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Major third
Major third
Major third
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Major third
InverseMinor sixth
Name
Other namesditone
AbbreviationM3, maj3, M3, maj 3
Size
Semitones4
Interval class4
Just interval5:4, 81:64, 9:7
Cents
12-Tone equal temperament400
Just intonation386, 408, 435
Just major third.
Pythagorean major third, i.e. a ditone
Comparison, in cents, of intervals at or near a major third
Harmonic series, partials 1–5, numbered Playⓘ.

In music theory, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third (Playⓘ) is a third spanning four half steps or two whole steps.[1] Along with the minor third, the major third is one of two commonly occurring thirds. It is described as major because it is the larger interval of the two: The major third spans four semitones, whereas the minor third only spans three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called "major".[2]

Diminished and augmented thirds are shown on the musical staff the same number of lines and spaces apart, but contain a different number of semitones in pitch (two and five).

Harmonic and non-harmonic thirds

[edit]

The major third may be derived from the harmonic series as the interval between the fourth and fifth harmonics. The major scale is so named because of the presence of this interval between its tonic and mediant (1st and 3rd) scale degrees. The major chord also takes its name from the presence of this interval built on the chord's root (provided that the interval of a perfect fifth from the root is also present).

A major third is slightly different in different musical tunings: In just intonation it corresponds to a pitch ratio of 5:4, or ⁠ 5 / 4 ⁠ (playⓘ) (fifth harmonic in relation to the fourth) or 386.31 cents; in 12 tone equal temperament, a major third is equal to four semitones, a ratio of 21/3:1 (about 1.2599) or 400 cents, 13.69 cents wider than the 5:4 ratio. The older concept of a "ditone" (two 9:8 major seconds) made a dissonant, wide major third with the ratio 81:64 (about 1.2656) or 408 cents (playⓘ), about 22 cents sharp from the harmonic ratio of 5:4 . The septimal major third is 9:7 (435 cents), the undecimal major third is 14:11 (418 cents), and the tridecimal major third is 13:10 (452 cents).

In 12 tone equal temperament (12 TET) three major thirds in a row are equal to an octave. For example, A♭ to C, C to E, and E to G♯ (in 12 TET, the differently written notes G♯ and A♭ both represent the same pitch, but not in most other tuning systems). This is sometimes called the "circle of thirds". In just intonation, however, three 5:4 major third, the 125th subharmonic, is less than an octave. For example, three 5:4 major thirds from C is B♯ (C to E, to G♯, to B♯) (⁠  B♯ / C ⁠ ). The difference between this just-tuned B♯ and C, like the interval between G♯ and A♭, is called the "enharmonic diesis", about 41 cents, or about two commas (the inversion of the interval ⁠ 125 / 64 ⁠ : (playⓘ)).

Consonance vs. dissonance

[edit]

The major third is classed as an imperfect consonance and is considered one of the most consonant intervals after the unison, octave, perfect fifth, and perfect fourth. In the common practice period, thirds were considered interesting and dynamic consonances along with their inverses the sixths, but in medieval times they were considered dissonances unusable in a stable final sonority.

In equal temperament, a diminished fourth is enharmonically equivalent to a major third (that is, it spans the same number of semitones). For example, B–D♯ is a major third; but if the same pitches are spelled as the notes B and E♭, then the interval they represent is instead a diminished fourth. The difference in pitch is erased in 12 tone equal temperament, where the distinction is only nominal, but the difference between a major third and a diminished fourth is significant in almost all other musical tuning systems. B–E♭ occurs in the C harmonic minor scale.

The major third is used in guitar tunings. For the standard tuning, only the interval between the 3rd and 2nd strings (G to B, respectively) is a major third; each of the intervals between the other pairs of consecutive strings is a perfect fourth. In an alternative tuning, the major-thirds tuning, each of the intervals are major thirds.

Interval sounds

[edit]
  • Minor thirds:
C-E♭
Strings playing the note C then E♭
Problems playing this file? See media help.
C-A
Strings playing the note C then A
Problems playing this file? See media help.
  • Major thirds
Major third (equal temperament)
The file plays middle C, followed by E (a tone 400 cents sharper than C), followed by both tones together.
Problems playing this file? See media help.
C-E
Strings playing the note C then E
Problems playing this file? See media help.
C-A♭
Strings playing the note C then A♭
Problems playing this file? See media help.

