Interval names

[mhoward]

The Musician's Institute book on Harmony and Theory, and also their Guitar Fretboard Workout, name the intervals of the major scale as: perfect unison, major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, and perfect octave. But I can't find any explanation of why some are called major and some perfect. Of course I also consulted Mike Dodge's great interval series, but although he refers to "perfect 5th" in his intervals lesson 2, I don't see any other mention of "perfect".

 

Can anybody explain the difference between a perfect interval and a major one?

[FFStratophile]

For every "major", there is a "minor", as in like minor 3rd, minor 6th. Perfects don't have anything like that.

[mhoward]

 

For every "major", there is a "minor", as in like minor 3rd, minor 6th. Perfects don't have anything like that.

 

 

Why not? Perfects can be diminished... how is that different? A major 3rd is 4 frets or half-steps, isn't it, like between R and 3? A minor 3rd would be 3 half-steps, like between 2 and 4. So why don't we have a major 4th of 6 half-steps between 4 and 7, and a minor 4th of 5 half-tones between say, 3 and 6? A diminished 4th is actually the equivalent of a augmented major 3rd.

[Mark Wein]

Why not? Perfects have diminished... how is that different? A major 3rd is 4 frets or half-steps, isn't it, like between R and 3? A minor 3rd would be 3 half-steps, like between 2 and 4. So why don't we have a major 4th of 6 half-steps between 4 and 7, and a minor 4th of 5 half-tones between say, 3 and 6? A diminished 4th is actually the equivalent of a augmented major 3rd.

 

Actually, a diminished 4th would be the same pitch as a major third. Your question is one that I have tried to answer for years, and now I feel like an idiot since I did a small online search and immediately found this:

• Unison, fourth, fifth, octave. These intervals may be perfect, augmented, or diminished.

  • They are called perfect because of their extremely simple pitch relationships resulting in a high degree of consonance and also because when they are inverted they remain perfect (a perfect fourth inverts to a perfect fifth and vice versa).

  • A perfect fourth is five semitones.

  • A perfect fifth is seven semitones.

  • A perfect octave is twelve semitones.

  • A perfect unison occurs between notes of the same pitch, so it is zero semitones.

  • In each case, an augmented interval contains one more semitone, a diminished interval one fewer.

• Second, third, sixth, seventh. These intervals may be major, minor, augmented, or diminished.

  • A tritone is six semitones.

  • Major seconds are two semitones, also called a whole step, minor seconds are one semitone, also called a half step.

  • Major thirds are four semitones, minor thirds are three semitones.

  • Major sixths are nine semitones, minor sixths are eight semitones.

  • Major sevenths are eleven semitones, minor sevenths are ten semitones.

  • In each case, the augmented interval contains one semitone more than the major interval, and the diminished interval one semitone fewer than the minor interval.

It is possible to have doubly-diminished and doubly-augmented intervals, but these are quite rare.

The name of an interval cannot be determined by counting semitones alone. There are four semitones between B and E? but this interval is not a major third, but rather a diminished fourth, a relatively rare interval (but which does appear naturally as part of the harmonic minor scale). In equal-tempered tuning, as on a piano, these intervals are indistinguishable by sound, but the diatonic function of the notes incorporated might be very different.

 

 

 

Hope it helps!

[mhoward]

Oh, that's very good... Your kung fu is strong! I like that explanation of the term "perfect":

They are called perfect because of their extremely simple pitch relationships resulting in a high degree of consonance and also because when they are inverted they remain perfect (a perfect fourth inverts to a perfect fifth and vice versa)....

I had to look up what it meant to invert an interval, and took your lead by checking wikipedia. In case there's anyone else curious about this, here's how they define it:

"An interval is inverted by raising or lowering either of the notes the necessary number of octaves, so that both retain their names (pitch class) and the one which was higher is now lower and vice versa, changing the perspective or relation between the pitch classes. For example, the inversion of an interval consisting of a C with an E above it is an E with a C above it - to work this out, the C may be moved up, the E may be lowered, or both may be moved.

Under inversion, perfect intervals remain perfect, major intervals become minor and the reverse, augmented intervals become diminished and the reverse."

[Mark Wein]

Oh, that's very good... Your kung fu is strong! I like that explanation of the term "perfect":

 

I feel bad that I really didn't know the correct answer right off the bat...I teach this stuff all the time, but this simple question is something that I think most of us just take for granted as "just the way it is"...I never had it explained to me in college, and never really researched it on my own...I guess you never stop learning!

[gennation]

Just look at the Circle of 5th's....5th's moving clockwise, 4th moving counter clockwise. One each side of a tonal center you have the 4th one step counter clockwise and the 5th clockwise. And each time you move another spot out you are still moving a 5th or a 4th from where you are. 5th's up, 4th's down.

 

4th's and 5th's are a strong constant in western music. There's a few ways to pick out how either on these notes is so common, or perfect, against a Root.

 

The 5th is also the same note in a basic triad or chord regardless whether it's Major or Minor chord/triad. C and Cm both contain the same 5th.

 

These two notes also stay consistent between the Major and Natural Minor scales. Although the the 2nd does also. So, that's not a "perfect" explanation

[mhoward]

The name of an interval cannot be determined by counting semitones alone. There are four semitones between B and E? but this interval is not a major third, but rather a diminished fourth, a relatively rare interval (but which does appear naturally as part of the harmonic minor scale ).

 

 

I was just reviewing this info again to try to internalize it. I think you must have had an Eb here that turned into "E?". What are the conditions when you can't figure out the interval by counting semitones? What's the difference between a M3 and diminished P4 which, as you pointed out earlier, have the same pitch?

[Mark Wein]

I was just reviewing this info again to try to internalize it. I think you must have had an Eb here that turned into "E?". What are the conditions when you can't figure out the interval by counting semitones? What's the difference between a M3 and diminished P4 which, as you pointed out earlier, have the same pitch?

 

Yeah..the Eb somehow was turned into a "?" in your quote...it shows up as a flat when I look at my original message (That part was copied from the wikipedia entry)

 

To be honest with you, outside of a theory book I have never seen a practical usage of a "diminished 4th"...has anyone ever run across this?

 

I assume that there is a reason for the diminished 4th, but I really can't tell you what it is...

[jlampson]

Consider this hearsay, but I seem to remember some theory tape stating that a "non-perfect" 5th is the same interval as a perfect 4th. I've been calling them 4ths, 5ths, etc., for so long that I, too, took it for granted that it was anything other than what it is.

John