Comprehensive Guide to Diatonic Modes, Functional Syntax, and Key Signature Derivations

Foundations of Tonal vs. Modal Syntax

• Tonal Music Structure:

  • Tonal music is established through functional chord progressions.
  • Normative functional categories ascribed to chords determine a normative syntactical ordering within a progression.
  • Progressions and chords follow one another in a logical sequence where specific chord categories succeed others according to established syntax.
  • Tonal order operates under harmonic gravity that directs musical movement away from home and brings it back.
  • A typical progression establishes a sense of departure from $C$ and return to $C$ by way of the dominant ($G$).
  • Functional categorization maintains a direct, one-to-one relationship with harmonic ordering: tonic chords are followed by predominant chords, which are followed by dominant chords, resolving back to tonic.
  • When musical compositions deviate slightly from this normative formula, progressions are still interpreted and understood through the framework of functional tonal syntax.

• Modal Music Structure:

  • Modal music is organized around a melodic finalis (or final), also referred to as a modal tonic.
  • The term "tonic" inherently carries the magnitude and historical baggage of tonal functional harmony; using the term "final" avoids this association.
  • Chord ordering in modal music is not bound by categorical harmonic functions.
  • The syntax of harmony in modal systems is substantially freer than the strictly ordered progressions found in tonal music.
  • Popular music possesses its own syntax, but it operates differently from traditional functional tonality, utilizing greater modal freedom.

Diatonic Collections and Definitions of Modes

• Diatonic Collection:

  • A collection is defined as an unordered group of notes that form the foundational basis of a musical passage or piece.
  • The white note diatonic collection (abbreviated as $WNDC$) consists of all the pitches of the $C$ major scale grouped together in an unordered bucket: $\{C, D, E, F, G, A, B\}$.
  • A diatonic collection is a specific seven-note collection generated by the circle of fifths (for example, the white note collection, the two-sharp collection, or the two-flat collection).
  • Collections encompass the major scale and all of its associated permutations.

• Scales and Modes:

  • A scale or a mode orders an unordered collection in a specific, sequential way.
  • For example, the $C$ major scale begins on one note of the white note collection and cycles through all pitches in an ascending or descending order.
  • Because a diatonic collection contains seven distinct pitches, starting on each pitch yields seven distinct possible orderings.
  • Every ordering of a collection constitutes a mode of that collection.
  • The term mode carries a complex, centuries-long history (documented in sources such as the New Grove Dictionary of Music, which features an entry on mode of approximately $200$ pages, referenced colloquially as the Negro dictionary music).
  • In standard practical analysis, the terms scale and mode can be used interchangeably.

• Relative vs. Parallel Systems:

  • Relative scales and modes share the exact same key signature and collection of pitches while starting on different finals.
  • Parallel scales and modes share the exact same final (pitch center) while utilizing different pitch collections and key signatures.

The Seven Diatonic Modes and Triadic Stability

• Modes of the White Note Diatonic Collection ($WNDC$):

  • Ionian Mode: Formed by setting $C$ as the final ($C-D-E-F-G-A-B$). Functionally identical to the major scale. The term "major" is applied when invoking tonal harmonic magnitude, whereas "Ionian" is used when stepping outside tonal function.
  • Dorian Mode: Formed by ordering the collection from $D$ to $D$ ($D-E-F-G-A-B-C$), altering the interval structure relative to the final.
  • Phrygian Mode: Formed by ordering the collection from $E$ to $E$ ($E-F-G-A-B-C-D$).
  • Lydian Mode: Formed by ordering the collection from $F$ to $F$ ($F-G-A-B-C-D-E$).
  • Mixolydian Mode: Formed by ordering the collection from $G$ to $G$ ($G-A-B-C-D-E-F$).
  • Aeolian Mode: Formed by ordering the collection from $A$ to $A$ ($A-B-C-D-E-F-G$). Known as natural minor in tonal systems; "natural minor" carries tonal connotations, while "Aeolian" is used in modal contexts.
  • Locrian Mode: Formed by ordering the collection from the seventh scale step, $B$ to $B$ ($B-C-D-E-F-G-A$).

• Harmonic Stability of the Final Triad:

  • Every mode except Locrian features either a major or minor triad built directly above its final:
  • Modes with major tonic triads: Ionian, Lydian, and Mixolydian.
  • Modes with minor tonic triads: Dorian, Phrygian, and Aeolian.
  • The Locrian mode builds a diminished triad above its final ($B-D-F$), containing a diminished fifth ($\text{d}5$).
  • Musical progressions cannot achieve genuine rest or resolution on an inherently dissonant chord, making the Locrian mode structurally unstable and the least functionally comfortable of all modes.
  • Locrian is rarely used for entire compositions outside of heavy metal genres, where guitarists and drummers utilize high distortion, extreme dissonance, heavy stomping rhythms, and aggressive sonic authority.