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Major third

View on Grokipedia
from Grokipedia
In music theory, a major third is a consonant interval that spans four semitones (or half steps) in the and encompasses three diatonic scale degrees, such as from C to E in the key of . This interval is distinguished from the , which spans only three semitones, by its brighter, more stable sonic quality, often evoking a of resolution or major . In , the major third corresponds to a of 5:4 (approximately 386 cents), providing a pure and harmonious consonance when tuned accordingly, though in it approximates this at 400 cents. The major third forms a foundational element of major triads, which consist of a root note, a above it, and a , creating the characteristic sound of major keys prevalent in Western classical, popular, and music. It appears prominently in the first three notes of the (e.g., do-mi) and contributes to the structural of progressions like the I-IV-V chord sequence. Historically, the major third's role evolved from approximations in by ancient Greek theorists, through Renaissance practices emphasizing its acoustic purity, into the standardized equal-tempered systems of the common practice era. In performance and composition, tuning the major third precisely can enhance emotional expressiveness, as deviations—such as the wider tempered version—may introduce subtle tension or color.

Definition and Fundamentals

Basic Definition

In music theory, the major third is a fundamental interval that spans three diatonic degrees within a scale, such as from the tonic note C to the mediant E in the C major scale. This interval encompasses four semitones in the twelve-tone equal temperament system commonly used in Western music. It is one of the two primary types of thirds, distinguished from the minor third, which spans only three semitones and three diatonic degrees but with a flattened third degree (e.g., C to E♭). The nomenclature "major" originates from the Latin word maior, meaning "greater," reflecting that this interval is larger in size compared to its counterpart, the minor third derived from minor, meaning "lesser." This distinction in terminology arose in medieval and Renaissance music theory to classify intervals based on their relative widths within diatonic contexts. Visually, the major third can be represented on a musical staff in treble clef, where the lower note C is placed on the ledger line below the staff, and the upper note E is placed on the bottom line of the staff. On a keyboard diagram, it appears as the distance from the white key C to the white key E, passing over the white D and the black keys D♯/E♭, covering four half-steps. As a core element of Western music theory, the major third functions as a building block for constructing scales, harmonies, and melodic lines, providing the characteristic bright and stable quality to major tonalities. Its frequency ratio approximates 5:4 in just intonation systems.

Interval Size and Ratio

The major third spans exactly four semitones in twelve-tone equal temperament, corresponding to a size of 400 cents. In just intonation, the major third is defined by the simple frequency ratio of 5:4, equivalent to approximately 386.31 cents. This just ratio derives from the Pythagorean major third (81:64, approximately 407.82 cents) by flattening it by the syntonic comma (81:80, or 21.51 cents), a adjustment commonly applied in just intonation systems to achieve purer thirds from the fifth-based Pythagorean framework. The standard measure of interval size in cents uses the formula cents=1200×log⁡2(f2f1),\text{cents} = 1200 \times \log_2 \left( \frac{f_2}{f_1} \right), where f2/f1f_2 / f_1 is the frequency ratio; applying this to the 5:4 ratio yields 1200×log⁡2(1.25)≈386.311200 \times \log_2(1.25) \approx 386.31 cents. For comparison, the —spanning three semitones or 300 cents in —has a just intonation ratio of 6:5, approximately 315.64 cents. In , these thirds deviate from their just counterparts, producing audible beats between close overtones when sounded simultaneously. For the major third, beats arise primarily from the mismatch between the fifth of the lower note and the fourth of the upper note, with frequency difference Δf≈f⋅∣5−4⋅24/12∣\Delta f \approx f \cdot |5 - 4 \cdot 2^{4/12}|, where ff is the lower note's frequency. For the minor third, beats occur between the sixth of the lower note and the fifth of the upper note, Δf≈f⋅∣6−5⋅23/12∣\Delta f \approx f \cdot |6 - 5 \cdot 2^{3/12}|. The following table compares the sizes and typical beat frequencies (for a base frequency near 262 Hz, as in middle C) in relative to :
IntervalEqual Temperament (cents)Just Intonation (cents, ratio)Approximate Beat Frequency in ET (Hz)
Major third400386.31 (5:4)10.4
300315.64 (6:5)14.1
Beat rates increase roughly proportionally with pitch height due to higher fundamental frequencies.

