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I have seen scale intervals described using P1 M2 M3 P4 etc and it's not clear what the P and M mean. I am guessing the M means major because I've also seen lower case m which probably means minor. But the meaning of P is not clear.

For example, I have seen the major scale (Ionian mode) described as

P1 M2 M3 P4 P5 M6 M7 P8
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    I guess, that P stands for perfect, since there is no minor nor major octave. – guidot Apr 9 '17 at 20:04
  • @guidot - there also is no major or minor 4th and 5th. – Tim Apr 10 '17 at 6:22
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P=perfect, M=major, m=minor, +=augmented, o=diminished.

The P is octave, fourth and fifth,as they appear the same in major or minor, unchanged from each.

Augmented (a semitone larger than P4, P5, etc.)is usually designated '+' sometimes '#', in a chord; diminished is 'o' or 'b' in a chord, occasionally '-', but that can get confused with the NNS '-' for minor. Not seen A5, but that could get mixed up with an A power chord!

So, E+ would be spelled E G# B#, with the 5 (B) sharpened. Eo is E G Bb. There's a lot of crossover between the naming of chords and intervals.

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    Note that "perfect" also applies to unisons, as in the 'P1' designation in the original question. – Richard Apr 10 '17 at 2:51
  • Exploring some other resources I have seen A5 for augmented perfect interval, and d5 for diminished. Is that something that is also in common use as an alternative to + and o? And would it be +5 and o5 for example? Maybe you could add some examples to your answer? – Todd Chaffee Apr 10 '17 at 11:27
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    @ToddChaffee I personally have seen both of those notations, and I expect most learned musicians, if they haven't seen them, would understand them. – Richard Apr 10 '17 at 12:41
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Intervals are two general categories perfect and imperfect. The perfect intervals - designated with 'P' - are unison, octave, fourth, and fifth.

P1 perfect union
P8 perfect octave
P4 perfect fourth
P5 perfect fifth

The imperfect intervals are third, sixth, and seventh. The imperfect intervals are of two basic qualities major 'M' and minor 'm'.

m2 minor second
M2 major second
m3 minor third
M3 major third
m6 minor sixth
M6 major sixth
m7 minor seventh
M7 major seventh

Each of the intervals can also be described as diminished 'd' or augmented 'A.' Diminished means one half step smaller than a perfect or minor interval, and augmented means one half step bigger than a perfect or major interval. Examples:

d5 diminished fifth
A4 augmented fourth
A2 augmented second (commonly found in the harmonic minor scale)
A6 augmented sixth (used with the various augemented sixth chords)
...etc

Keep in mind some interval pairs are enharmonic equivalents meaning their distances are the same, but their names are different:

P1 perfect unison = d2 diminished second
P8 perfect octave = A7 augmented seventh
m7 minor seventh = A6 augmented sixth

...some of those enharmonic equivalent names are a little strange and would be used in special notation situations.

The some other details to consider. 'Tritone' is a special name for the d5. Also, there are compound intervals which are bigger than an octave, ex. M10 major tenth = P8 + M3.

Check out the Wikipedia page for intervals for a more complete overview.

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