occurs when multiple performers sing or play the exact same pitch at the exact same frequency level simultaneously.

  • Octave: Occurs when performers sing or play the same pitch name but at different frequency levels (e.g., one performer at $220\,\text{Hz}$ and another at $440\,\text{Hz}$).

• Solfege Syllables and Formal Technical Pitch Names:

  • Solfege utilizes hand signs and vocal syllables ($Do, Re, Mi, Fa, Sol, La, Ti, Do$) to represent scale steps.

  • Standard musical terms corresponding to solfege syllables:

  • $1^{\text{st}}$ Scale Degree ($Do$): Tonic

  • $2^{\text{nd}}$ Scale Degree ($Re$): Supertonic

  • $3^{\text{rd}}$ Scale Degree ($Mi$): Mediant

  • $4^{\text{th}}$ Scale Degree ($Fa$): Subdominant

  • $5^{\text{th}}$ Scale Degree ($Sol$): Dominant

  • $6^{\text{th}}$ Scale Degree ($La$): Submediant

  • $7^{\text{th}}$ Scale Degree ($Ti$): Leading Tone

  • $8^{\text{th}}$ Scale Degree ($Do$): Tonic (Octave higher)

• Function of the Leading Tone:

  • The interval of the seventh ($7^{\text{th}}$) scale degree ($Ti$) is termed the "leading tone" because its acoustic proximity creates melodic tension that naturally pulls or leads back home to the tonic ($Do$).

Chords, Triads, Harmony, and Key Signatures

• Chords and Triads:

  • The terms chord and triad are often used interchangeably, though complex musical styles like jazz feature chords with more than three notes.

  • The prefix tri- means three ($3$).

  • A triad is a three-note chord played simultaneously (at the exact same time).

  • Standard triads are constructed using stacked intervals of a third ($3^{\text{rd}}$). For example, a C major triad consists of C, E, and G ($C-E-G$).

  • Musical works such as "Lean on Me" build their primary accompaniment strictly using triads.

• Harmony:

  • Harmony consists of secondary pitches played or sung alongside a main melody.

  • Formed by selecting additional notes from the supporting triad that complement the primary melody, adding rhythm, color, and musical depth.

• Modulation:

  • Modulation is the act of changing keys within the middle of a piece of music, transitioning from the original key to a new key.

  • Frequently observed in traditional Baptist hymn singing traditions, where key shifts occur mid-song.

• Keys and Key Signatures:

  • A key establishes the note range, tonal foundation, tonic note, tonic triad, and active scale of a composition.

  • Key Signature Placement: Positioned directly after the clef signs at the beginning of a musical staff.

  • Formatted using sharp symbols ($\sharp$), flat symbols ($\flat$), or no symbols ($0$ sharps, $0$ flats).

  • $0$ sharps and $0$ flats designates the key of C Major.

  • $2$ sharps designates the key of D Major.

  • $6$ sharps designates the key of C-sharp ($C\sharp$) Major, making $C\sharp$ the tonic note ($Do$).

  • Twofold Purpose of Key Signatures:

  1. Identifies the key, tonic note, tonic triad, and operational scale for the performer.

  2. Saves time and printing ink by establishing global accidentals, removing the need to write individual sharp or flat symbols in front of every single note throughout the manuscript (e.g., a sharp on the F line means all F notes are played as $F\sharp$ unless overridden by a natural accidental $\natural$).

Types of Scales, Tonal Patterns, and Consonance vs. Dissonance

• Scale Structure:

  • A scale consists of $7$ distinct notes plus an $8^{\text{th}}$ octave note ($7 + 1 = 8$ notes total).

  • Diatonic Step Formula for Major Scales:     $\text{Tonic} \rightarrow \text{Whole Step} \rightarrow \text{Whole Step} \rightarrow \text{Half Step} \rightarrow \text{Whole Step} \rightarrow \text{Whole Step} \rightarrow \text{Whole Step (Leading Tone)} \rightarrow \text{Half Step (Tonic)}$

  • The final half step between the leading tone and the octave tonic provides harmonic resolution.

• Scale Variations Throughout Music History:

  • Major Scale: Associated with bright or "happy" tonal qualities.

  • Minor Scale: Associated with somber or "sad" tonal qualities.

  • Major and Minor scales represent the two primary scale structures that survived history to become standard norms in Western music.

  • Whole Tone Scale: A scale constructed entirely of whole-step intervals.

  • Chromatic Scale: A scale constructed entirely of consecutive half-step intervals, used to add tonal color within a piece rather than as a core structural foundation.

  • Blues Scale: A stylized scale incorporating altered pitch degrees.

  • Atonal: Music lacking a central home pitch, key center, or scale system.

  • Pentatonic Scale:

  • The prefix penta- means five ($5$).

  • A five-note scale.

  • Can be demonstrated visually by playing only the five black keys on a piano.

  • The traditional hymn "Amazing Grace" is composed entirely on a pentatonic scale.

• Consonance vs. Dissonance:

  • Consonance: Harmonic combinations that sound easy, free, smooth, and resolved, producing no angst or tension.

  • Dissonance: Harmonic combinations designed to create auditory tension, edge, and angst.

Musical Symbols: Slurs, Ties, Legato, and Accents

• General vs. Precise Expressive Directives:

  • Legato: A general Italian term written at the beginning of a musical section directing the performer to play smoothly and connectedly.

• Curved Line Markings: Slurs vs. Ties:

  • Slur:

  • A curved line connecting two or more different notes.

  • Indicates that those specific, localized notes must be played smoothly and connectedly (legato).

  • Tie:

  • A curved line connecting two of the exact same pitch.

  • Directs the performer to sound the first note and hold it continuously for the combined duration of both notes without re-articulating the second.

  • Frequently used across measure bar lines or when surrounding parameters above the notes change while the pitch sustains.

• Accents:

  • Symbols used by composers to alter note attacks, add drama, stress, or expressive flavor.

  • Tenuto: Represented by a straight horizontal line over or under a note, directing the performer to apply a heavy, plotting weight or stress.

  • Other accent symbols range from light stress for pitch definition to extreme heavy stress.

Tempo, Metronomes, and Speed Measurement

• Tempo:

  • Tempo is defined strictly as the rate of speed of a piece of music.

• Metronome Development and Functionality:

  • Traditional Mechanical Metronomes: Old wind-up models with removable lids. They often ticked unevenly unless propped up sideways on their lids.

  • Electric Metronomes (such as those produced by Franz): Powered electrically to maintain steady timing and produce high volume output capable of being heard over practicing instruments.

  • Digital/Mobile Applications: Modern software metronomes are accessible on mobile phones, but frequently suffer from low volume ceilings and unnecessary auxiliary features (such as drum or triangle sounds) that obscure the fundamental beat.

• Standard Metronome Markings:

  • Standard metronome speeds range from $40\,\text{BPM}$ to $208\,\text{BPM}$ (beats per minute).

  • $40\,\text{BPM}$: Represents an extremely slow tempo.

  • $120\,\text{BPM}$: Represents standard march tempo.

  • $208\,\text{BPM}$: Represents an extremely fast tempo.