Harmonic Properties

Consonance and Stability

In traditional , particularly from the medieval period onward, the major third is classified as an imperfect consonance, distinguished from perfect consonances such as the , , and due to its frequency ratio of , which, while simple, is more complex than the 2:1 or 3:2 ratios of perfect intervals. This classification emerged as developed around the 9th to 13th centuries, when theorists like Walter Odington began recognizing the major third as an imperfect consonance in polyphonic structures such as discant, though it was treated with more caution than perfect consonances in rules. The psychoacoustic basis for the major third's consonance lies in its low beating rates between interacting partials and its alignment within the series, where the interval approximates the relationship between the fourth and fifth harmonics (ratios 4:1 and 5:1 relative to the fundamental), promoting perceptual stability through minimal interference and neural . When two tones form a just major third ( ), the beating frequency between their fundamentals is relatively slow compared to dissonant intervals like the minor second, reducing auditory roughness, while partial coincidences in the harmonic series enhance fusion and harmony. This alignment contributes to the interval's sense of repose, as the upper tone's lower partials closely match of the lower tone, minimizing dissonance from inharmonic clashes. In the consonance hierarchy of , the major third ranks below perfect consonances (, , , and sometimes ) but above dissonant intervals such as seconds and sevenths, and on par with other imperfect consonances like the and sixths, reflecting its intermediate perceptual stability. Experimental studies confirm this ordering, with listeners rating imperfect consonances like the major third as more pleasant and stable than dissonances but less so than perfect ones, due to greater harmonic simplicity in the latter. This hierarchy influences compositional practices, where major thirds provide moderate resolution without the full repose of a perfect consonance. The major third contributes to stability in common chord progressions such as I-IV-V in major keys, where it forms the defining interval in the root-position triads of the tonic (I) and (IV), offering a sense of color and partial resolution that supports the overall tonal center before the dominant (V) introduces tension. In the authentic resolving from V to I, the major third in the tonic triad reinforces closure by aligning with the series of the , creating a stable, bright sonority that contrasts with the leading-tone pull of the dominant. This role underscores the interval's function in establishing diatonic harmony without overpowering the structural primacy of perfect consonances.

Harmonic vs. Non-Harmonic Contexts

In harmonic contexts, the major third functions vertically as a stacked interval within chords, particularly as the upper partial in root-position major triads such as C-E-G, where it defines the chord's characteristic brightness and major quality. This vertical alignment contributes to the triad's consonance and stability, evoking an uplifting and stable sonority central to tonal harmony. In contrast, non-harmonic contexts treat the major third linearly, as a melodic interval in horizontal lines without simultaneous vertical stacking, often appearing as a skip in melodies or as part of contrapuntal motion. Here, it serves as a connective element, such as in stepwise progressions or passing skips, emphasizing motion rather than support. Theoretically, this distinction traces to medieval treatises, where the major third was classified as an imperfect consonance—less stable than perfect consonances like the fifth—and thus restricted in strict to avoid overuse or consecutive parallels, reflecting its transitional role between consonance and potential dissonance. By the 13th century, theorists like Franco of Cologne classified it as an imperfect consonance, permitting its use in discant and , though with caution to alternate with perfect consonances in strict styles. Examples illustrate this divide: in tonal harmony, the major third reinforces vertical structure, as in the major triad's role within common-practice progressions like I-IV-V-I; in modal music, such as , it appears melodically as a linear skip without triad formation, prioritizing contour over harmony; and in atonal contexts, it functions purely as a non-functional interval in serial or twelve-tone compositions, detached from any stacking implications.

Auditory and Perceptual Aspects

Sound Characteristics

The major third exhibits a bright, open, and uplifting arising from the reinforcement of , where the frequency of the upper note coincides with a prominent partial of the lower note, enhancing perceived clarity and . This alignment contributes to its overall sense of stability and appeal in auditory perception. In Western musical contexts, the major third carries strong emotional connotations of and resolution, often evoking feelings of and affirmation. A familiar example appears in the opening phrase of the tune "When the Saints Go Marching In," where the interval between "Oh" and "when" delivers an immediate sense of uplift and celebration. When demonstrated through isolated pure tones, a major third at the frequency ratio produces a smooth, unwavering sound free of interference, highlighting its inherent purity. In contrast, the equal-tempered major third introduces a gentle beating effect due to the slight mistuning of its partials, imparting a dynamic yet less stable quality often described as shimmering. Relative to the , which conveys a darker and more introspective tone, the major third's brighter character underscores its role in creating optimistic and resolved auditory experiences.

Tuning System Variations

In just intonation, the major third achieves its purest form with a frequency ratio of 5:4, corresponding to approximately 386.3 cents, which produces a highly consonant interval well-suited to the natural adjustments made by vocalists and string players during performance. This tuning system prioritizes simple integer ratios derived from the harmonic series, minimizing beats and enhancing harmonic stability in contexts like a cappella singing or unaccompanied strings. Pythagorean tuning, constructed by stacking pure perfect fifths (3:2 ratio, 702 cents each), results in a major third of about 408 cents (81:64 ratio), which is noticeably wider than the just version and introduces a sharper, less consonant quality. This deviation, known as the syntonic comma (approximately 21.5 cents), arises because the tuning favors fifths over thirds, often necessitating "wolf" intervals—such as a compromised fifth—in remote keys to close the circle of fifths. Equal temperament compromises the major third to exactly 400 cents to ensure uniform semitones across all keys, introducing a slight dissonance compared to but enabling modulation without retuning. This 14-cent flattening from the Pythagorean third (or 13.7-cent from just) creates a balanced but less pure , widely adopted in modern keyboard instruments for its versatility. Other historical systems like meantone and Werckmeister temperaments offer variations that temper this compromise. Quarter-comma meantone purifies the major third to around 386.3 cents in common keys by fifths, though it produces wider "wolf" thirds (e.g., ~427 cents) in distant keys, limiting its use to fewer tonalities. Werckmeister III, a , yields major thirds ranging from 390.2 cents (e.g., C-E) to 407.8 cents (e.g., F#-A#), providing usable purity across all keys without extreme wolves, bridging toward .
Tuning SystemMajor Third Size (cents)RatioKey Characteristics
Just Intonation386.35:4Purest consonance; ideal for vocals/strings.
Pythagorean40881:64Wider, sharper; favors fifths, creates wolves elsewhere.
Quarter-Comma Meantone~386.3 (common keys)~5:4Pure in select keys; wolves in remote ones.
Werckmeister III390.2–407.8VariesBalanced across keys; no extreme wolves.
400(2^{4/12})Uniform but slightly dissonant; fully chromatic.

