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When constructing an interval, e.g. a major third from A I work like this:

  1. Count three notes including the starting one, so A, B, C
  2. Now check on the circle of fifths whether A major scale has an accidental on C(it has a #)
  3. If it has I add the accidental to the last note - therefore I get C#

Is this the right? I run into problems when constructing an interval from a note which doesn't have a major scale, e.g. creating a major third from G#. I get to B but how do I check for accidentals then? Should I somehow utilize the minor scales? If I should then with scales which have both major and minor version which one should I use and when. Thanks for the advice.

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One trick you can use is to remove the accidental from your starting note in order to make it a more common major scale, and then add the sharp back to the answer at the very end. I'll use your example:

  1. I want a major 3rd above G#
  2. Using your method, I know the answer should be some kind of B
  3. Whoa, G# Major is a crazy scale!
  4. Let's pretend it's just a G
  5. G major only has 1 sharp, so I would use B natural to be a major 3rd
  6. but I have to add back the sharp I eliminated in step 4
  7. B# is a major 3rd above G#

It sounds complicated when you spell it all out like that, but it's actually a pretty handy and relatively quick method for building or identifying intervals. I think there are better ways, but if the major scale thing works for you, then this should make it more useful.

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    For the uninitiated, B# is found (in equal temperament) at the place occupied by C. However, in this instance, technically, it will be called B#, as Pat Muchmore indicates. – Tim Aug 17 '14 at 6:31
  • Thanks this was very helpful. One more question though, what if there is already an accidental on the calculated note? If I wanted a major third above A# and used this trick I would get a major third above A which is C# to which I still have to add a sharp. Would I get C##? – pseudomarvin Aug 17 '14 at 7:09
  • See my answer below. – Tim Aug 17 '14 at 7:28
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    @pseudomarvin Exactly! It's called a double sharp. Technically, it has it's own symbol a little like a fancy x (invented by JS Bach himself!), but on a forum like this ## is fine. – Pat Muchmore Aug 17 '14 at 12:27
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I use a simpler method; counting semitones. A major third has 4 semitones. So using your example I would think of A, then count up four semitones (Bb, B, C, C#) landing on C#.

  • Interval, Semitone Count
  • Unison, 0
  • Minor Second, 1
  • Major Second, 2
  • Minor Third, 3
  • Major Second, 4
  • Perfect Fourth, 5
  • Tritone, 6
  • Perfect Fifth, 7
  • Minor Sixth, 8
  • Major Sixth, 9
  • Minor Seventh, 10
  • Major Seventh, 11
  • Octave, 12
  • (Minor Ninth, 13... etc)

The way you are doing it, using tonality and the circle of fifths seems overly complicated for figuring out which note is a Major Third above "A".

Now, if it matters to you whether the note is a C# or a Db, then yes you should consult the key and/or harmonic context to choose the correct enharmonic spelling.

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    It should matter.Putting augmented and diminished intervals into your chart will reveal that, for instance, an augmented fifth has the same no. of semitones as a minor sixth. From C, the former is a G#, the latter an Ab.Same place on most instruments, different place on the music, indicating a different function. – Tim Aug 17 '14 at 6:37
  • True. I have a tendency to over simplify. In part because I love post-tonal theory so much. Yes, my answer is about finding the correct key/fret/pitchClass... – Matthew James Briggs Aug 17 '14 at 19:06
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    This is the wrong way to do it. C - C# and C to Db is the same semitones away from the root but in no way the same interval. – Neil Meyer Sep 1 '14 at 11:16
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Use only the major scale as a datum point. As there are different minor scales, it will confuse the issue. Count up using sequential letter names to arrive at the right name. This will put the note on the correct line or space.

For example, a major third above A#. A,B,C. Thus it's a C.Because A# key has loads of #s, the C will have to be Cx (C##).Yes, it's where D lives, but in that key, there's A#, B#, Cx, D#, E#, Fx, and Gx. Hardly surprising pieces aren't (often) written in A# !! Try Bb instead - most people won't notice the difference ! And funnily enough, the major third above Bb is D.

It could also have been referenced using the scale of A, and adding that extra # to the answer.As in A-C# = major third.

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I just wanted to stop by and point out that every note starts a major scale, including G#. The G# major scale would be G#, A#, B#, C#, D#, E#, F##. Since that's rather silly to use in real life, most people will remove one sharp from every note, find the major third in 'G', and then add a sharp back when they're are done:

G# A# B# C# D# E# F##

G A B C D E F#

The major third of G is B. Now, add it back and you have B#, which is correct.

You can also spell the scale enharmonically, as in Ab. This would give you:

Ab Bb C Db Eb F G Ab

Now you find the third and it's "C", which is the correct interval but actually it should technically be spelled as B# if you're looking for the major third from G#.

In time, you will learn to quickly recognize which scales push past 7 sharps or 7 flats, and avoid them by spelling them enharmonically.

Just remember that if the root of the scale has a #, that means the scale will have 7 more sharps than a major scale built on a root without. So G# must have 7 more sharps than G major, and it works with flats, too: Bb has 7 more flats than B major. (But since B major has 5 sharps, we can think of it as -5 flats. Adding 7 to -5 results in 2, the number of flats in Bb major.)

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Remember also that if you bring a Major interval closer to each other by a semitone you have a minor interval. So for instance C - E is Major but either note being brought closer to the other will give you a minor interval. Like C# - E or C - Eb.

If the interval is tricky you can lower (Or raise) both notes to make the indentifying of the interval easier. So For instance if you have C# to D##. You can lower them both by a semitone ie C - D#. C - D is major. C - D# will be an augmented second and so will C# - Dx.

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