Confusion about intervals in chromatic VS diatonic scales

Question

I hear terms like "fifths" and "minor thirds" and "thirds" used all the time in musical theory discussion and while I know some places I can use these terms I'm unclear if there are multiple meanings/uses.

In a major scale, there is an interval between the tonic and the dominant but that's 4 steps along the scale and these steps are not equidistant in size. Whereas on my bass guitar, my strings are tuned each 5 semitones up so the intervals are equal on the chromatic scale. It seems like sometimes in music theory the intervals we discuss are between scale degrees and other times are referring to the underlying chromatic scale.

I think my question is therefore: do we use the same terms in both cases or are they subtly different and I just need to get them committed to memory? e.g. we have "a fifth" and "a perfect fifth" are they the same or different, and so on.

Answer 1

The "a fifth" is a general and can be talked about as any kind of 5th while the "a perfect 5th" is specific. Diatonic vs Chromatic does not matter in either case as intervals are independent of scales. G to D is always a perfect 5th regardless of the context.

Scale degrees are not the same thing as intervals, although in heptatonic scales (7 note scales) they almost always correlate to the letter distance between the two notes. An interval is two measurements : the distance in letter names and the "normalized" distance in semitones. The normalized aspect is just that certain intervals have certain spaces where they are typically found and others where they are not. For example C to Eb is a minor third however if spelled C to D# this interval is then an Augmented second since the interval is "bigger than normal". This answer goes into specifics a little more.

Answer 2

The intervals take the major scale as a datum point, basically. Thus, a maj 3 is, from C>E. Minor third comes a semitone smaller, and is thus C>Eb, or C#>E. Everything works from note names. The 5th is usually a P5, as in C>G. With perfects, stretch the gap by a semitone, and it's augmented, squash it by the same, it's diminished. As in aug 5 = C>G# (note, not Ab), dim 5 + C>Gb (note, not F#). Apart from 4ths, 5ths and octaves, which all start as 'perfect' from the major (and minor!) scale, the other intervals are maj or min, which actually makes little sense - the major second is in both maj and min scale, but when it's made smaller by a semitone, it's then a minor second. As in - C>D =maj 2nd. C>Db= min 2nd.

So, just about all the intervals can and will have one, two, or more names, technically. Take C>A (as far as playing those two notes is concerned - now we go by sound). C>A =maj 6th. C>Bbb= dim 7th.

The odd one for me (and other guitarists) is 'min6th'. The min6th interval is C>Ab. BUT - in say Cm6 chord, the added note in A, not Ab. That's because Cm = C, Eb, G,-Cmin, but add a 6th (A) and it now is Cm6.

Sorry this is complex, and I haven't covered it all by any means, but it's a start, I hope.

Answer 3

In a major scale, there is an interval between the tonic and the dominant but that's 4 steps along the scale and these steps are not equidistant in size.

Yes - and that interval (from the first note of the scale to the fifth) is itself called the 'fifth'. A bit confusing, but that is its name!

on my bass guitar, my strings are tuned each 5 semitones up so the intervals are equal on the chromatic scale.

And hence, the interval between your bass strings, going in the direction E-A-D-G, is not a 'fifth' (7 semitones), but a 'fourth' (5 semitones).

It seems like sometimes in music theory the intervals we discuss are between scale degrees and other times are referring to the underlying chromatic scale.

Usually they are talking about diatonic (e.g. major) scale degrees.

we have "a fifth" and "a perfect fifth" are they the same or different, and so on.

usually, a fifth = a perfect fifth = 7 semitones.

Tim's answer talks more about cases where a fifth may actually be bigger or smaller, but none of those have to do with directly referencing the chromatic scale.

Answer 4

An interval has two properties. The first is the interval number and the second is the interval quality. The names of the intervals reflect that. For example, for a "perfect fifth", the interval number is "five" and the interval quality is "perfect". Similarly, for a "major third", the interval number is "three" and the interval quality is "major".

