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The Diatonic Tapestry: Weaving Western Music's Core

A scholarly exploration into the fundamental building blocks of Western tonality, from ancient origins to modern harmonic structures.

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What is Diatonic?

The Seven-Note Foundation

In the realm of music theory, a diatonic scale is fundamentally a heptatonic (seven-note) scale. Its defining characteristic lies in its precise intervallic structure: it comprises five whole steps (whole tones) and two half steps (semitones) within each octave. Crucially, these two half steps are positioned to be maximally separated from each other, either by two or three whole steps. This arrangement contributes significantly to the scale's inherent sense of tonal direction and stability.

Constructed by Fifths

A remarkable property of any diatonic scale is that its seven distinct pitches can be derived from a sequential chain of six perfect fifths. For instance, the natural pitch classes that constitute the C-major scale—C, D, E, F, G, A, B—can be generated by starting a series of perfect fifths from F: F–C–G–D–A–E–B. This foundational relationship highlights the deep mathematical and acoustical underpinnings of diatonic harmony.

Keyboard's Natural Layout

The design of modern musical keyboards inherently reflects the diatonic structure. Any sequence of seven successive white keys, such as C–D–E–F–G–A–B, naturally forms a diatonic scale. While transpositions of this fundamental diatonic scale necessitate the use of black keys, the white keys themselves provide a tangible, accessible representation of the diatonic system. Furthermore, a diatonic scale can be conceptualized as two tetrachords separated by a whole tone, a structural insight we will explore further.

Etymological Roots

The term "diatonic" originates from the Ancient Greek word ''diatonikós'' (διατονικός). While its precise etymology remains somewhat uncertain, it most likely refers to the intervals being "stretched out" in the ancient Greek tuning systems, contrasting with the more compressed intervals found in the chromatic and enharmonic genera. It is important to note that this definition specifically excludes other seven-note scales, such as the harmonic minor or melodic minor, which, despite having seven notes, do not adhere to the maximal separation of semitones characteristic of true diatonic scales.

Historical Evolution

Ancient Origins

The diatonic scale's lineage stretches back to antiquity. Archaeological evidence suggests that the Sumerians and Babylonians utilized a version of the diatonic scale, as indicated by cuneiform inscriptions detailing musical compositions and tuning systems.[1][2] The reconstruction of Hurrian songs further supports the diatonic nature of their tuning, which involved a series of six perfect fifths. Additionally, 9,000-year-old flutes discovered in Jiahu, China, demonstrate an evolution from 4-hole to 7- and 8-hole instruments, with the latter exhibiting striking similarities to diatonic hole spacings and sounds.[3]

Medieval Church Modes

During the Middle Ages, the scales corresponding to the church modes were inherently diatonic. While there are seven possible modes derived from a diatonic scale, the one starting on B (the Locrian mode) was generally avoided due to its diminished fifth above the reference note. Medieval theory primarily focused on four diatonic scales, which, through transposition and the use of B♭, encompassed the modern Dorian, Phrygian, Lydian, and Mixolydian modes of C major, alongside the Aeolian and Ionian modes of F major.[X]

Renaissance Refinements

The Renaissance period saw further systematization of diatonic scales. Heinrich Glarean, in his seminal work ''Dodecachordon'', posited that modal scales incorporating a B♭ were essentially transpositions. He meticulously described six "natural" diatonic scales (excluding the Locrian) and six "transposed" ones, each featuring a B♭. This comprehensive framework resulted in a total of twelve scales, providing the theoretical basis for his treatise's title and laying groundwork for future tonal developments.[X]

Modern Dominance

By the dawn of the Baroque era, the concept of musical "key" became firmly established, expanding the possibilities for diatonic scale transpositions. Major and minor scales subsequently rose to prominence, dominating Western music until at least the early 20th century. Their intervallic patterns were particularly well-suited to reinforcing a central triad, a cornerstone of tonal harmony. Nevertheless, the ancient church modes continued to appear in classical, 20th-century, and jazz music, demonstrating the enduring versatility of the diatonic system.[X]

Theoretical Frameworks

The Diatonic Universe

Expanding upon Glarean's insights, the six natural scales (Ionian, Lydian, Mixolydian with a major third/first triad; Dorian, Phrygian, Aeolian with a minor one) can be augmented by the Locrian scale, which features a diminished fifth above its reference note. When considering all possible transpositions across the twelve notes of the chromatic scale, this yields a total of eighty-four distinct diatonic scales. This vast array underscores the flexibility and richness embedded within the diatonic system.

Keyboard Evolution

The modern musical keyboard, with its familiar arrangement of white and black keys, evolved from an earlier diatonic design that featured only white keys.[4] The black keys were incrementally introduced to serve several crucial functions: to enhance consonances, particularly thirds, by providing a major third on every degree; to facilitate all twelve possible transpositions of the diatonic scale; and to offer musicians clearer navigational cues on the keyboard.

