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Music Theory Interval Calculator에 대한 종합 교육 가이드를 준비 중입니다. 단계별 설명, 공식, 실제 예제 및 전문가 팁을 곧 확인하세요.
The Music Theory Interval Calculator provides a comprehensive analysis of diatonic and chromatic intervals within tonal and modal harmonic systems, identifying not just the interval name and semitone count but the specific harmonic function, voice-leading implications, and theoretical context of any interval within a given key. While the basic Music Interval Calculator identifies interval names from two notes, this advanced tool goes deeper into the functional theory of intervals — analyzing how a specific interval functions within a key (for example, the tritone between the 4th and 7th scale degrees of a major scale is the characteristic dissonance of the dominant seventh chord that drives V7 to I resolution), how the same interval functions differently in different harmonic contexts (an ascending minor third as a root-to-minor-third versus as a 5th-to-7th of a dominant chord), and what voice-leading resolutions are expected or available for each interval type. It also covers compound intervals (ninths, tenths, elevenths, thirteenths), enharmonic reinterpretation (how the same interval can be respelled and recontextualized for modulation), and the historical theoretical frameworks for classifying intervals from Pythagorean theory through Renaissance modal theory, Common Practice tonal harmony, jazz functional harmony, and post-tonal pitch-class theory. This tool is designed for advanced music students, composers, arrangers, and music teachers who need a rigorous theoretical framework alongside practical interval identification. The calculator covers all interval sizes from unison through double octave, all interval qualities (perfect, major, minor, augmented, diminished, doubly augmented, doubly diminished), and their enharmonic equivalents across all 12 tonal centers.
Diatonic Interval Number = Letter distance + 1 (C to E = 3rd) Semitone Count determines Quality: e.g., 4 semitones = Major 3rd, 3 semitones = Minor 3rd Harmonic Function = Scale Degree relationship within the key Voice Leading: Dissonant intervals resolve by half-step or whole-step motion
- 1Step 1: Input two notes to identify the basic interval (number and quality).
- 2Step 2: Specify the key context for harmonic function analysis.
- 3Step 3: Calculate scale degrees of both notes within the key.
- 4Step 4: Identify the diatonic function (e.g., 3-7 in C major = E-B = major 7th, part of CMaj7 chord).
- 5Step 5: Classify consonance/dissonance classification (historical and contemporary).
- 6Step 6: Identify expected voice-leading resolution for dissonant intervals.
- 7Step 7: Provide enharmonic equivalents and their reinterpretation possibilities.
- 8Step 8: List chords that characteristically contain this interval.
In C major, B (leading tone, scale degree 7) and F (subdominant, scale degree 4) form a tritone. This interval is the defining tension of the G7 chord (V7). Resolution: B resolves up to C (leading tone to tonic), F resolves down to E (4th degree to 3rd). Together they resolve to C-E, the tonic triad.
C to E is the root-to-third of the tonic triad. As an imperfect consonance, it is stable but not as neutral as perfect intervals. In classical voice leading, the major third between bass and upper voice often signals a first-inversion chord.
D-F is the root and minor third of the supertonic minor chord (Dm in C major). As a diatonic minor third, it functions as the basis of the pre-dominant harmony that frequently leads to V (G major) before returning to I.
G-F is the root to minor seventh of the G7 dominant chord. The minor seventh above the dominant root is a mild dissonance that resolves to the third of the tonic (E in C major). G stays or resolves to E; F resolves down to E. This 5–7 interval is the engine of dominant-tonic resolution.
The augmented sixth (Ab to F#) is enharmonically identical to a minor seventh (10 semitones) but functions as a dramatic pre-dominant harmony. Both notes resolve outward by half step to the octave G: Ab resolves down to G, F# resolves up to G, producing a unison or octave on the dominant.
Professionals in finance and lending use Music Theory Intervals as part of their standard analytical workflow to verify calculations, reduce arithmetic errors, and produce consistent results that can be documented, audited, and shared with colleagues, clients, or regulatory bodies for compliance purposes.