Mode Calculation Method 1: Altered Scale Steps and Key Signature Math

• Scale Step Alterations Relative to the Parallel Major Scale:

  • Every mode can be derived by altering specific scale steps of a major scale sharing the same final:
  • Lydian: Major scale with $\flat 0$ and $\sharp 4$ (contains $+1$ sharp relative to major).
  • Ionian: Major scale with no alterations ($1, 2, 3, 4, 5, 6, 7$).
  • Mixolydian: Major scale with $\flat 7$ (contains $-1$ sharp / $+1$ flat relative to major).
  • Dorian: Major scale with $\flat 3$ and $\flat 7$ (contains $-2$ sharps / $+2$ flats relative to major).
  • Aeolian: Major scale with $\flat 3$, $\flat 6$, and $\flat 7$ (contains $-3$ sharps / $+3$ flats relative to major).
  • Phrygian: Major scale with $\flat 2$, $\flat 3$, $\flat 6$, and $\flat 7$ (contains $-4$ sharps / $+4$ flats relative to major).
  • Locrian: Major scale with $\flat 2$, $\flat 3$, $\flat 5$, $\flat 6$, and $\flat 7$ (contains $-5$ sharps / $+5$ flats relative to major).

• Key Signature Mathematical Operations:

  • Key signatures can be calculated algebraically by treating sharps as positive integers and flats as negative integers:
  • Adding a sharp: $+1$
  • Adding a flat: $-1$
  • If a calculation requires adding flats to a sharp key, flats cancel out sharps sequentially.

• Worked Examples Using Method 1:

  • $E$ Lydian:
  • $E$ major possesses $4$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp$).
  • Lydian adds $\sharp 4$ ($+1$ sharp).
  • The fourth scale step of $E$ major is $A$ natural; raising it produces $A\sharp$.
  • $4 + 1 = 5$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp, A\sharp$).
  • $B\flat$ Dorian:
  • $B\flat$ major possesses $2$ flats ($B\flat, E\flat$).
  • Dorian adds $\flat 3$ and $\flat 7$ ($+2$ flats).
  • $2 + 2 = 4$ flats ($B\flat, E\flat, A\flat, D\flat$).
  • $B$ Mixolydian:
  • $B$ major possesses $5$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp, A\sharp$).
  • Mixolydian adds $\flat 7$ ($-1$ sharp).
  • $5 - 1 = 4$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp$).
  • $F\sharp$ Phrygian:
  • $F\sharp$ major possesses $6$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp, A\sharp, E\sharp$).
  • Phrygian adds $\flat 2, \flat 3, \flat 6, \flat 7$ ($-4$ sharps).
  • $6 - 4 = 2$ sharps ($F\sharp, C\sharp$).
  • $F$ Locrian:
  • $F$ major possesses $1$ flat ($B\flat$).
  • Locrian adds $\flat 2, \flat 3, \flat 5, \flat 6, \flat 7$ ($+5$ flats).
  • $1 + 5 = 6$ flats ($B\flat, E\flat, A\flat, D\flat, G\flat, C\flat$).
  • $D$ Phrygian:
  • $D$ major has $2$ sharps.
  • Phrygian adds $4$ flats.
  • Subtracting $4$ from $2$ gives: $2 - 4 = -2$, which equals $2$ flats ($B\flat, E\flat$).

Mode Calculation Method 2: Scale Steps, Solfège, and Parent Major Keys

• Numerical and Solfège Order of Diatonic Modes:

  • Mode $1$: Ionian = Do mode (built on scale step $1$
  • Mode $2$: Dorian = Re mode (built on scale step $2$
  • Mode $3$: Phrygian = Mi mode (built on scale step $3$
  • Mode $4$: Lydian = Fa mode (built on scale step $4$
  • Mode $5$: Mixolydian = Sol mode (built on scale step $5$
  • Mode $6$: Aeolian = La mode (built on scale step $6$
  • Mode $7$: Locrian = Ti mode (built on scale step $7$

• Calculating Signatures via Parent Key Steps:

  • Determine which major scale contains the mode's final on the mode's specific structural scale degree.
  • $A$ Lydian:
  • Lydian is the fourth mode (Fa mode).
  • Determine which major scale contains $A$ as scale step $4$.
  • $A$ is scale step $4$ of $E$ major.
  • $E$ major has $4$ sharps; therefore, $A$ Lydian has $4$ sharps ($F\sharp, C\sharp, G\sharp, D\sharp$).
  • $C\sharp$ Mixolydian:
  • Mixolydian is the fifth mode (Sol mode / scale step $5$
  • Working through the relative scale relationships, identifying the parent scale signature determines the exact sharps or flats required without calculating alterations independently.
  • $G\sharp$ Locrian:
  • Locrian is the seventh mode (Ti mode / scale step $7$
  • Determine which major scale contains $G\sharp$ as scale step $7$.
  • $G\sharp$ is scale step $7$ of $A$ major.
  • $A$ major has $3$ sharps; therefore, $G\sharp$ Locrian has $3$ sharps ($F\sharp, C\sharp, G\sharp$).

