Jan 1

Minor Fourths, Major Fifths

by Anton Schwartz

We’ve all been taught that most intervals are either major or minor… but that unisons, fourths and fifths are special intervals, considered “perfect.”

Let’s question that for a minute. I’m going to describe an alternative way of thinking about it that I think makes more sense. Not to convince anyone to adopt it—I’d say the standard terminology is more or less here to stay. But let’s consider an alternative just for the sake of shedding some sensible new light on harmonic ideas we take for granted. I think you’ll enjoy it.

The age-old terminology

Ok, so look at the circle of fifths:

CircleOfFifthsWeb IntervalsCFBbEbAbDbGbF#GDAEB

Let’s label each note by its “scale degree” in the key of C. In other words, the interval formed by each note when it is placed above C:

CircleOfFifthsWeb IntervalsP1P4m7m3m6m2d5A4P5M2M6M3M7

We’re using the standard abbreviations for intervals: perfect (P), major (M), minor (m), augmented (A) and diminished (d).

Notice how most of the notes on the right side are major (green) and most on the left side are minor (blue). The exceptions are the perfect intervals P4 and P5.

Revamping the age-old terminology

What if we were to rename our perfect fourth and fifth?
What if we called them the minor fourth and major fifth instead?

At the bottom of the circle is the tritone. Instead of calling that note the augmented fourth or diminished fifth, let’s call it the major fourth or minor fifth.

Here’s a summary of the changes:

  • perfect fourth → “minor fourth”
  • perfect fifth → “major fifth”
  • augmented fourth → “major fourth”
  • diminished fifth → “minor fifth”

Ok, so why on earth would we want to do all that?

For starters, look what it does to the circle of fifths:

CircleOfFifthsWeb IntervalsP1m4m7m3m6m2m5M4M5M2M6M3M7

Everything clockwise from the root—the “bright” sounds—are now considered major.

Everything counterclockwise from the root—the “dark” sounds—are now considered minor.

The tritone, which can be either bright (the augmented fourth) or dark (the diminished fifth) depending on context, is now major or minor, accordingly. (I previously discussed these notions of bright and dark in a blog post called Harmonic Brightness & Darkness—you might want to check that out.)

Pretty nifty, no?

A musical world with minor fourths and major fifths? Perhaps not as crazy as it sounds… #musictheory Click To Tweet

Look at what the new terminology does to the various modes of the major scale. First let’s look at all the modes, along with the notes in each scale, according to standard nomenclature:

Locrian d5 m2 m6 m3 m7 P4 P1
Phrygian m2 m6 m3 m7 P4 P1 P5
Aeolian m6 m3 m7 P4 P1 P5 M2
Dorian m3 m7 P4 P1 P5 M2 M6
Mixolydian m7 P4 P1 P5 M2 M6 M3
Ionian P4 P1 P5 M2 M6 M3 M7
Lydian P1 P5 M2 M6 M3 M7 A4
KEY:       Diminished       Minor       Perfect       Major       Augmented   

Look at how much simpler and more systematic it is using the new terminology:

Locrian m5 m2 m6 m3 m7 m4 P1
Phrygian m2 m6 m3 m7 m4 P1 M5
Aeolian m6 m3 m7 m4 P1 M5 M2
Dorian m3 m7 m4 P1 M5 M2 M6
Mixolydian m7 m4 P1 M5 M2 M6 M3
Ionian m4 P1 M5 M2 M6 M3 M7
Lydian P1 M5 M2 M6 M3 M7 M4
  • The only perfect interval is also the only scale degree present in all the modes.
  • The darkest mode, Locrian, is now made up of a root plus all its minor scale degrees.
  • The brightest mode, Lydian, consists of a root plus all its major scale degrees.

The new system still preserves the rule that inversions of major intervals are minor intervals and vice versa: the inverted minor fourth is the major fifth, and the inverted major fourth is the minor fifth.

Lastly, the new system eliminates the need for the terms “diminished” and “augmented” in classifying intervals. Granted, one will still want to use those terms for various purposes (such as the diminished seventh interval), but now every interval can be named major or minor, with the exception of unison and octaves, which are perfect.

Without a doubt, this is a cleaner way of categorizing notes… and it makes our major/minor terminology align a little more closely with our notions of sonic brightness & darkness.

Some Counterarguments

There are many possible objections. Let me field a few:

OBJECTION: “The unison, fourth and fifth are called perfect because none of the other intervals sound as pure.”

The unison is the most “pure” sound. Unison means two notes with exactly the same frequencies. Indeed, that is different from all other intervals, and deserves the unique label “perfect”.

After the unison, the octave has the simplest ratio – namely, 2:1. It too is considered perfect. I didn’t mention it earlier simply because adding an octave (or octaves) never affects an interval’s quality of major, minor, etc. Since unison is perfect, the octave interval is perfect too.

After those, the fourth and fifth have the simplest frequency ratios – namely, 3:2 (the fifth) and 4:3 (the fourth). But the major third (5:4) comes quite close; why not call that call that perfect as well? The purity of the fourth and fifth doesn’t put them in a qualitatively different class from the other intervals, just at one end of a consonance/dissonance continuum, of which semitone, tritone and major seventh are at the other extreme. We don’t have a special designation for those intervals; nor should we have one for fourth & fifth.

OBJECTION: The perfect fifth is contained in both the minor and major triad. If we called it a major fifth, a minor triad would have a minor third and a major fifth.