University professors and instructors incorporate Music Theory Intervals into course materials, homework assignments, and exam preparation resources, allowing students to check manual calculations, build intuition about input-output relationships, and focus on conceptual understanding rather than arithmetic.
Consultants and advisors use Music Theory Intervals to quickly model different scenarios during client meetings, enabling real-time exploration of what-if questions that would otherwise require returning to the office for detailed spreadsheet-based analysis and reporting.
Individual users rely on Music Theory Intervals for personal planning decisions — comparing options, verifying quotes received from service providers, checking third-party calculations, and building confidence that the numbers behind an important decision have been computed correctly and consistently.
Extreme input values
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in music theory intervals calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
Assumption violations
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in music theory intervals calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
Rounding and precision effects
In practice, this edge case requires careful consideration because standard assumptions may not hold. When encountering this scenario in music theory intervals calculations, practitioners should verify boundary conditions, check for division-by-zero risks, and consider whether the model's assumptions remain valid under these extreme conditions.
| Interval | Semitones | Scale Degrees (C major) | Harmonic Function | Voice Leading |
|---|---|---|---|---|
| Perfect Unison | 0 | 1–1 or any same | Stability, unison doubling | No resolution needed |
| Major 2nd | 2 | 1–2, 2–3, etc. | Stepwise motion, mild dissonance | Steps down or up by step |
| Minor 3rd | 3 | 2–4 (D–F), 3–5 (E–G) | Minor chord member | Often stable in chord |
| Major 3rd | 4 | 1–3 (C–E), 4–6 (F–A) | Major chord member, imperfect consonance | Stable; tonic-3rd very stable |
| Perfect 4th | 5 | 1–4 (C–F) | Pre-dominant, ambiguous above bass | Contextual — resolves down above bass |
| Tritone (A4/d5) | 6 | 4–7 (F–B) or 7–4 (B–F) | Maximum tension, dominant function | Resolves outward or inward by half-step |
| Perfect 5th | 7 | 1–5 (C–G), 5–2 (G–D) | Open consonance, harmonic foundation | Highly stable, no resolution needed |
| Minor 6th | 8 | 3–1 (E–C octave down) | Imperfect consonance, inverted major 3rd | Stable, often in first inversion |
| Major 6th | 9 | 1–6 (C–A) | Warm consonance, inverted minor 3rd | Stable, typical in parallel 3rds/6ths |
| Minor 7th | 10 | 5–4 (G–F), dominant 7th | Mild dissonance, resolves to 3rd (E) | Resolves downward (F→E) |
| Major 7th | 11 | 1–7 (C–B) | Sharp dissonance, leading tone | Resolves upward to tonic (B→C) |
| Perfect Octave | 12 | 1–1 (octave) | Perfect consonance, identity | No resolution needed |
What is the difference between a diatonic and chromatic interval?
A diatonic interval is one that occurs naturally between two notes of the same major or minor scale without any added accidentals. In C major, C to E is a diatonic major third. A chromatic interval involves at least one note that is not in the diatonic scale — C to Eb in C major is a chromatic (non-diatonic) minor third. In harmonic analysis, chromatic intervals often indicate borrowed chords, secondary dominants, modal mixture, or chromatic voice leading. The distinction matters for understanding the functional context of an interval.
What is interval inversion and why is it theoretically important?
Inverting an interval by moving one note by an octave produces the complementary interval — both always sum to the octave (12 semitones and 9 in generic number). Major inverts to minor and vice versa; perfect remains perfect; augmented inverts to diminished. This principle matters for voice leading analysis (an interval in the bass that inverts produces different harmonic implications), for understanding chord inversions (a root-position major third becomes a first-inversion minor sixth when the bass note moves up an octave), and for identifying inversionally related motive transformations in fugue and counterpoint.
What is enharmonic reinterpretation of intervals?
Enharmonic reinterpretation occurs when an interval is re-spelled to a different notation representing the same pitch content, which changes its theoretical context and functional implications. The most important example is the augmented sixth (A6) which is enharmonically identical to a minor seventh (m7) — both have 10 semitones. However, the augmented sixth (e.g., Ab to F#) resolves outward to a unison or octave, while the minor seventh (e.g., G to F) resolves inward (F resolves down). Composers like Schubert and Beethoven exploited this ambiguity for modulations, resolving an A6 as a Ger+6 chord in one key and reinterpreting it as a dominant seventh chord in another.