Applied Modal Improvisation and the Chord-Scale System

• Real-Time Application:

  • Musicians reading lead sheets and chord changes during live performance cannot pause the pulse while the rhythm section and drummer continue playing.
  • Instantaneous mental access to modal pitch content is essential.

• Chord-to-Mode Pairings:

  • The chord-scale system pairs specific chord qualities with appropriate modes that align with their underlying harmonic structures.
  • Minor seventh chords ($\text{m}^7$) commonly pair with the Dorian mode.
  • For example, encountering an $F\text{m}^7$ chord prompts the immediate selection of the $F$ Dorian scale.
  • Performing in $F$ Dorian requires instant knowledge of its pitch alterations relative to $F$ major ($\flat 3, \flat 7$, resulting in $3$ flats: $B\flat, E\flat, A\flat$) so improvisation fits the harmonic framework seamlessly.

Diatonic Collection Generation and Triadic Qualities

• Generating Collections via the Circle of Fifths:

  • A diatonic collection can be constructed by chaining six consecutive ascending fifth intervals (seven pitches total).
  • Beginning on $E\flat$:
  • Pitch sequence: $E\flat - B\flat - F - C - G - D - A$
  • Reorganizing these pitches within an octave yields the two-flat diatonic collection ($B\flat, E\flat$).

• Analyzing Scale Steps within the Two-Flat Collection:

  • Defining $C$ as scale step $1$ produces the pitches $C, D, E\flat, F, G, A, B\flat$.
  • Comparing these to $C$ major ($1, 2, 3, 4, 5, 6, 7$) reveals alterations $1, 2, \flat 3, 4, 5, 6, \flat 7$, identifying the mode as $C$ Dorian.
  • Defining $D$ as scale step $1$ produces the pitches $D, E\flat, F, G, A, B\flat, C$.
  • Comparing these to $D$ major reveals alterations $1, \flat 2, \flat 3, 4, 5, \flat 6, \flat 7$, identifying the mode as $D$ Phrygian.

• Naming Conventions of Modes:

  • Modes are always identified and named by their specific final (pitch center), never by the parent collection or root of the relative major scale.
  • In a two-flat collection where $D$ is the final, the mode must be designated as $D$ Phrygian, not "$B\flat$ Phrygian".

• Triad Distribution Across Diatonic Modes:

  • Every standard diatonic mode contains an identical distribution of triadic qualities shifted across different scale steps:
  • Exactly $3$ major triads.
  • Exactly $3$ minor triads.
  • Exactly $1$ diminished triad.
  • Shifting collections across scale degrees changes the functional quality of specific steps.
  • For example, in the Lydian mode, the triad constructed on scale step $2$ (the supertonic) is a major triad ($\text{II}$), contrasting with the minor supertonic ($\text{ii}$) of standard major keys.

Questions & Discussion

• Mathematical Subtraction of Flats and Sharps:

  • Question/Concern (Josiah): Confusion arose regarding the mathematical calculation of signatures when subtracting flats from sharps (e.g., $2$ sharps plus $4$ flats yielding negative $2$).
  • Clarification: Sharps represent positive numerical values and flats represent negative values. If a musician holds $2$ sharps and applies $4$ flats, the first $2$ flats cancel out the $2$ sharps entirely to reach zero; the remaining $2$ flats leave a net key signature of $2$ flats ($B\flat, E\flat$).

• Understanding the Alteration Label "$\flat 7$":

  • Question/Concern: A student questioned whether the label "$\flat 7$" indicated adding "the seventh flat" of the circle of fifths to the signature.
  • Clarification: The notation "$\flat 7$" does not mean inserting the seventh flat from the order of flats; rather, it indicates lowering the seventh scale step of the parallel major scale by a half step.

• Identification of the $E\flat$ Collection and Modes:

  • Question/Discussion (Randall): When isolating pitches in the two-flat diatonic collection, an attempt was made to classify a mode with the formula $1, 2, 3, \sharp 4, 5, 6, 7$ as Mixolydian or "$E\flat$ Mixolydian / Lydian".
  • Clarification: That calculation was off by one step. $E\flat$ major contains $3$ flats ($B\flat, E\flat, A\flat$). To determine the mode accurately, one must examine the exact scale degree alterations in relation to the final rather than confusing relative major collections.