Interval Patterns

The fundamental structure of any diatonic scale can be concisely represented by a sequence of elementary intervals: 'T' for a whole tone (whole step) and 'S' for a semitone (half step). This symbolic representation allows for a clear and universal understanding of the intervallic relationships within different diatonic scales. For instance, the major scale, a cornerstone of Western music, adheres to a specific and recognizable pattern of these intervals.

The major scale, for example, is represented as:

T–T–S–T–T–T–S

This sequence defines the characteristic sound and structure of all major scales, regardless of their starting pitch.

The Major Scale

Ionian Mode Unveiled

The major scale, also known as the Ionian mode, stands as one of the most fundamental diatonic scales in Western music. It is composed of seven distinct notes, with an eighth note that duplicates the first at an octave higher, completing the scale. The characteristic pattern of intervals separating these eight notes is T–T–S–T–T–T–S, creating its bright and uplifting quality.

Solfège and Degrees

In solfège, a system for teaching sight-singing, the syllables used to articulate each degree of the major scale are ''Do–Re–Mi–Fa–Sol–La–Ti–Do''. Beyond these mnemonic syllables, each of the seven degrees of the scale also carries a traditional name, particularly when considered within a tonal context. These names define their harmonic function and relationship to the tonic.

Consider the C-major scale, formed by successive natural notes starting from C:

Notes in C major: C D E F G A B C
Degrees in solfège: Do Re Mi Fa Sol La Ti Do
Interval sequence: T T S T T T S

The traditional names for the degrees of the major scale are:

  • 1st – Tonic (the key note, providing tonal center)
  • 2nd – Supertonic (one step above the tonic)
  • 3rd – Mediant (midway between tonic and dominant)
  • 4th – Subdominant (one step below the dominant)
  • 5th – Dominant (the most important harmonic function after the tonic)
  • 6th – Submediant (midway between tonic and subdominant, in the lower octave)
  • 7th – Leading tone (a half step below the tonic, creating strong pull)
  • (8th – Tonic, an octave higher)

The Natural Minor Scale

Relative Minor Connection

For every major scale, there exists a corresponding natural minor scale, often referred to as its "relative minor." This scale utilizes the identical sequence of notes as its relative major but commences from a different starting point—specifically, the sixth degree of the major scale. It then progresses step-by-step to the octave of this new starting note, creating a distinct, often more somber, tonal character.

A Minor Example

A prime illustration of a natural minor scale is the A natural minor scale, which is formed by the successive natural notes beginning from A: A–B–C–D–E–F–G–A. This scale shares its notes with C major, but by shifting the tonal center, it evokes a different emotional and harmonic landscape. Its unique intervallic pattern differentiates it from the major scale.

Notes in A minor: A B C D E F G A
Interval sequence: T S T T S T T

The degrees of the natural minor scale, particularly in a tonal context, share similar names with those of the major scale. However, a key distinction lies in the seventh degree, which is termed the subtonic because it is a whole step below the tonic. The designation "leading tone" is typically reserved for seventh degrees that are a ''half step'' (semitone) below the tonic, as observed in the major scale, creating a stronger pull towards the tonic.

The Diatonic Modes

Shifting Perspectives

The entire collection of diatonic scales can be systematically categorized into seven distinct modes. As previously discussed, all major scales share the same interval sequence (T–T–S–T–T–T–S), which Glarean termed the Ionian mode. By simply selecting a different degree of any major scale as the new tonic, six additional scales or modes can be generated. This method reveals the inherent modal diversity within a single diatonic system.

Seven Distinct Characters

Another way to conceptualize the modes is to consider an underlying diatonic system—a series of diatonic notes without a fixed reference point. By assigning each of the seven notes in an octave of this system as the reference note (tonic) in turn, seven unique diatonic scales emerge, each characterized by its own distinctive interval sequence and resulting musical character. Transposition, in this context, preserves the modal identity.

The following table illustrates the seven modern diatonic modes, their relationship to the major scale, their characteristic interval sequences, and examples using white keys and transposed to a C tonic:

Mode Also known as Starting note relative
to major scale		 Interval sequence Example with white keys Example with tonic C
Ionian Major scale C T–T–S–T–T–T–S C–D–E–F–G–A–B–C
Dorian D T–S–T–T–T–S–T D–E–F–G–A–B–C–D C–D–E♭–F–G–A–B♭–C
Phrygian E S–T–T–T–S–T–T E–F–G–A–B–C–D–E C–D♭–E♭–F–G–A♭–B♭–C
Lydian F T–T–T–S–T–T–S F–G–A–B–C–D–E–F C–D–E–F♯–G–A–B–C
Mixolydian G T–T–S–T–T–S–T G–A–B–C–D–E–F–G C–D–E–F–G–A–B♭–C
Aeolian Natural minor scale A T–S–T–T–S–T–T A–B–C–D–E–F–G–A C–D–E♭–F–G–A♭–B♭–C
Locrian B S–T–T–S–T–T–T B–C–D–E–F–G–A–B C–D♭–E♭–F–G♭–A♭–B♭–C

The "white-key" examples demonstrate the modes as they naturally occur on a piano keyboard, while the "tonic C" examples illustrate how each mode's unique intervallic structure is preserved when transposed to a common starting pitch.

