Note 1
Note 2
Interval
P5
Ratio: 3:2 | Consonant
دليل مفصل قريبًا
نعمل على إعداد دليل تعليمي شامل لـ Music Interval Calculator. عد قريبًا للاطلاع على الشروحات خطوة بخطوة والصيغ والأمثلة الواقعية ونصائح الخبراء.
The Music Interval Calculator determines the interval name, semitone count, frequency ratio, consonance level, and diatonic function of the interval between any two musical notes. A musical interval is the distance in pitch between two notes, measured in semitones (chromatic half steps) and named according to music theory conventions that include both a quality (perfect, major, minor, augmented, diminished) and a size number (unison, second, third, fourth, fifth, sixth, seventh, octave). Intervals are foundational to all aspects of Western music theory — they define the structure of scales (a major scale is built from the intervals W-W-H-W-W-W-H), the character of chords (a major chord contains a major third and a perfect fifth), the function of melody (a leap of a perfect fourth has a different character than a step of a minor second), and the degree of consonance or dissonance (intervals are classified from highly consonant — unison, octave, perfect fifth — to highly dissonant — minor second, tritone). The frequency ratio between two notes determines whether they produce beating (dissonance) or ring cleanly together (consonance). Intervals with simple frequency ratios (2:1 for octave, 3:2 for perfect fifth, 4:3 for perfect fourth) are most consonant. In equal temperament, these ratios are approximated but not exact, creating slight beating even in 'consonant' intervals. The calculator covers all intervals within two octaves, identifies enharmonic equivalents (augmented fourth = diminished fifth = tritone), and provides the diatonic interval name as it appears in each major and minor scale context.
Interval (semitones) = |Note2 MIDI - Note1 MIDI| Frequency Ratio = 2^(semitones/12) Interval Name: determined by scale degree distance and accidental quality
- 1Step 1: Identify the two notes (e.g., C4 and G4).
- 2Step 2: Count the semitones between them (C to G = 7 semitones).
- 3Step 3: Count the diatonic letter steps (C to G spans 5 letters: C, D, E, F, G → a 'fifth').
- 4Step 4: Determine quality: a fifth with 7 semitones is a 'perfect fifth.'
- 5Step 5: Calculate frequency ratio: 2^(7/12) ≈ 1.4983.
- 6Step 6: Classify consonance: perfect fifth is highly consonant (imperfect consonance in classical theory).
- 7Step 7: Identify diatonic function — in C major, a C-G fifth is scale degrees 1 and 5 (tonic to dominant).
The perfect fifth is the most important interval in Western harmony. It is the interval of the dominant relationship and has been the basis of two-voice counterpoint since medieval music.
The tritone divides the octave exactly in half. In medieval music it was called 'diabolus in musica' (the devil in music) due to its harsh dissonance. In jazz, it is the defining interval of dominant 7th chords.
The minor third is the interval that distinguishes minor from major chords. It has a frequency ratio close to 6:5 = 1.2 in just intonation. A minor chord root to its third.
The major sixth is an imperfect consonance, considered pleasant. Its inversion is the minor third. Famous melodic examples: the opening of 'My Bonnie Lies Over the Ocean.'
The minor second is the smallest standard interval in equal temperament. It produces strong dissonance and beating due to its complex frequency ratio. It is used dramatically in horror film scores.
Professionals in finance and lending use Music Interval Calc 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 Interval Calc 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 Interval Calc 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 Interval Calc 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 interval calculator 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 interval calculator 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 interval calculator 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.
| Semitones | Interval Name | Abbreviation | ET Ratio | JI Ratio | Consonance |
|---|---|---|---|---|---|
| 0 | Perfect Unison | P1 | 1.0000 | 1:1 | Perfect consonance |
| 1 | Minor Second | m2 | 1.0595 | 16:15 | Sharp dissonance |
| 2 | Major Second | M2 | 1.1225 | 9:8 | Mild dissonance |
| 3 | Minor Third | m3 | 1.1892 | 6:5 | Imperfect consonance |
| 4 | Major Third | M3 | 1.2599 | 5:4 | Imperfect consonance |
| 5 | Perfect Fourth | P4 | 1.3348 | 4:3 | Perfect consonance* |
| 6 | Tritone | TT | 1.4142 | √2 | Maximum dissonance |
| 7 | Perfect Fifth | P5 | 1.4983 | 3:2 | Perfect consonance |
| 8 | Minor Sixth | m6 | 1.5874 | 8:5 | Imperfect consonance |
| 9 | Major Sixth | M6 | 1.6818 | 5:3 | Imperfect consonance |
| 10 | Minor Seventh | m7 | 1.7818 | 16:9 | Mild dissonance |
| 11 | Major Seventh | M7 | 1.8877 | 15:8 | Sharp dissonance |
| 12 | Perfect Octave | P8 | 2.0000 | 2:1 | Perfect consonance |
What makes an interval consonant or dissonant?
