Piano World Home Page Forums Our Most Popular Forums Adult Beginners Forum Why can't perfect intervals be minor/major?

I know they are called perfect because of the specific frequency relationships between the tones, like 2:1 for octaves. But this doesn't explain why they can only be raised or lowered by no more then a half step. Also what would be the quality of C to Gbb (or why can't I write so)?

It is possible to raise or lower by two half-steps. For example, C to Gbb is a doubly diminished fifth.


There are a variety of ways to describe why some intervals come as perfect and other intervals come as major/minor. Here is the way I like best:

An experiment: at the keyboard, start at C and play the notes of the C major scale up from middle C and down from middle C. Count the white keys from C up or down to each note of the C major scale (including C as the first white key you count). Also count the half-steps.

For example: C up to E is 3 white keys (C, D, E). It is 4 half-steps (1 - C to C#, 2 - C# to D, 3 - D to D#, 4 - D# to E).

Compare your results for counting up a certain number of white keys versus counting down the same number of white keys.

For example: C down to A is also 3 white keys (C, B, A). It is 3 half-steps (1 - C to B, 2 - B to A#, 3 - A# to A).

The phenomenon of the same number of white keys, but different number of half-steps leads us to call those two intervals major vs. minor. The phenomenon of the same number of white keys, AND the same number of half-steps, leads us to call that interval perfect.

Try it out and report what you find.



Augmented and diminished are used when you raise or lower by a half-step out of the families of perfect and major/minor. (While keeping the letter name the same). Doubly augmented and doubly diminished are used when you raise or lower by two half-steps.

For example:

C to Gbb - doubly diminished fifth
C to Gb - diminished fifth
C to G - perfect fifth
C to G# - augmented fifth
C to Gx - doubly augmented fifth


Note that if you change the note names, you also change the way the interval is named, in classical harmony:

C to F - perfect fourth
C to F# - augmented fourth
C to G - perfect fifth
C to Ab - minor sixth
C to A - major sixth

There are musical reasons for when to notate these pitches one way or the other. On a fixed-pitch instrument like the piano, the notation doesn't make a difference to the sound, although it might suggest something about the shape of the musical line. On a variable-pitch instrument like the violin, the notation may change how the player intones the note. For example, a violinist might play G# and Ab as slightly different pitches, because of how these note names are used in the context of a musical line.

Incidentally, if anyone can provide citations of early known written references to intervals as perfect, major, or minor, and ditto for augmented and diminished, I would be very grateful.

Ideally, I'd like to find the earliest known references we have, and then trace historically forwards. But any references at all would be gratefully appreciated.

malkin, is that a reply to me or to rpw?

I did not try the experiment. It is late and I am tired.

However, this section of your explanation stands out to me.

The reason is that I am pretty sure the concept of a perfect interval has nothing to do with keys on a piano.

I would be interested in the explanation of a perfect interval in terms of notes on a staff or some other musical characteristic.

Not a biggie ... just a thought that jumped into my head ... sleepy as it is ...

Goodnight (And Happy New Year)

I am sure the explanation I sought is in there someplace.

Intervals explained by notes on a staff: count the lines and spaces, including the starting and ending line and/or space, and that will give you the number of the interval. For example middle C up to the first F after it: line space line space. That's 4, so this is some kind of fourth. That F up to B: space line space line, so this is also some kind of fourth.

What the position on the staff won't tell you is the quality of the interval: major, minor, perfect, augmented, diminished, etc.


For finding the quality of an interval, you have to look further than the staff.

As far as the keys on the piano, they correspond to notes. Intervals measure distances between notes. The piano keyboard is a nice visual way to look at notes, and the C major scale, on all white keys, is a convenient way to look at a major scale.

But if you don't want to use the piano:

Pick a major scale. Consider notes in the scale going up from the tonic, and notes going down. For each note going down, count the number of scale notes to get there, counting the tonic as 1. Also count the number of half-steps up or down to each note. Compare your results for counting up a certain number of scale steps to your results for counting down the same number of scale steps.

For example, tonic up to mediant is 3 scale steps, and 4 half-steps. Tonic down to sub mediant is also 3 scale steps, but only 3 half-steps.

As another example, tonic up to dominant is 5 scale steps and 7 half-steps. Tonic down to subdominant is the same: 5 scale steps and 7 half-steps.

The phenomenon of the same number of scale steps but different number of half-steps leads us to call those two intervals major vs. minor. The phenomenon of the same number of scale steps, AND the same number of half-steps, leads us to call that interval perfect.


I don't say that this is the original way these words arose. I do find it to be a useful pattern to suggest a difference between the intervals that come perfect vs. the intervals that come major/minor. It also echoes how I read historical ideas about tuning which tend to have just one size of fourth and one size of fifth, but pretty quickly come up with other kinds of intervals that come in both small (minor) and large (major) varieties.

I find it useful to explore interval naming from many different angles. So you may find what you seek in the Wikipedia article, but I think it can be helpful to also examine this major scale up-and-down pattern.

When I first learned of major, minor and perfect, I played around with it to see if there were any common patterns. Fwiw, here's what I came up with.

If you invert a major 3rd, you get a minor 6. (CE vs. EC)
If you invert a minor 3rd, you get a major 6. (CEb vs. EbC)

This pattern holds true for all major and minor intervals. It also always adds up to 9 (major 3rd, minor 6th -- 3 + 6 = 9: major 2nd, minor 7th -- 2 + 7 = 9, etc.)