Theoretical and Practical Applications

Role in Scales and Chords

In the , the forms the interval between the first and third scale degrees, establishing the tonal foundation of the major mode. For instance, in the scale, the notes and E create this major third, which distinguishes the major scale from its minor counterpart by providing a sense of and resolution. This interval is essential for defining the scale's overall character, as it appears in key positions such as the tonic triad. Within triads, the major third serves as the interval from the root to the third in a root-position major chord, differentiating it from the minor third in minor chords. In the C major triad (C-E-G), the major third between C and E imparts a consonant, stable quality to the harmony, forming the basis of major tonality in Western music. This structure is evident in the tonic, subdominant, and dominant triads of the major scale, where the major third contributes to the chord's uplifting sonority. In extended harmonies, the major third plays a key role in seventh chords, particularly the major-major seventh, where it spans from the to the third (e.g., C-E in Cmaj7: C-E-G-B), maintaining the major quality while adding tension through the major seventh above the . Chord inversions further highlight its function in ; for example, in first inversion (e.g., E-G-C for ), the major third becomes the bass note, facilitating smoother transitions between chords by allowing stepwise motion in inner voices. This positioning aids in common-practice principles, where the third's placement minimizes parallel octaves and promotes contrary motion. Notational conventions reflect these roles through chord symbols such as "Cmaj" or "CΔ" for major triads and seventh chords, indicating the presence of the major third in lead sheets and scores. Scale degree analysis, using (e.g., I for the tonic major triad), underscores the major third's position as the ^3 in the , essential for .

Historical Development

In , particularly within the system attributed to around the 6th century BCE, the major third was derived from stacking four perfect fifths (81:64 ratio), resulting in a sharp interval approximately 22 cents wider than the just major third (). This mistuning caused the major third to beat 6–32 times per second when sounded harmonically, rendering it severely dissonant and thus avoided in simultaneous use, though it was melodically tolerable in scalar contexts. The major third's ratio (81:64) was viewed as imperfect compared to the pure consonances of octaves, fifths, and fourths, reflecting a mathematical emphasis on small integer ratios that prioritized perfect intervals over thirds. During the medieval period, the major third transitioned to classification as an imperfect consonance in and early treatises, marking a gradual acceptance beyond mere melodic roles. In the , d'Arezzo's Micrologus categorized intervals into perfect (unisons, fourths, fifths, octaves) and imperfect (major and minor thirds, major sixths), allowing thirds in parallel but restricting their use to avoid dissonance with prevailing . By the late , English practices increasingly incorporated major thirds as consonant intervals, influencing continental developments in where they served as supportive harmonies in discant and motets. The brought a pivotal shift, with the major third fully embraced in polyphonic textures due to advancements in tuning that enhanced its purity. Composers like employed major thirds prominently in motets such as [Ave Maria... virgo serena](/page/Ave_Maria_ ..._Virgo_serena) (c. 1475–1480), where they form the basis of triadic harmonies tuned syntonically (5:4 ratio) to minimize beating and support imitative . This acceptance was facilitated by meantone temperaments, proposed by Bartolomé Ramos de Pareja in 1482 and refined by in 1558, which tempered fifths to yield just major thirds, favoring the harmonic sweetness of thirds and sixths over the sharpness of Pythagorean intervals in increasingly complex vocal polyphony. From the Baroque era onward, the major third achieved central status in tonal harmony, underpinning major triads and key definitions across all modulating contexts. Johann Sebastian Bach's (1722, 1742) exemplifies this integration, using well-tempered systems to explore major thirds in preludes and fugues through all 24 keys, enabling fluid tonal progressions where the interval defines chord quality and resolution. In the , even atonal compositions repurposed the major third devoid of tonal function, as in atonal triads featuring augmented fourths or "major" variants for coloristic effects, seen in works by composers like who treated it as one interval among equals in pitch-class sets.

References

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