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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?

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    The distance between the first and second tone of a minor scale is a major second... – Meaningful Username Mar 4 '15 at 13:40
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    Have you actually played a major scale or a minor scale on an instrument yourself, or are you just reading about scales on a website or in a book ? If you would actually play a few scales on your instrument, you would hear the distinction and you would answer your own question. – user1044 Mar 4 '15 at 14:35
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    Be careful about loose usage of the term "whole step". In music, a semitone is called a "half step", twice that is a "whole step". (In British English we say "semitone" and "tone".) A scale starting on C may have D as the next note. Or Db. A "whole step" or a "half step". Either way, it's the second note of the scale! – Laurence Payne Apr 24 '15 at 19:57
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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.

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    please tell me why C to Db and C to C# is not the same and how the way it gets written down is important .i only know a rule is "don't mix sharps and flats together in a single scale".Isn't the reason ? – Loc Vu Mar 2 '15 at 11:31
  • C to D is called a second. Db is a sort of D (in name) and gets written on the stave as D. C and C# get written where C is on the stave. If you talk about note names in a diatonic scale, each note has a letter name, no missing letters, no repeat letters. C to Db will not be written the same as C to C#. # and b are mixed in some minor scales/keys. But the rule is otherwise generally followed. – Tim Mar 2 '15 at 11:54
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    In the harmonic minor scale, the 7th note will be raised with an accidental. In G minor, key signature 2 flats, that will be an F sharp. There is no "don't mix flats and sharps" rule. – Laurence Payne Mar 4 '15 at 13:14
  • @LaurencePayne - well aware of that! Generally, I prefer to read something in #s that has altered notes still written in #s. For example, in Amaj., I would expect an occasional D# rather than an Eb.But technically this may be written wrongly. Guitarists seem to be the main culprits! – Tim Mar 4 '15 at 14:25
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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.

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    +1 for quickly & concisely getting to the root of the OP's confusion. To clarify: in a diatonic scale, the term "step" can be used generically to refer to both whole steps (M2's) and a half steps (m2's) that occur in the scale. Though I don't think I've ever heard a m3 (a skip) referred to as a step. – Caleb Hines Mar 3 '15 at 0:40
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    In undergraduate counterpoint courses, m3s belong to the category of stepwise motion. See Fux's Counterpoint, and all textbooks that stem from it. – Mark Mar 3 '15 at 5:43
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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.

  • A succinct way to describe intervals. Like the 'small/smaller' ides for ;minor/diminished'. +1 – Tim Mar 8 '15 at 8:24
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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.

  • i don't understand this " then there wouldn't be any minor 2nd interval " if we don't have 2nd minor interval so why we can't have "perfect second" (funny) :D – Loc Vu Mar 2 '15 at 11:39
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    @LocVu: I meant that if all minor intervals were defined by intervals between the root and other scale tones of the natural minor scale, then the "minor" second would be identical to the major second, and we wouldn't get a (real) minor 2nd at all. But we know that there is one, because we do have intervals of a semi-tone, e.g. in a major scale between the 3rd and 4th note, and between the 7th note and the root. – Matt L. Mar 2 '15 at 12:30
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    Very nice, I've never really connected the concept of the major scale descending have all of the minor intervals. That may become a good teaching tool for me. – Basstickler Mar 2 '15 at 13:46
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    Thank you so much for this answer. I've spent a few days trying to understand the significance of interval qualities. It just seemed so arbitrary and every mnemonic I could invent was flawed. This explanation totally clicked for me and is also incredibly elegant. This explanation even made the relationship to inversions click. Thank you! – Bo Jeanes Jul 29 '15 at 1:25
  • @BoJeanes I'm glad this explanation works for you, but the real explanation is in user19146's answer: whether an interval is a second, third, fourth, etc., depends on the letter names, counting inclusively, and whether the interval is major or minor depends on the distance in semitones (half steps), where the minor interval is always one semitone smaller than the major. This system includes the perfect intervals and extends to diminished and augmented intervals as well. Major intervals are not called major because they exist in the major scale. – phoog Feb 11 at 20:36
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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.

  • An Augmented unison also consist of one semitone. – Neil Meyer Mar 2 '15 at 17:45
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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.


1It 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.

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

  • "original" is probably an overstatement. I doubt anyone was tuning just major thirds in the days before polyphony or when the major third was considered a dissonance (12th century and earlier). Since fourths and fifths were more important in those days, Pythagorean major thirds seem rather more likely. It's also worth noting that the Ptolemaic major scale as you've outlined it does not support the ii chord, which is in some styles more common than the IV chord. – phoog Feb 11 at 20:53
  • @phoog I doubt your doubt is warranted. The ancient Greeks had quite advanced harmony and scales, at least 5-limit if not 7-limit. Like so much of antique culture, it was largely lost in the Middle Ages and we were back to 3-limit monophonic melody, but the diatonic scales they used then are still remnants of the Greek time (and the names of the “church modes” witness that. Note however that these modes were originally not just shifted copies, but actually had different, non-Pythagorean fine tuning.) – leftaroundabout Feb 12 at 0:04
  • As for “ chord more common than chord” – well, not really; is essentially a minor variant of classic the double-dominant, which is a borrowed chord and as such not exactly bound to the scale's tuning. Only relatively recently has become such a standard in-scale chord of its own right. Especially for Jazz, all this discussion is of course moot because enharmonics are all over the place – 12-edo is always assumed there. – leftaroundabout Feb 12 at 0:13
  • ...not that you need 12-edo for a proper chord though: any meantone temperament will do. – leftaroundabout Feb 12 at 0:18
  • Do you have any evidence that ancient Greek music employed harmony in the sense in which we use the word today? Certainly Pythagoras seems not to have identified the 5:4 interval as one of interest. That the medieval modes were given Greek names does not show that the diatonic scale is a remnant of the Greek time, but that medieval theorists thought that they were. – phoog Feb 12 at 0:24
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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!

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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.

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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.

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