Confusion about major and minor second intervals

Question

Why is a major second interval different from a minor second interval considering that in the natural scales formulae they are both one whole step?

Answer 1

On the face of it, it doesn't make sense. But intervals are taken from the major scale notes. Thus a major 3rd is, say, from C to E. When an interval is made smaller by a semitone, it's called a minor. Thus a minor 3rd is C to Eb. Yes, it happens to be in the minor scale/key as well. This applies to most intervals, but not perfect ones - fifths, for instance. Major 7ths would be C to B, whereas C to Bb is a minor 7th.

The major second, in your question, is C to D, so when that is changed into C to Db, it's called a minor 2nd. Note that C to C# is NOT the same, even if, on most instruments, it sounds it. The way it gets written down is important. It doesn't mean that the Db is in the minor scale.

The 6th is another confusing one. C to A is major 6th, and C to Ab is minor 6th. However, a minor 6th CHORD doesn't have a minor 6th interval. It's spelled C Eb G A - with a minor triad, but a major 6th interval.

Going back to perfects - there are no minor 5ths. If C to G is a perfect 5th, then C to Gb is called a diminished 5th.Perfect 4ths are treated the same.

So, in summary - 2nds,3rds, 6ths and 7ths can all be major or minor, and if they are made even smaller, by another semitone, they are called diminished. Perfect 4ths and 5ths change to diminished when they are one semitone smaller.

Answer 2

The terminology is confusing here, because "major" and "minor" have two different meanings. One meaning is "major and minor scales". The other, which is taken directly from Latin, is that "major" means "big" and "minor" means "small".

A "second" means an interval between two successive note-letters in a scale - taking into account any sharps or flats in the scale, of course. In both major and minor scales, there are two different sizes of seconds - one and two semitones wide. The could just be called small seconds and big seconds, but the conventional Latinized names are minor seconds and major seconds.

The same naming system applies to thirds, sixths, and sevenths as well.

Fourths, fifths, and octaves are different. First, they sound different from the other intervals. Historically, the sound of 4th, 5ths and 8ves was described as "perfect" compared with "imperfect" for all the other intervals. The "perfect" intervals are the same size for almost all positions in major and minor scales. The very few exceptions (like F to B in C major and minor) are called "augmented" or "diminished", which just means "bigger than perfect" and "smaller than perfect".

Final note: in the harmonic minor scale, there is one second that is three semitones wide (A flat to B natural, in C harmonic minor). The term "augmented" is used for that, i.e. "bigger than a big second". Similarly, B natural to A flat is "smaller than a small seventh", and called a "diminished" seventh.

Answer 3

You wrote:

considering that in the natural scales formulae, they are both one whole step

This is the crux of your question. M2 and m2 (major 2nd and minor 2nd) intervals are not both whole steps. Only the M2 is a whole step. The m2 is a half step. Nonetheless, in the diatonic scale, each can represent a step. Step-wise motion includes m2s and M2s, and also even m3s in most textbooks. So they represent steps, but just not necessarily whole steps.

Answer 4

The major intervals 2, 3, 6, and 7 come indeed from the major scale. However, as you noted, the corresponding minor intervals do not come from the (natural) minor scale, because then there wouldn't be any minor 2nd interval.

All minor intervals can be obtained from the descending major scale. If we use C major as an example, a minor 2nd is the interval between C and the B below the C. A minor third is the interval from C down to A, a minor 6th from C down to E, and, finally, a minor seventh from C down to D. Equivalently, you get all the minor intervals (2, 3, 6, 7) from the phrygian mode, which is an inverted major scale in the sense that the sequence of intervals when ascending is the same as the sequence of intervals of a descending major scale.

Answer 5

A major second interval consists of 2 semitones (or as you say a whole step) whereas a minor second interval consists of a semitone.

Example of major second is C - D.

Example of minor second interval is B - C.

" considering that in the natural scales formulae, they are both one whole step ?" this is wrong. Of the second intervals only the major second consists of a whole step.

Answer 6

I'm not sure what you mean by “the natural scales formulae”, but it should be clear that any “natural scale” will not “naturally” have steps of the same size.

The diatonic scales were discovered long before the 12-edo tuning that we now use for playing these scales on piano etc., and for measuring the size of intervals therein. The original derivation uses no equally-spaced grid at all, but defines intervals by their frequency ratio. For the purposes of “harmonic music” we basically need the Ptolemaic scale of just intonation. You get it by making the I, IV and V chords just major chords, which are the “ideal consonant sound”:

• I is, well, the base frequency, by convention we call it ¹/₁.
• iii has to be the the pure major third in the I chord, that requires a relative frequency ⁵/₄.
• V is the pure fifth in the I chord, rel.freq. ³/₂.
• IV is the pure fourth (so I will be the fifth of the IV chord) ⇒ relative frequency ⁴/₃.
• vi is the pure major third above IV, rel.freq. ⁴/₃ · ⁵/₄ = ⁵/₃.
• ii is the fifth in the V chord (one octave down), rel.freq. ³/₄ · ³/₂ = ⁹/₈.
• vii is the pure¹ major third above V, rel.freq. ³/₂ · ⁵/₄ = ¹⁵/₈.

