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A scale with 7 notes, in an octave, is called a Heptatonic Scales.

Heptatonic scales are further divided based on tone and semitones arrangements.

If a Heptatonic scale have five tones and two semitones, where the two semitones are separated from each other by either two or three tones, then it's called Diatonic Scale or Diatonic Heptatonic Scale.

Diatonic Scales are further divided based on more specific tones and semitones arrangements. If the arrangement between five tones and two semitones is TTSTTTS then the Diatonic scale is called a Major Diatonic scale.

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Yes you are correct, I'll just put it in simpler terms.

The major scale is both diatonic and heptatonic.

Heptatonic just means that there are 7 notes per octave in the scale.

The diatonic scales just a name for the specific name for scales that contain a specific whole step, half step pattern TTSTTTS in some way, shape, or form.

All the 7 natural modes of the major scale are diatonic because they are all based off the same whole step. half step pattern:

Major/Ionian    TTSTTTS
Dorian          TSTTTST
Phrygian        STTTSTT
Lydian          TTTSTTS 
Mixolydian      TTSTTST
Minor/Aeolian   TSTTSTT 
Locrian         STTSTTT
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  • In the last line, '7 natural modes of major scale...', is it correct? I thought Diatonic scale has 7 modes, and major scale is a one of the modes.
    – Quazi Irfan
    Commented Aug 10, 2015 at 9:05
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    @iamcreasy: The seven modes include the major scale / ionian mode. In total there are seven modes, simply because there are seven different notes in a diatonic scale.
    – Matt L.
    Commented Aug 10, 2015 at 17:10
  • A scale is recognizable by its mode. Google defines a mode as “a way or manner in which something occurs or is experienced, expressed, or done.” This means a scale’s mode refers to the way the notes move forward—its unique scale step pattern. So while a diatonic scale indeed has seven possible modes, the major scale (i.e., Ionian mode) has but one.
    – Udon Joe
    Commented Apr 22, 2019 at 18:24
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As already mentioned in Dom's answer, everything you wrote is correct. I'd just like to add a few things concerning the term diatonic.

As you said, one meaning of "diatonic scale" is a scale with five whole tones and two half tones where the two half tones are maximally separated, i.e. at least by two whole tones. This includes the major scale and all its modes, and, consequently, also the natural minor scale.

However, this definition would exclude the melodic minor scale, which also has five whole tones and two half tones, but the two half tones are separated by only one whole tone. Also the harmonic minor scale would be non-diatonic according to this definition, because it has one augmented second. So there is also a more inclusive usage of the term diatonic scale, which includes these two other forms of the minor scale as diatonic. Since it seems that there's no generally accepted definition of diatonic scale (either including or excluding the melodic and harmonic minor scales), this is a source of confusion.

One nice property of diatonic scales, in the narrow, exclusive definition, is the fact that they can be generated by stacking perfect fifths on top of each other. E.g., if you take the sequence of perfect fifths F-C-G-D-A-E-B you get all notes of the C major scale. If you take F as the root, you get F lydian. This property of the lydian scale, that it can be generated by stacking six perfect fifths on top of each other, was the main motivation for viewing the lydian scale as the fundamental scale in George Russell's Lydian Chromatic Concept.

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    Interesting last para. Surely the same reasoning could be used for any mode, as taking C as mother, D Dorian has the same notes. As has E Phrygian, etc., all made from stacked 5ths?
    – Tim
    Commented Aug 10, 2015 at 15:53
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    @Tim: If you stack six perfect fifths on top of each other you always get the lydian scale with the lowest note as the root. If you want another mode, you need to find the relative lydian scale and start stacking with the root of that lydian scale. E.g., if you want the notes of A dorian, you need to find the lydian scale with the same notes, which is C lydian, and then you can start stacking six perfect fifths starting from C to get the notes of A dorian.
    – Matt L.
    Commented Aug 10, 2015 at 17:07
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    Thanks for that. What I don't get now is which is the lowest note. There's F,C,G,D,A,E and B in order, so is F, as the first, deemed to be the lowest?
    – Tim
    Commented Aug 10, 2015 at 17:38
  • @Tim: Yes, F up to C is a perfect fifth. Down to the next lower C would be a perfect fourth.
    – Matt L.
    Commented Aug 10, 2015 at 18:40
  • It would be nice to put that "you get the lydian scale if you take the lowest note (F) as the root" into the answer, because without that the argument of "This property of the lydian scale, that it can be generated by stacking six perfect fifths", following the "get the notes from the fifths" part is indeed confusing, especially because the paragraph starts with "One nice property of diatonic scales ... is the fact that they can be generated by stacking perfect fifths". (At least it did confuse me, too, exactly the same way as @Tim. :) ) The answer is otherwise great (+1ed).
    – Sz.
    Commented Mar 23, 2019 at 19:49

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