3 ms·

A little more info for those who are curious: The perfect intervals (unison, 4th, 5th, 8ve) can be modified by being diminished or augmented, which shrinks or e

A little more info for those who are curious: The perfect intervals (unison, 4th, 5th, 8ve) can be modified by being diminished or augmented, which shrinks or expands the interval by one half step. The other intervals (2nd, 3rd, 6th, 7th) can be either diminished, minor, major, or augmented. The major interval is what you'd get if you're measuring the intervals on a major (Ionian) scale; minor is -1 half step, dimished -2, augmented +1. My intuition about which intervals are major / minor and which are diminished comes from the intervals that create the differences between the major and minor scales. The major scale uses all major intervals; natural minor uses minor 3rd, 6th and 7th; Dorian minor has a major 6th, and harmonic minor a major 7th. That still doesn't account for why the 2nd is called major / minor -- you could argue that you use it in Phrygian mode, but then you'd have to acknowledge that you use the diminished 5th in Locrian mode, so why not call that the major / minor 5th? (But almost no music is written in the Locrian mode). Another intuition is that the fourth and fifth are the most consonant intervals (because the ratio of their frequencies is simplest) and so an adjustment of a half step is more of an increase in dissonance than a similar adjustment on another interval. Finally, non-perfect 4th and 5th intervals are simply encountered much less frequently than other intervals (with the exception of the tritone between the 3rth and 7th of a dominant V chord, the characteristic dissonance that sets up the V-I authentic cadence).

HillOBeans 12y ago
Notice also that in major keys, there is only a half-step between the 3rd and the 4th tones, meaning the diminished 4th interval will sound as a major 3rd. The augmented 4th (or diminished 5th - a.k.a tritone) perfectly splits the octave in this tuning system. You can go up or down by an augmented 4th or diminished 5th as many times as you want and only ever be playing the same two note-names.
theOnliest 12y ago
Your intuition is basically right: perfect octaves/fifths/fourths are called "perfect" because they have the most acoustically pure: 2:1, 3:2, and 4:3, respectively. They're also the oldest consonances, described supposedly by Pythagoras but extant in the Euclidean "Sectio canonis" (~3rd C. BCE). The other intervals weren't considered consonant until much later (the middle ages), and didn't get their "major/minor" names until a bit later, in the Renaissance. Before this, they were known by their Latin names (M3 = ditone, m3 = semiditone, and so on). The m2 was found in (at least) two forms until the advent of equal temperament, usually known as the major and minor semitones. The "major" intervals are those found in the major scale (M2, M3, M6, M7). The minor intervals aren't named in relation to the minor scale, but rather in relation to their major equivalents (a minor second is lower than a major second). "Minor" comes from "molle," which is "soft": the major third is "softened" to become the minor third, and so on.
memset 12y ago
One neat property of "perfect" intervals is that, when you invert them, they remain perfect! Perfect unison inverts to unison. Perfect octave inverts to an octave. Perfect 4th (C to F) inverts to a perfect 5th! And vice-versa. Contrast to a major third, or major second, which, when inverted, becomes a minor 6th (or minor seventh.) That is, the interval quality of perfects remains the same, where as major/minor/augmented/diminished intervals change qualities.
mrbrowning 12y ago
It's worth noting that the perfect fourth, when it involves the bass, is considered a dissonance in Common Practice music,* and even in the freer harmonic contexts of twentieth century music it's a bit of a cipher: it acts as a dissonance in relatively consonant contexts and as a consonance in relatively dissonant contexts. * If you read Schoenberg's Harmonielehre, he has some pretty idiosyncratic but somewhat plausible theories about why the 6/4 chord is dissonant, involving the overtones of the bass being diatonic (say we're talking about C 6/4 and the relevant overtones being B and D) but also dissonant with regards to the nominal root of C. That the 6/3 chord is relatively consonant is explained by the fact that the overtones of the bass in that arrangement suggest a sufficiently distant key so as not to plausibly oppose the sounding fundamentals. I think the more likely explanation is the historical one, which treats the 6/4 as the reification of the frequently used motif of a suspension from the pre-dominant harmony over the dominant bass that then passes downward to the goal tones (in C major, the archetypal lines would be A -> G -> F -> E and F -> E -> D -> C over a bassline like F (or D) -> G -> G -> C). The 6/4 chord's dissonance, then, is merely a result of the fact that its appearance came to unequivocally imply a certain resolution.

HillOBeans 12y ago

Notice also that in major keys, there is only a half-step between the 3rd and the 4th tones, meaning the diminished 4th interval will sound as a major 3rd. The augmented 4th (or diminished 5th - a.k.a tritone) perfectly splits the octave in this tuning system. You can go up or down by an augmented 4th or diminished 5th as many times as you want and only ever be playing the same two note-names.

theOnliest 12y ago

Your intuition is basically right: perfect octaves/fifths/fourths are called "perfect" because they have the most acoustically pure: 2:1, 3:2, and 4:3, respectively. They're also the oldest consonances, described supposedly by Pythagoras but extant in the Euclidean "Sectio canonis" (~3rd C. BCE). The other intervals weren't considered consonant until much later (the middle ages), and didn't get their "major/minor" names until a bit later, in the Renaissance. Before this, they were known by their Latin names (M3 = ditone, m3 = semiditone, and so on). The m2 was found in (at least) two forms until the advent of equal temperament, usually known as the major and minor semitones. The "major" intervals are those found in the major scale (M2, M3, M6, M7). The minor intervals aren't named in relation to the minor scale, but rather in relation to their major equivalents (a minor second is lower than a major second). "Minor" comes from "molle," which is "soft": the major third is "softened" to become the minor third, and so on.

memset 12y ago

One neat property of "perfect" intervals is that, when you invert them, they remain perfect! Perfect unison inverts to unison. Perfect octave inverts to an octave. Perfect 4th (C to F) inverts to a perfect 5th! And vice-versa. Contrast to a major third, or major second, which, when inverted, becomes a minor 6th (or minor seventh.) That is, the interval quality of perfects remains the same, where as major/minor/augmented/diminished intervals change qualities.

mrbrowning 12y ago

It's worth noting that the perfect fourth, when it involves the bass, is considered a dissonance in Common Practice music,* and even in the freer harmonic contexts of twentieth century music it's a bit of a cipher: it acts as a dissonance in relatively consonant contexts and as a consonance in relatively dissonant contexts. * If you read Schoenberg's Harmonielehre, he has some pretty idiosyncratic but somewhat plausible theories about why the 6/4 chord is dissonant, involving the overtones of the bass being diatonic (say we're talking about C 6/4 and the relevant overtones being B and D) but also dissonant with regards to the nominal root of C. That the 6/3 chord is relatively consonant is explained by the fact that the overtones of the bass in that arrangement suggest a sufficiently distant key so as not to plausibly oppose the sounding fundamentals. I think the more likely explanation is the historical one, which treats the 6/4 as the reification of the frequently used motif of a suspension from the pre-dominant harmony over the dominant bass that then passes downward to the goal tones (in C major, the archetypal lines would be A -> G -> F -> E and F -> E -> D -> C over a bassline like F (or D) -> G -> G -> C). The 6/4 chord's dissonance, then, is merely a result of the fact that its appearance came to unequivocally imply a certain resolution.