Now... if you order these and do the maths, you'll find there are actually not just two, but three different steps! Namely,

• The greater tone is found between I and ii as well as IV and V and also vi and vii, with ratio ⁹/₈ each. That is 204 cents (i.e., a little bit wider than a whole tone step on a 12-edo instrument such as piano).
• The lesser tone (not to be confused with minor) is found between ii and iii as well as V and vi, with ratio ¹⁰/₉, which is 182 cents. Significantly smaller than a whole tone in a 12-edo.
• The semitone is found between iii and IV as well as vii and I, with ratio ¹⁶/₁₅, or 112 cents. A bit wider than a 12-edo semitone.

Now, while the major chords sound indeed amazing in the Ptomemaic scale, other things you'd like to do musically are complicated by all these different intervals; that's why most western instruments with fixed pitch detune the steps a bit, so the system becomes easier to overview for composers and players.

The greater and lesser tones are reasonably similar, so if you approximate them both by one single size in between you can still have pretty consonant chords in your scale. That's the idea behind meantone temperaments (12-edo is one of these).
OTOH, the semitone is arguably not similar to either of the whole tone steps, so if tried to also include these in a “one size, fits all” step, the chords would really sound out of tune². But it's quite close to half the size of a whole step. 12-edo makes it exactly half the size, so your overall scale then lies on a fixed grid of semitones, where whole notes simply are a double step.

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¹_{It is widely accepted that at least the vii note, which is the leading tone from the dominant to the tonic, should typically be played higher than this value, to emphasise that the dominant is a dissonance that wants to resolve to the tonic.}

²_{Which doesn't mean you can't use such a scale musically}.

Answer 7

In music theory "Whole step" has a special meaning. The distance from one note on the piano keyboard to the next highest (whether it be a black note, C to C# or a white one, E to F) is called a "Half Step". Two half steps make a "Whole step". In British English we say "semitone" and "tone".

A major scale goes Whole step, Whole, Half, Whole, Whole, Whole, Half. (I hope I got that right!). So don't call the distance between EACH note of a scale a "Whole step", you'll just confuse yourself!

Not every interval in a minor scale is a minor interval. From ^1 to ^2 in both the major and minor scales is a major 2nd, a 'whole step'. Both C major and C minor (any variety) scales start with C, D. They both contain a Perfect 4th (C, F) and a Perfect 5th (C, G) too.

Answer 8

A minor second is a semi tone closer to the root note than a Major Second. D - Eb is a Minor Second. D to E is a Major second.

As a general rule of thumb if you have a Major interval and you bring the notes closer to each other by either raising the bottom note or lowering the top note by a semi tone then you have a minor interval.

Answer 9

Why is a major second interval different from a minor second interval considering that in the natural scales formulae they are both one whole step?

They are not both whole steps.

• Major second (M2) = 2 semi-tones (whole-step)
• Minor second (m2) = 1 semi-tone (half-step)

These interval distances and names apply no matter the scale or chord.

In an octatonic scale, major scale, various inverted seventh chords, chromatic chord, etc. a major second is always 2 semi-tones and a minor second is always 1 semi-tone.

How the interval is written in staff notation or letter names does matter for naming the interval (C to Ebb is a diminished third, but is enharmonically a major second.) But that is an issue of enharmonic interval naming, and is really a different subject that doesn't need to be explained here.

Answer 10

It seems that your question can be rephrased as

Why are the major and minor second different when the second degree of both the major and minor scale is the same, a whole step above the first degree?

This bespeaks a misconception about where the words "major" and "minor" come from in intervals' names. The fact that most of the major and minor intervals can be found as the corresponding degree of the corresponding scale is a historical accident. Therefore it is a pattern that the second doesn't follow rather than a strict rule. The strict rule is that a minor interval is always a half step smaller than the corresponding major interval.

The major scale and the natural minor scale both have seven seconds. Every pair of adjacent pitches is a second. If you look at all the seconds, you see that they come in two sizes, namely one semitone (B-C and E-F) and two semitones (A-B, C-D, D-E, F-G, and G-A). To differentiate these two types of seconds, theorists called one type "bigger" and the other "smaller." These theorists were writing in Latin, and the Latin words meaning "bigger" and "smaller" are "major" and "minor."

Similarly, there are two classes of thirds: A-C, B-D, D-F, and E-G are smaller -- minor -- while C-E, F-A, and G-B are bigger -- major.

In arriving at this system, the interval B-F or F-B was essentially discounted, so the augmented fourth was not called "major" nor was the diminished fifth called "minor." The terms were applied only to the second and third along with their inversions the sixth and seventh.

There is another point to be made: not only didn't the major and minor intervals get their names from the major and minor scales; in fact the opposite is true. The major and minor scales got their names from their third degree. The major scale is so called because its third is major, and the minor scale because its third is minor.

Why is the third degree given this special power over the naming of scales? It is because the third degree determines the quality of the tonic chord.

Answer 11

A minor second, literally a smaller second, is an interval of one semitone.
A major second, literally a larger second, is an interval of one whole tone.

They're called minor and major because one of them is smaller and the other is larger.

Same pattern goes for the thirds, sixths, sevenths, ninths, tenths, thirteenths and so on. One of the pair is smaller (in Latin, minor), the other is always half a tone larger (in Latin, major).

The minor and major key are only named after the fact that they contain a minor and major third above their root tone, respectively. The names are basically shorthand for "the one with the minor (smaller) third in it" and "the one with the major (larger) third in it".

It wouldn't make sense trying to distinguish them by something they have in common.

No strict claims in that about the other tones in the scale. In fact, minor key music frequently makes use of the major seventh.