Tetrachordal Construction

A diatonic scale can also be elegantly described as two tetrachords separated by a whole tone. A tetrachord is a series of four notes spanning a perfect fourth. For instance, in the modern understanding, the C major scale's two tetrachord structures are [C–D–E–F] and [G–A–B–C], each exhibiting a T–T–S (tone-tone-semitone) pattern. The medieval conception, however, centered on a single tetrachord structure (T–S–T) derived from the D scale, viewing other diatonic scales as variations of overlapping or conjoined tetrachords.

For the natural minor of A, the tetrachords are different:

[A–B–C–D] – [E–F–G–A]

The first tetrachord is T–S–T, and the second is S–T–T.

The medieval perspective on tetrachordal structure, based on the D scale [D–E–F–G] – [A–B–C–D] (each T–S–T), viewed other diatonic scales through differently overlapping disjunct and conjunct tetrachords:

E scale: E–F–G | A–B–C–D = D–E
F scale: F–G | A–B–C–D = D–E–F
G scale: G | A–B–C–D = D–E–F–G
A scale: A–B–C–D = D–E–F–G | A
B scale: B–C–D = D–E–F–G | A–B
C scale: C–D = D–E–F–G | A–B–C

Here, G | A signifies the disjunction of tetrachords, always between G and A, while D = D indicates their conjunction on the common note D.

Tuning Systems

Pythagorean Tuning

One of the earliest methods for tuning diatonic scales is Pythagorean tuning, achieved through the iteration of six perfect fifths. For example, starting from F and building a chain F–C–G–D–A–E–B results in the pitches of a C major scale. In this system, six of the fifth intervals are precisely 3/2 (1.5), while the remaining interval, B–F', forms a discordant tritone (729/512 ≈ 1.4238). Whole tones are 9/8 (1.125), and diatonic semitones are 256/243 (≈ 1.0535). This ancient tuning system, dating back to Mesopotamia,[5] highlights the foundational role of perfect fifths in scale construction.

The following table illustrates the pitch ratios in Pythagorean tuning, relative to C=1/1:

note F C G D A E B
pitch 2⁄3 1⁄1 3⁄2 9⁄4 10⁄3 5⁄1 15⁄2
bring into main octave 4⁄3 1⁄1 3⁄2 9⁄8 5⁄3 5⁄4 15⁄8
sort into note order C D E F G A B C'
interval above C 1⁄1 9⁄8 5⁄4 4⁄3 3⁄2 5⁄3 15⁄8 2⁄1
interval between notes 9⁄8 10⁄9 16⁄15 9⁄8 10⁄9 9⁄8 16⁄15

Equal Temperament

Equal temperament represents a significant departure from older tuning systems, dividing the octave into precisely twelve equal semitones. In this system, the frequency ratio of a semitone is the twelfth root of two (approximately 1.059463, or 100 cents), and a whole tone is the sixth root of two (approximately 1.122462, or 200 cents). This temperament can be achieved through a succession of tempered fifths, each with a ratio of 27/12 (approximately 1.498307, or 700 cents). Equal temperament prioritizes consistent intervallic relationships across all keys, making modulation seamless, though individual intervals may deviate slightly from acoustically pure ratios.

Just Intonation

Just intonation, in contrast, aims for acoustically pure intervals, particularly perfect fifths and perfect major thirds, by using frequency ratios based on simple powers of prime numbers (2, 3, and 5), also known as five-limit tuning. This system often results in highly consonant chords but can introduce challenges when modulating between keys, as some intervals may become "wolf" intervals. Leonhard Euler's Tonnetz visually represents just intonation, where the diatonic scale forms a specific lattice structure of perfect fifths and major thirds. Ptolemy's intense diatonic scale, described by Ptolemy and later by Zarlino, is a notable example of a just intonation tuning for the diatonic scale, often considered the "natural" scale by 17th and 18th-century theorists.

The Tonnetz representation of the diatonic scale in just intonation:

A E B
F C G D

Here, F–A, C–E, and G–B, aligned vertically, represent perfect major thirds. The horizontal lines F–C–G–D and A–E–B represent series of perfect fifths. The notes on the top line (A, E, B) are lowered by the syntonic comma (81/80) compared to their Pythagorean counterparts, and the D–A fifth is slightly narrower. The tritone F–B is 45/32 (≈ 1.40625).

The pitch ratios for Ptolemy's intense diatonic scale (a form of just intonation) are:

notes C D E F G A B C'
pitch 1⁄1 9⁄8 5⁄4 4⁄3 3⁄2 5⁄3 15⁄8 2⁄1
interval between notes 9⁄8 10⁄9 16⁄15 9⁄8 10⁄9 9⁄8 16⁄15

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References

References

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