That’s true. But minor scales have lots of major notes. For instance, the Dorian, Harmonic Minor, Natural Minor and Melodic Minor scales all contain a major second. Yet they’re still minor scales. Major sixths and major sevenths figure into minor scales as well, and minor tetrachords. If minor scales and chords can contain notes we call major, it’s not clear to me that minor triads can’t be allowed to.

OBJECTION: The names major fourth and minor fifth are already in use to mean something else.

Yes. In quarter-tone terminology, a major fourth is midway between the perfect fourth and the tritone… and a minor fifth is midway between the tritone and the perfect fifth. It seems pretty clear to me that they just used those terms because they were available. In our use, the sound of the major fourth is the logical successor to the sounds of the major sixth, major third, major seventh, progressing around the circle of fifths. The quarter-tone use has no similar justification.

OBJECTION: Who cares? I’m used to things the way they are.

At some level I agree. But it’s also true that words have consequences, and our terminology shapes not just how we talk but how we think. I believe that if we did away with the concept of the perfect fourth and perfect fifth, kids would get to learn a simpler system that better reflects the sounds it describes… and they would be just a bit better set up for success in music.

Your thoughts?

Got an argument for or against that I haven’t touched on? Leave a comment. Or join the discussion on facebook.

11 Responses

  1. Stephen Mills says:

    I wonder, for the sake of argument, if you have dichotomized a gradient, that is, if tones move from neutral P1 to progressively darker to the left and progressively brighter to the right in your diagrams?

    • Yes, the gradient is unquestionably the way to think about it — have a look at my Harmonic Brightness and Darkness post. I agree that the terms “minor” and “major” imply an unfortunately dichotomy—I can’t change that so I’m just proposing a way to clean them up a bit. :)

  2. Susan says:

    Hi Anton,

    I remember learning about the “perfect” intervals as those whose notes lie within each other’s major scales. I.e., that with a perfect 5th, the bottom note lies in the major scale of the 5th above it, and that the 5th lies in the major scale of the note below it. They were related to one another in that regard. But I have no idea where the term “perfect” came from.

    I love reading your blogs!!!

    Susan

    • Neat, Susan—I’ve never heard that test before. It’d work with Phygian too—the fourth and the fifth are the only two intervals that are in each other’s Phrygian scale. But I can see why that test isn’t as catchy as yours. :)

      As for the term perfect, it evidently has the same origin as “Perfect Time” meaning 3/4 time. Namely, the number three. In this case the third harmonic being the source of the fifth and its inverse, the fourth. Three = perfect because of the Trinity, of course! :)

  3. Nate says:

    I like it. It’s visual and aural;a neat,clear conception.

  4. Edward says:

    So are you going to put any citations for where you got these ideas, or are you going to just try and pretend that there aren’t already books detailing this you lifted these ideas from? I’m all for education, but the key to education is having CITATIONS.

    Otherwise you look like a complete hack trying to rip off George Russel’s ideas as their own. Collier’s like half your age and at least cites this book when he presented the same idea a year ago.

    Wait – let me guess – you learned to “improve jazz” with solo transcription books too, right? pff

    • Unfortunately, I don’t have any citations for you, Edward. I’ve never read this stuff anywhere—which of course in no way means that it doesn’t exist. I figured before I wrote this post that someone must have proposed the minor fourths, major fifths terminology before (perhaps lots of people) but I put in a half hour searching online and came up with nothing. So I’d be grateful if you could point me where to look.

      As for George Russell, I know of his Lydian Chromatic work but I’ve never read him. But from what you say, it sounds like I really need to. Thanks for the tip.

    • Joe says:

      I am perplexed by your response Edward. I am assuming you are referring to Russell’s Lydian Chromatic Concept; could you cite your source? I am assuming so since that is the only book most jazz musicians refer to regarding Russell. If so, I have been through the book and can not find where he refers to Major 5ths and minor 4ths, as Anton does. Could you give a page number? He does refer to parent scales and chord/scale relationship, relating them to Lydian and a few other scales of his own devising. But that was nothing new even in 1959, and that is not even what Anton postulates. Regarding Collier, are you referring to the concept of negative harmony?
      I could see the comparison, but that emanates more from Steve Coleman and Ernst Levy, and again is not what Anton is posing.
      While Anton’s concept is not conventional, it is worthy of thought, even if to just enjoy another perspective of how tonality can be arranged and understood. He is not citing sources because, as I understand, this is his own concept, just as Russell does not cite sources in his own book. Certainly a musician with a novel idea of his own, who is courageous enough post for comment, is not deserving of character slights. pff.

    • Cam says:

      Neither George Russel or Jacob Collier ( I assume thats who you are referring to) say anything about renaming intervals to create a more coherent system.
      You may have missed the point of the article or misunderstood..? Maybe you could list some of the books that present this idea as you mentioned.

  5. Stephen Mills says:

    Just a fun question. If you take this one step further (in your last diagram) and make the C in C lydian into C#, you now have C# locrian. Can you envision converting this darkest mode (in C#) into a bright mode by playing it (very judiciously, I would think) over a C chord?

    • Absolutely, Stephen! I would be inclined to call that scale G Lydian instead of C# Locrian. (Two names for the same set of notes.) That way it’s clear that it’s the brightest mode of the major scale, Lydian, of the key that’s one notch brighter than the root (namely, G instead of C). I discuss that in the post on Brightness and Darkness and also the one on Pentatonics. Check ’em out! :)

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