If you invert a perfect interval, you get another perfect interval. CG = P5; GC = P4. You have not changed qualities the same way. The pattern is different. I don't know if you can truly "invert" unisons and octaves since if the notes change places they are the same.

Supposing that we called CG "major 5th", so that CGb is "minor 5th". Then if the same pattern held true as for the other majors and minors, then an inverted "major 4th" (new name for perfect fifth) would have to give us a "minor 5th" (4 + 5 = 9; major becomes minor). Our "major 4th is GC. Inverted it is CG. We've defined the "minor 5th" as being CBb. Therefore we did not get the same pattern.

None of the intervals presently called perfect will follow the inversion pattern that is consistent for majors and minors.

For what it's worth.

Then C# to Gbb - triply diminished and Cx to Gbb - quadruply diminished . (Is this where microtonality begins?)

I understand the counting half steps thing, though I feel like it's a consequence and not the reason. It's nice to know this effect in any case. Thank you.

Now, that article...

That's an interesting way to put it: "consequence, not the reason." What would you say is the reason?

I use counting half-steps as a convenient way to see that the size of intervals is different or the same, because I'm not very good at hearing that they're different when they're off of different base notes: for example A up to C vs. C up to E. One could use transposition to the same base note, or comparing within different major scales (for example the analog of C up to E in A major is A up to C#, and A up to C is smaller than that), but those introduce an additional complication which for me at least is beyond what I want to include in what's trying to be a relatively simple explanation.

But I also see half-steps as fairly basic so I'm curious about what you see as a more basic reason, for which the half-step counts are a consequence.

+1.

I would also add perfect 1 and perfect 8 in addition to perfect 4 and 5.

<Jumping in unannounced> For me, I'm not answering for rpw here, it's easier to look at the interval as a number of steps away from, er, a more standard interval (whether read or heard) as in a flattened seventh or minor third, rather than counting the number of steps up to the interval itself.

But to do that you have to know the "standard" intervals. That privileges the standard interval names in a way which I don't want to do in the up-and-down investigation I laid out.

There's a whole lot else to investigate about intervals after the investigation I described -- or even before it! the investigation doesn't have to be done first in one's interval-learning -- , such as how to find intervals between any two notes to get to the point where you have standard intervals that you can do that "compare to a standard interval" idea. Indeed, I use that method myself normally for identifying intervals, and almost never count half-steps. But the "standard interval" approach doesn't (in my view) explain why intervals are divided as they are into perfect vs. major/minor.

How do you explain why 1458 come as perfect but 236 come as major/minor?

What do those numbers refer to?

A third is two adjacent lines or spaces and a seventh is four of the same. The accidentals, either at the spot or in the key sig., provide the modifications. I don't count the semitones from the lower note up.

I know you don't hear the same way I do but I hear a seventh as a sound I know and understand as "a seventh" rather than as the number of steps apart the two notes are. I know they are a set number of 'frets' away but I don't know the number off-hand or put any significance on that number.

Shorthand. Restated: "How do you explain that unisons, fourths, fifths and octaves come as perfect and seconds, thirds, and sixths come as major/minor?"

zrtf90, I don't hear intervals as numbers of half-steps. And in fact, apart from this investigation, I almost never count half-steps. If the half-steps seem out of place in the up-and-down investigation I described, replace it with this:

"compare the intervals with the same number of scale steps (or lines and spaces on the staff, if you prefer) up and down from middle C. Are they the same size (by however you measure size, aurally, or comparing to sizes up from the tonic in a major scale, or comparing to whatever else you know about intervals) or are they different sizes? If they're the same size, this is a type of interval we call perfect. If they're different sizes, this is a type if interval we call major/minor."

Again, the point of the exercise is not particularly to learn how to identify intervals. It has a very narrow goal: to illustrate a musical distinction between the intervals we call perfect and the intervals we call major/minor, that might help someone make sense that it's not completely arbitrary that 1458 come as perfect and 236 come as major/minor.

keystring has given another way of looking at that distinction.

How do you motivate or explain that distinction?

Fourths and fifths are fifths and fourths when inverted. The fourth isn't so much the next note along in the harmonic series, as the third and sixth are, but the fifth inverted.

When a major sixth is inverted it becomes a minor third and vice versa.

Gee, I was trying to count 1,458 perfect intervals on a piano!

Edit: Cross posting again! I was only referencing rpw's consequence vs reason.

This is just a hypothesis, but I would guess that the "perfect" nomenclature comes from the Pythagorean tradition of building scales off of intervals of fifths. It was determined that frequencies related by a ratio of 2:1 sounded so good together that they should be considered equivalent - it is the (modern-day) octave. The next pleasing ratio they found was 3:2, which is the (modern-day) fifth. The sonority was so excellent that they used the 2:1 and 3:2 ratios to construct a scale. The idea is to start with a base frequency F and repeatedly multiply it by 3/2 and reducing by 2/1 to keep frequencies within an octave (or however large one desires). It leads to some problems, particularly that this scheme does not terminate to a finite number of tones. You have to make approximations and take concessions to get it to stop, some of which lead to the modern 12-tone equal tempered system.