Errors in understanding
it should be M7 not m7 it is a full 7 interval with no modification, so major
The size of an interval is not determined by whether the notes do or do not include modification.
it should be m2 not 2+ the sharp reduces the interval, so + makes no sense
Sharps raise the pitch, flats lower the pitch. In this case, the sharp moves the upper note further away from the lower note.
Explanation
How intervals are defined
Two factors determine the interval: 1) the letter names involved (i.e., the "spelling" and 2) the absolute distance (i.e., number of half steps) between the notes.
The problems of interval naming
Unequal natural note distances
The core of the problem is that the natural notes (A B C D E F G
) are not all the same distance apart. For A
to B
is an M2, while B
to C
is an m2. This can be confirmed on the guitar by playing A B C
on a single string. Moving from A
to B
will be a move by two frets, but B
to C
will be a single fret.
"Enharmonic equivalence"
The situation is further complicated by the fact that the standard tuning system means that some notes with different spellings produce the same sound ("enharmonic equivalence"). F#
and Gb
are "the same note", as are G#
and Ab
. As a result, "the same notes" can be represented by different intervals, depending on the spelling. A
to B
is an M2, but A
to Cb
is a d3.
Interval naming strategies
Two ways to conceive of intervals
- My preferred way to think about intervals is the number of half steps (a.k.a minor seconds) from the lower note to the higher note. That is, the number of guitar frets on a single string from the lower note to the higher one.
- Another common way to think of intervals is in relation to the major scale of the lower note. If the lower note is C, then the C major scale is the basis for calculation. If the lower note is Ab, then the Ab major scale is the basis. The interval names correspond to the major scale, not the minor scale.
How to determine intervals: D to C
- Using the "half-step" way of understanding intervals, count the frets from the open D string up to C. There will be a total of 10 frets (half steps), which is the definition of an m7. (Remember that spelling is key. D to B# is 6+ even though there are the same number of half steps/frets involved.)
- For the "major scale" approach, since D is the lower note, we think in terms of the D major scale. In D major, Cs are sharp, so D to C# is M7. Since we're looking at a C natural — a half step lower than C# — this is m7.
How to determine intervals: F to G#
- Counting half-steps/frets from F to G#, there are three, making this 2+. (Again, were this spelled F and Ab, it would be m3, even though the half-step/fret count is the same.)
- Since F is the lower note, we consider the F major scale. In F major, G is a natural note, so F-G is an M2. Since the G here is raised one half step (one fret) by the sharp, we have 2+.