Scales and Modes

A set of pitch classes forming a specific type of pitch collection.

Scales and Modes ​

A set of pitch classes forming a specific type of pitch collection.

7. Keys and Modes ​

7.1 Pitch Collections, Modes, and Scales ​

  • Key (Tonality): A set of pitch classes forming a specific type of pitch collection.
  • Pitch Collection (Звукоряд): A sequence of musical pitches ordered by height (ascending or descending). Individual pitches are called scale degrees (historically termed scala in European musicology).
  • Mode (Лад): Theoretical evolution of the concept:
  • 1937 (Yuri Tyulin): "A logically differentiated system unifying tones based on their functional relationships."
  • 1940s (Boris Asafyev): "The organization of tones in their interaction within the musical system of a given era."
  • 1978 (Tatyana Bershadskaya): "A pitch system of subordination based on logical (subordinative) differentiation of tones."
  • 1988 (Yuri Kholopov): "A system of pitch relationships unified by a central pitch or sonority, as well as the concrete musical system embodying this organization."
  • Scale (Гамма): The sequential execution/performance of pitches within a pitch collection.
  • Tonic: The central pitch and primary point of stability in a key.
  • Interval Collection: Raw intervals gain harmonic and melodic function only when evaluated within a modal context. Modern Scale & Key Analysis (Pitch Class Set Theory)
  1. Octave Equivalence: Pitches separated by octaves share the same pitch class identity.
  2. 12-Tone Equal Temperament (12-TET): Division of the octave into 12 equal semitones.
  3. Binary Code: A 12-bit binary string representing scale steps (0–11). For example, C Major (Ionian) is 100101001010.
  4. Decimal Code: Integer values from 0 to 4095 ($2^{12}-1$). Any of the 4,096 possible pitch collections can be identified by a unique decimal number.
  5. Interval Pattern:
  • In steps: Whole–Whole–Half–Whole–Whole–Whole–Half (W–W–H–W–W–W–H)
  • In semitones: [2, 2, 1, 2, 2, 2, 1]
  1. Interval Content: Unison, minor 2nd, major 3rd, perfect 4th, perfect 5th, minor 6th, major 7th.
  2. Pitch Class Set: {0, 2, 4, 5, 7, 9, 11}Scale Distribution Statistics
  • Total scale combinations starting on a fixed tonic: 2,048 ($2^{11}$)
  • Scales containing no step larger than 4 semitones (Major 3rd): 1,490 | Number of Tones | Number of Scales | | --- | --- | | 1 | 0 | | 2 | 0 | | 3 | 1 | | 4 | 31 | | 5 | 155 | | 6 | 336 | | 7 | 413 | | 8 | 322 | | 9 | 165 | | 10 | 55 | | 11 | 11 | | 12 | 1 | *Reference: Ian Ring's Scale Classification*

7.2 Major, Minor, and Diatonic Modes ​

  • Pentatonic Scale: 5-note scale systems, most commonly anhemitonic (lacking half steps).
  • Diatonicism (from Ancient Greek diatonikós, diá = "through" + tónos = "tone"): A 7-note interval system whose pitches can be arranged as a chain of 6 consecutive perfect fifths (e.g., F–C–G–D–A–E–B). Forms diatonic scales featuring alternating patterns of 2–3 whole steps separated by single half steps.
  • Major Mode: Diatonic scale with a major 3rd, major 6th, and major 7th (Ionian mode).
  • Minor Mode: Diatonic scale with a minor 3rd, minor 6th, and minor 7th (Aeolian mode).
  • Relative Keys: Major and minor keys sharing the exact same pitch collection. A relative major key is located a minor third above its relative minor tonic (e.g., C Major and A Minor).
  • Natural / Church Modes: Modal rotations of the diatonic pitch collection. The Seven Diatonic Modes
  • Ionian: Major scale structure (1–2–3–4–5–6–7). Bright, stable, foundational.
  • Dorian: Minor scale with a major 6th (1–2–♭3–4–5–6–♭7). Folk, jazz, modal funk.
  • Phrygian: Minor scale with a minor 2nd (1–♭2–♭3–4–5–♭6–♭7). Dark, characteristic of Flamenco.
  • Lydian: Major scale with an augmented 4th (1–2–3–♯4–5–6–7). Bright, ethereal, film scoring.
  • Mixolydian: Major scale with a minor 7th (1–2–3–4–5–6–♭7). Blues, rock, Celtic music.
  • Aeolian: Natural minor scale (1–2–♭3–4–5–♭6–♭7). Melancholic, classical, somber.
  • Locrian: Diminished profile with minor 2nd and diminished 5th (1–♭2–♭3–4–♭5–♭6–♭7). Highly unstable, rare.