What are the Pythagorean, just, and equal temperament differences in interval ratios?
Each tuning system generates slightly different frequency ratios for the same named interval. The perfect fifth: Pythagorean = 3:2 (exactly 702 cents), Just = 3:2 (same), Equal Temperament = 700 cents (2 cents flat). The major third: Pythagorean = 81:64 (408 cents, quite sharp), Just = 5:4 (386 cents, pure), ET = 400 cents (14 cents flat of Pythagorean, 14 sharp of just). The just major third is the purest for choral and string music; ET is the most practical for keyboard instruments. Pythagorean tuning optimizes fifths at the expense of thirds. These differences, while small in cents, are perceivable in sustained choral or string quartet contexts.
How do intervals function differently in jazz versus classical harmony?
In classical functional harmony, intervals are analyzed primarily by their resolution tendency within a tonal context — dissonances must resolve, and the tritone especially demands resolution. In jazz harmony, many historically dissonant intervals are treated as stable consonances within extended chord vocabulary. The major 7th (11 semitones) is resolved in classical counterpoint but forms the stable top of a major seventh chord in jazz. The minor 9th (13 semitones) is harshly dissonant as a simple harmonic interval in classical voice leading (it should not appear between adjacent voices) but is comfortable in jazz voicings as a distributed tension note above a bass note 9 semitones below.
What is the concept of 'tendency tones' and how do they relate to intervals?
Tendency tones are scale degrees that have strong melodic and harmonic drive toward specific resolutions due to their interval relationship to the tonic and dominant. The leading tone (scale degree 7, one semitone below the tonic) has the strongest upward tendency — the half-step interval to the tonic creates strong melodic pull. The subdominant (scale degree 4) has a weaker downward tendency toward the mediant (scale degree 3). These tendencies operate at the interval level: any minor second creates half-step tension that wants to resolve. Any augmented interval (augmented 4th, augmented 6th) expands outward. Any diminished interval (diminished 5th, diminished 7th) contracts inward.
What are doubly augmented and doubly diminished intervals?
Doubly augmented intervals are two semitones wider than a perfect interval or one semitone wider than an augmented interval. A doubly augmented fourth (C to F##) has 7 semitones — enharmonically the same as a perfect fifth. These intervals are theoretically possible but extremely rare in standard tonal music, appearing only in highly chromatic voice leading or in specialized theoretical analysis. Doubly diminished intervals are correspondingly two semitones narrower than perfect. They arise in enharmonic notation of complex modulations and in theoretical systems but almost never appear in notated music as practical intervals.
How does harmonic function change across different modal contexts?
The same interval has different functional character in different modal contexts. In Dorian mode on D (D-E-F-G-A-B-C-D), the interval D-F is a minor third, but it is the tonic-to-minor-third of the Dorian tonic chord (Dm). In Mixolydian mode on G (G-A-B-C-D-E-F-G), the interval G-F is a minor seventh that is not the dissonant dominant seventh but the characteristic minor subtonic degree — stable within Mixolydian context. Modal analysis requires understanding which note is the tonal center before assigning harmonic function to any interval.
전문가 팁
Practice singing and playing every interval from memory. Start with unison, octave, and perfect fifth (the most consonant), then add major and minor thirds and sixths, then master major and minor seconds and sevenths, and finally the tritone. Ear training for intervals is the foundation of all advanced music listening and composition skills.
알고 계셨나요?
The interval of a perfect fifth (3:2 ratio) is so fundamental to human auditory perception that it was independently discovered and used as the basis of musical tuning in ancient Greece, ancient China, ancient India, and pre-Columbian Mesoamerica — with no cross-cultural contact between these civilizations. This universality suggests the perfect fifth is not culturally learned but is a perceptual truth rooted in the physics of sound and the architecture of the human auditory system.
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