Minor Fourths, Major Fifths
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:
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:
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:
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 TweetLook 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.
Further reading…
You might enjoy this related blog post about the “Neutral Scale“.
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. :)
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! :)
I like it. It’s visual and aural;a neat,clear conception.
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.
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.
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.
All I have to add is : Collier? LOL!
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! :)
Hi, Remember that most of the basic theoretical terms came from classical theory which came from the designers of scales which came from the design of the tempered chromatic scale itself. Most intervals when stacked using same intervals create closed systems of some notes other than the original note itself (ex. stacked maj 3rds make augmented triads. Stacked min 3rds make diminished triads before coming back to the source note. P unisons are unique in that when you stack them you never get anything but the source note. P4ths and P5ths share the same special properties with each other however. Starting from the source note you can stack perfect 4ths and you will not get back to the source note until you run through every note in the chromatic scale! When improvising with P4th triad chords it creates an anything goes harmonic backdrop. The whole cromatic scale is opened up for improvising breaking the ear free from the most common scale systems 7 notes on 5 notes off that is in most common usage in western music. McCoy Tyner just walked in the room. Larry
I agree with what you’re saying about P4 and P5 being usable to reach all of the 12 scale degrees—in math (group theory) they would call them “generators” of the chromatic scale for that reason. But I can’t say I see how that justifies calling them “perfect” intervals. Have you seen that argument made elsewhere? Semitones and major sevenths have the same property, but we don’t consider them perfect intervals.
It might have something to do with home vs active in linear writing. Implied rest P5 root on bottom. P4 not completely at rest when the root is on top. Probably a vestige of the way ears worked before trained alternatives. Funny how in most fields of studt theory is something you have but in music it is widely percieved (falsely) as something you know. I’ve heard younger musicians say “I know theory” many times not understanding that common usage is what makes it appear to be so.
Dear Anton,
I have created a color harmony theory that uses the same wave harmony/ Dissonance’s as in music theory.
I learned music theory to see if it had a relationship to the color theory I created/discovered. Your bright and dark sides in the circle of fifths are transposed in my theory by a set of five warm and five cool primary and secondary colors and two secondary colors made from a mixture of one cool and one warm primary color each.
The first and last colored notes within a musical scale equal warm and cool versions of each other and the first and last notes in C Major equal two violets. One warm and one cool violet color. Those two violets are created by mixing the fifth color in the warm spectrum of colors with the first color in the cool spectrum of colors and the fifth color in the cool spectrum of colors with the first color in the warm spectrum of colors. Both of those first and fifth colors are primary colors and both of the warm and cool spectrums of primary and secondary colors follow the color order in the electromagnetic spectrum. The two violet colors equal the devil notes in the key of C and are the only two colored notes in the circle of fifths that are made from a combination of warm and cool, primary, colors.
If you would like to see more of my work or ask me a question or two about it I would be honored to fill you in or answer your questions.
Sincerely,
Michael
Anton, thank you for coming up with this food for thought.
Major and minor indicate 2 steps, one above and another below a (non-existent) center. In contrast, perfect implies a center and a step above (augmented) and one below (diminished). So at the simplest level, for some degrees of the scale we conceive of 2 possible states, M and m, and for other ones we think of 3, (dim, P, aug). I am not sure why this is so or if there is any reason for it to be so (?).
I mostly agree, Ed, and that, to me, is incentive to consider them all simply major or minor. But there are some complications to your claim. There is no diminished fourth, leaving the fourth with only two states (perfect and augmented… which I would call minor and major). The seventh, by contrast, is not perfect but still has three states: major, minor and diminished. That being the case, I see no reason a priori why the fifth shouldn’t be minor, major or augmented. And we speak (wrongly, some such as W.A.Mathieu contend) of a “sharp 9” in addition to major and minor, giving that interval three states as well. In other words…
Thank you for your food for thought!
Anton, you say “There is no diminished fourth, leaving the fourth with only two states (perfect and augmented… ”
My understanding is the diminished fourth coincides with the M3 in our equal temperament system.
You also mention the diminished 7th, which would correspond to M6.
Yes, in theory there is a diminished fourth just as there is a diminished second, third and sixth. In practice those terms are not used by most musicians other than to describe the mis-notation of passages. But diminished seventh is used commonly and doesn’t mean the same thing as a major sixth—even though, as you say, they describe the same pairs of pitches in equal temperament.
Hi Anton,
Here are the three qualities of the 5ths and the two qualities of the 3rds in action. When you consider triads, there are 4 possible chords: M, m, d, and A. Those are made from M and m 3rds (two qualities), and d, P, and A 5ths (three qualities).
That’s right. In the standard nomenclature those fifth intervals are called diminished / perfect / augmented. In this proposal they are called minor / major / augmented… analogous to sevenths, which are named diminished / minor / major in both nomenclatures.
Hi Anton,
You say “…analogous to sevenths, which are named diminished / minor / major…”
Not exactly analogous, as in the case of the 5ths the unaltered state is in the center, call it perfect or major. The alterations go either up or down.
Whereas with the 7th, the unaltered state is the major and the alterations you indicate only go down once and twice respectively. Unless you consider m7 to be the unaltered state?
In my proposal there is no “unaltered” state except for the root, so the 5th does become analogous to the 7th. You can say that each degree has four states: diminished, minor, major, augmented… though some of them make for rarely used terminology, just like in the current system. I agree that in the current system there is the disanalogy you speak of between the 5th and 7th. I consider that an argument in favor of my proposal. :)