Consonance and dissonance are determined by the complexity of the frequency ratio between two notes. Simple integer ratios (2:1, 3:2, 4:3) produce consonance because the overtones of the two notes align frequently, creating a stable, beating-free sound. Complex ratios (like 45:32 for an equal-temperament tritone) produce many non-aligning overtones that create rapid beating, perceived as dissonance. Historical and cultural definitions of consonance also matter — the major third was considered dissonant in medieval music but is fundamental to Renaissance and later harmony.
What is the difference between harmonic and melodic intervals?
A harmonic interval is when two notes are played simultaneously (a chord or dyad). A melodic interval is when two notes are played successively (one after the other, as in a melody). The same interval — say, a perfect fifth — sounds different in these contexts. As a harmonic interval, a fifth rings out openly and powerfully. As a melodic interval (a fifth leap in a melody), it creates a sense of space and emphasis, like the opening of Beethoven's Fifth Symphony or the 'Star Wars' theme.
What is an inversion of an interval?
Inverting an interval means moving the lower note up an octave (or the upper note down an octave), changing the interval to its complementary form. The sum of an interval and its inversion is always 9 (in terms of scale degree numbers) and 12 semitones (an octave). So: minor second (1 semitone) inverts to major seventh (11 semitones); major third (4 semitones) inverts to minor sixth (8 semitones); perfect fourth (5 semitones) inverts to perfect fifth (7 semitones). Perfect intervals invert to perfect intervals. Major intervals invert to minor, and vice versa.
What is the tritone and why is it so important in music?
The tritone (6 semitones, augmented fourth or diminished fifth) is the only interval that divides the octave exactly in half. It has a frequency ratio of √2 ≈ 1.4142, which is one of the most irrational ratios possible. This extreme irrationality maximizes beating between overtones, creating maximum dissonance. The tritone is the defining tension interval in dominant seventh chords — the interval between the third and seventh of a G7 chord (B-F) is a tritone that strongly wants to resolve to a consonant interval. This resolution drives the entire tonal system of Western music.
What are compound intervals?
A compound interval spans more than one octave. A ninth (14 semitones) is a compound second (9th = octave + second). A tenth is a compound third. A twelfth is a compound fifth. Compound intervals have the same harmonic quality as their simple counterparts — a major ninth sounds 'like' a major second but in a wider register. In harmonic analysis, compound intervals are usually reduced to their simple equivalents (a 9th chord contains a 2nd above the octave, but we call it a 9th for voice-leading and naming clarity).
How do intervals define chord quality?
Every chord is defined by the intervals between its notes, measured from the root. A major chord = major third (4 semitones) + perfect fifth (7 semitones). A minor chord = minor third (3 semitones) + perfect fifth (7 semitones). A diminished triad = minor third + diminished fifth (6 semitones). An augmented triad = major third + augmented fifth (8 semitones). Understanding these interval stacks allows you to build any chord from any root on any instrument.
What is enharmonic equivalence in intervals?
Enharmonic intervals are intervals that are spelled differently but sound identical (have the same number of semitones). The augmented fourth (C to F#, 6 semitones) and the diminished fifth (C to Gb, 6 semitones) are enharmonic equivalents — they are both tritones but notated differently depending on context. In C major, C to F# is an augmented fourth (F# goes against the key signature), while C to Gb might appear in certain chromatic or modulating contexts. The correct spelling depends on the harmonic function.
How are intervals used in counterpoint?
Counterpoint — the art of combining independent melodic lines — is governed largely by interval rules. In strict species counterpoint (as taught by Johann Joseph Fux and used in Bach's style), consonant intervals (unisons, thirds, fifths, sixths, octaves) are used freely, while dissonant intervals (seconds, fourths, sevenths, tritones) must be approached and resolved according to specific rules. Parallel perfect fifths and octaves between voice parts are forbidden in classical counterpoint because they reduce voice independence. These rules form the basis of Western harmonic practice from 1400–1900.
نصيحة احترافية
Memorize interval sounds by associating them with famous melodic examples: Perfect fourth = 'Here Comes the Bride'; Perfect fifth = 'Star Wars' theme; Minor second = 'Jaws' theme; Major sixth = 'My Bonnie Lies Over the Ocean'; Octave = 'Somewhere Over the Rainbow.'
هل تعلم؟
The tritone was so feared in medieval church music that composers actively avoided it. The Latin phrase 'Mi contra Fa est diabolus in musica' (Mi against Fa is the devil in music) described the prohibition against the augmented fourth. Yet this same interval became the cornerstone of jazz harmony in the 20th century, prized for its tension and resolution character.
احصل على نصائح الرياضيات الأسبوعية
انضم إلى مشتركي 12,000+ الذين يحصلون على نصائح حول الآلة الحاسبة كل أسبوع.