Interval numbers count the scale degrees, including both the first and the last note. So the interval number of the interval between a C and the G above it is five, since you count five scale degrees: C D E F G.

Interval qualities tell how many chromatic steps there are between the two notes. For fourths, fifths and octaves (eighths), 5, 7, and 12 semitones respectively (this time not counting the first note) are called "perfect" fourths, fifths, and octaves. So, the C-G interval is a perfect fifth, because it involves five scale degrees (hence fifth) and seven semitones (hence perfect according to the previous definition).

For these intervals (4, 5, and 8), if the interval is one semitone smaller than perfect, its quality is "diminished". If it's larger by one semitone, it's "augmented". So, the B-F interval is a "diminished fifth" because it involves five scale degrees but only 6 semitones. On the other hand, the F-B interval is an "augmented fourth" since it involves four scale degrees but it's 6 semitones instead of 5. As you can see, evet though both intervals have the same width in terms of chromatic semitones, they are named differently.

There are also "doubly diminished" and "doubly augmented" intervals but they are rare. For example the F-B# interval would be called a doubly augmented fourth, which is different than the F-C interval which is perfect fifth. Even though B# and C are enharmonically equivalent and both intervals have the same width in terms of semitones, they are not the same. Check here if you don't know the difference between B# and C.

One possible source of confusion is that the interval quality is often omitted when talking about perfect intervals. So when someone says a "fifth", they usually mean a "perfect fifth".

For seconds, thirds, sixths, and sevenths, there are no "perfect" intervals. They can be either minor or major (or diminished, augmented, doubly diminished, doubly augmented etc.). Minor intervals are 1, 3, 8, and 10 semitones wide respectively while the major intervals are 2, 4, 8, and 11 semitones wide. If it's smaller, it is diminished, if it's larger, it is augmented. So, the F-Ab interval is a minor third because it involves three scale degrees and it's 3 semitones wide. On the other hand, the F-G# interval is an augmented second because it involves two scale degrees and it's 3 semitones wide, one wider than a major second.

Here's a quick list of intervals with their widths in semitones:

                Diminished  Minor  Perfect  Major  Augmented
Unison (first)  -1(*)       -      0        -      1
Second          0           1      -        2      3
Third           2           3      -        4      5
Fourth          4           -      5        -      6
Fifth           6           -      7        -      8
Sixth           7           8      -        9      10
Seventh         9           10     -        11     12
Octave (eighth) 11          -      12       -      13

(*) Some theorists reject the existence of diminished unison.

Answer 5

I'd just like to clarify that in tonal music the interval of a fifth is called a fifth not due to scale degrees, but rather because of the inclusive counting system used in music. For example the interval between G and G (staying on the same note) is counted as a unison (or 1, if we used a digit) and not as zero. G to A is then a second, and so on. If one then counts all of the relevant spaces between G and D, you will then have a total of five units of distance.

Related to other comments you made in your post, in tonal music, not all intervals are equidistant, that is the nature of the tonal system. Because as you pointed out, the underlying scale used for counting intervals is not all equidistant from note to note.

The chromatic scale is by and large not used when discussing intervals in tonal music because the chromatic scale is not really used in tonal music, although there are chromatic notes in tonal music, they are still conceived in relation to a major or minor underlying scale.

Answer 6

Some answers are getting SO complicated!

It's a 5th if 5 letter names are included. C,D,E,F,G. 5 letters. So any C (natural, sharp or flat) to any G (natural, sharp or flat) is some sort of fifth. Now, imagine a major scale starting on the lower note. If the top note is the 5th note of that scale, it's a Perfect 5th. If a semitone lower, it's a Diminished 5th. If a semitone higher, an Augmented 5th.

4ths, 5ths, unisons and octaves can be Diminished, Perfect or Augmented. 2nd's, 3rds, 6ths and 7ths have an additional option. The scale note is called Major. One semitone down - minor. Another - diminished. One up is still Augmented.

A guitarist who thinks in terms of fret-counting rather than staff notation is going to find this un-intuitive. Sorry.