"In music theory, an interval is a difference in pitch between two sounds."
Understanding what intervals are, how to measure them, and how to identify them by ear.
Pitch: A musical tone's measurable frequency level or height.
Octaves: An interval with a frequency ratio of 2:1; two pitches occupy the same name.
Half Steps: The smallest distance between two distinct pitches in Western music.
Whole Steps: Any interval that consists of two half steps.
Sharps and Flats: Musical symbols that indicate the alteration of the pitch of a note.
Enharmonic Notes: Two different names given to the same pitch.
Intervals: The distance between two pitches measured in half steps.
Major Intervals: An interval of two whole steps.
Minor Intervals: An interval of one-and-a-half-tone steps.
Perfect Intervals: The most stable and consonant intervals.
Augmented Intervals: An interval that is one half-step larger than a perfect interval.
Diminished Intervals: An interval that is one half-step smaller than a perfect interval.
Inversion: Flipping a musical interval upside-down by moving the higher note to a lower octave.
Compound Intervals: Large intervals that consist of octaves and smaller intervals combined.
Ear Training: Developing the ability to recognize intervals by ear.
Perfect intervals: Intervals between two notes that are either both major or both minor (P1, P4, P5, P8).
Major intervals: Intervals that are wider than perfect intervals by one half step (M2, M3, M6, M7).
Minor intervals: Intervals that are narrower than perfect intervals by one half step (m2, m3, m6, m7).
Augmented intervals: Intervals that are wider than major intervals by one half step (aug1, aug2, aug3, aug4, aug5, aug6, aug7, aug8).
Diminished intervals: Intervals that are narrower than minor intervals by one half step (dim2, dim3, dim4, dim5, dim6, dim7, dim8).
Compound intervals: Intervals that are larger than an octave (P9, M9, m9, aug9, dim9, P10, M10, m10, aug10, dim10, etc.).
Harmonic intervals: Intervals in which the notes are played together simultaneously (unison, 2nd, 3rd, 4th, 5th, 6th, 7th, octave).
Melodic intervals: Intervals in which the notes are played sequentially (ascending or descending).
Enharmonic intervals: Two different names for the same interval (for example, F# and Gb are enharmonic equivalents of each other).
Inverted intervals: An interval that has its order of notes reversed (for example, the inversion of a major 3rd is a minor 6th).
"An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody."
"An interval may be described as vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord."
"In Western music, intervals are most commonly differences between notes of a diatonic scale."
"Intervals between successive notes of a scale are also known as scale steps."
"The smallest of these intervals is a semitone."
"Intervals smaller than a semitone are called microtones."
"Some of the very smallest ones are called commas."
"Commas describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes."
"Intervals can be arbitrarily small, and even imperceptible to the human ear."
"In physical terms, an interval is the ratio between two sonic frequencies."
"Any two notes an octave apart have a frequency ratio of 2:1."
"Even though the human ear perceives this as a linear increase in pitch."
"Intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio."
"The most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.)."
"These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled."
"The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals."
"Examples include the minor third or perfect fifth."
"Spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals."
"The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonically equivalent notes such as G–G♯ and G–A♭."