7.3 Scale Degrees and Functional Harmony ​

  • Harmonic Function: Every scale degree forms a specific structural relationship with the tonic.
  • Stability vs. Instability (Tonal Tension):
  • Expressions of musical force: tendency, potential motion, energy, rest, and unstable equilibrium.
  • Tonal attraction and resolution (тяготение и разрешение).
  • Stable degrees: 1, 3, and 5 (forming the tonic triad).
  • Primary Degrees (I, IV, V):
  • Scale pitches divide into three functional groups anchored by the primary scale degrees: I (Tonic), IV (Subdominant), and V (Dominant).
  • Building triads on degrees I, IV, and V reveals all members of each functional group.
  • Functional Roles:
  • Tonic (I): Represents rest, stability, and completion. Tonic sonorities resolve accumulated harmonic tension and conclude musical phrases.
  • Subdominant (IV): Acts as the engine of harmonic progression, creating motion away from the tonic, building moderate tension, and initiating key modulations.
  • Dominant (V): Generates maximum harmonic tension opposing the tonic. Pulls strongly back toward the tonic for resolution.
  • Secondary Scale Degrees:
  • Leading Tone / Subtonic (7th): 7th scale degree (half step below tonic = half-step leading tone; whole step below = subtonic).
  • Supertonic (2nd): 2nd scale degree (step above tonic).
  • Mediant (3rd): 3rd scale degree (midway between Tonic and Dominant).
  • Submediant (6th): 6th scale degree (midway between Subdominant and Tonic).
  • Harmonizing the Scale: Constructing chords built on every degree of a key.
  • Diatonic Chords: Chords formed strictly using notes belonging to the scale.
  • Roman Numeral Notation: Functional shorthand (uppercase for major quality, lowercase for minor quality, added numbers for extensions).

7.4 Exotic, Blues, and Symmetrical Modes ​

  • Non-Western / Exotic Modes:
  • Double Harmonic Major / Byzantine / "Gypsy" scale (1–♭2–3–4–5–♭6–7)
  • Arabic Maqam systems
  • Indian scale systems (Thaats / Ragas)
  • Blues Scales: Hexatonic (1–♭3–4–♭5–5–♭7) and heptatonic structures incorporating microtonal "blue notes".
  • Symmetrical Modes:
  • Whole-Tone Scale: 6-note scale built exclusively of major 2nds.
  • Chromatic Scale: 12-note scale built exclusively of minor 2nds.
  • Octatonic Scale: 8-note scale alternating whole steps and half steps.
  • Olivier Messiaen: Modes of Limited Transposition — theoretical framework categorizing symmetrical pitch structures.
  • Raga & Indian Classical Systems:
  • Raga: A melodic framework for composition and improvisation in Indian classical music.
  • Swaras: The seven basic notes: Sa, Ri, Ga, Ma, Pa, Dha, Ni.
  • Janaka Raga: Parent / fundamental scale types.
  • Melakarta System: The 72 parent scale framework of Carnatic music:
  • Categorized into 2 main categories of 36 ragas based on the tuning of Ma (Shuddha Ma vs. Prati Ma).
  • Divided into 6 groups (Chakras) of 6 ragas based on variations of Ri and Ga.
  • Each group contains 6 ragas defined by variations of Dha and Ni.
  • Janya Ragas: Derived / child ragas created by altering, omitting, or reordering notes from parent Melakarta scales.