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I'm clearly thinking about this wrong, because it just doesn't make any sense to me.

The way I'm mentally modelling intervals, a minor second should just be named a second (interval encompassing 2 semitones), a major second should actually be named a third (interval encompassing 3 semitones), a minor third should be named a fourth (interval encompassing 4 semitones), and so on.

It just doesn't make sense to me why an interval of 2 semitones and an interval of 3 semitones are both called seconds, or why 3 semitones and 4 semitones are both thirds, etc, or what makes the fourth and fifth perfect. I've tried reading all about these in a million places and can't find any good explanation.

  • So, C-Db would be a second, C-D a third and C-D# a fourth? C-D is a second; the number of semitones the quality of the second it is- minor/major/augmented/diminished – Shevliaskovic Sep 8 '15 at 18:17
  • But is it nothing more than an arbitrary naming scheme?? – temporary_user_name Sep 8 '15 at 18:19
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    The intervals were "invented" backwards, in a manner of speaking. Meaning, the early western music didn't start off with semitones and then build larger intervals from there, instead they started with octaves, then fifths and fourths and thirds and sixths and finally seconds and sevenths. It wasn't until people wanted to start modulating that all the semitones and sharps and flats, etc., were needed, but they didn't want to change the names. A lot of musical terms don't makes sense the same way they did when they were coined. – Todd Wilcox Sep 8 '15 at 18:19
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You want to name intervals "absolutely" whereas the standard naming of them is in terms of "scale steps".

Now all of our Western music actually tends to happen in scales: one typical simple accompaniment of a melody is to just play the same melody a third down or a sixth up. But whether this third happens to be a minor or major one depends on its position in scale.

There are a lot of chord material you can play up and down the white keys of a piano by just keeping your hand pattern and walking up and down, and it will appear to make sense.

If you instead do the same but keep the semitone pattern instead, stuff is bound to sound strange. So since the interval relations in Western music depend more on scale steps than anything else, it makes sense to describe them in terms of that.

  • Well, you would just not name it a 3rd, since it would go from 1-12 instead of 1-7 with alterations The relationships wouldn't change I'm still trying to understand why we stick with this kind of notation :( – Alvaro Aug 14 '18 at 23:16
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The intervals are not named in relation to their distance in a chromatic scale, but rather by their distance in a diatonic scale. In other words, the interval names reflect the number of diatonic scale steps between two notes. Since diatonic scale steps come in two sizes (whole steps and half steps) there are different ways to combine them, and the resulting interval can have different sizes.

Given the shape of the diatonic scale (WWHWWWH) most intervals happen come in two flavors - a larger "major" version and a smaller "minor" version. Most fourths and fifths, though, have the same size as others. The sole exception is the tritone between the 4th and 7th scale degrees.

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I'll also note that in fully chromatic, post-tonal music, where the diatonic scale is not referential, music theorists use exactly the system outlined by Aerovistae. The interval between c and c# is ic1, between c and d is ic2, c and d# is ic3, etc. The number "4" is associated with what in tonal music, would be a "major third." (ic = "interval class")

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First off, a distance of two semitones is a major 2nd while the distance of three semitones is a minor third or could be an augmented second.

How we name intervals is very useful for constructing chords and scales since we have 7 letter names(A to G) for notes out of the 12 we use and typically only have the distance of a whole tone (or two semitones) between notes in a scale.

Let's look at this solely from a distance perspective at first. The distance from unison to octave are as follows in semitones:

 0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12

In C these notes would map to:

 C - C#/Db - D - D#/Eb - E - F - F#/Gb - G - G#/Ab - A - A#/Bb - B  - C 

As you can see, both 0 and 12 map to C and the furthest you could be away from a C in semitones is 6. This leaves us with 5 notes on each side with 1 - 2 - 3 - 4 - 5 closer to 0 and 7 - 8 - 9 - 10 - 11 closer to 12.

Now let's look at the standard interval names. In this I will use M for major, m for minor, P for Perfect and tt for tritone (which is considered both an augmented 4th and a diminished 5th).

 P1 - m2 - M2 - m3 - M3 - P4 - tt - P5 - m6 - M6 - m7 - M7 - P8

There are a few things to notice that should help you understand intervals better.

  • The tritone (or 6 semitones away) has a perfect interval above and below (P4 - tt - P5).
  • The note you are basing the name off of (C in this case which is both 0 and 12) is also perfect (P1 for unison P8 for octave) .
  • The other notes are group into twos (because of the two semitones typical max in scales) with the smaller one being minor and the bigger one being major (m2 - M2 - m3 - M3) and (m6 - M6 - m7 - M7).

When you look at it this way, you can see the symmetrical nature of intervals and how they are used to build scales.

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Intervals are not named based on their distance from a note as much as their relational distance from one letter to another letter. In the C major scale for example, C is the letter designated to represent the first note of the scale. G is the letter representing the 5th note of the scale. So, any interval from the letter C to the letter G will be called some type of 5th. The type of 5th is then determined by whether the letter G is flat, natural, or sharp. From C to Gb would be called a diminished 5th. From C to G would be called a perfect 5th. From C to G# would be called an augmented 5th.

The distance from C to Ab would be the same number of semitones away from C to G#, yet because the relationship between the two letters is different, the interval name is different. This interval would be called a minor 6th.

  • Major intervals are named because of both their relational distance from one letter to another letter and their relationship to the major scale. Every note within the major scale takes on the interval name major or perfect relative to the first note of the scale. – Christopher Gaston Sep 9 '15 at 3:51
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Intervals really have nothing to do with counting semi tones. An interval in essence is just the space between two notes be it an harmonic interval that is the space between two notes played together or a melodic one where the notes are played one after the other.

The semitones are not the issue here. C - F , C - E# and C - Gbb are all the same amount of semitones away from each other but are in no way the same interval.

You start from the bottom note and count till you get to the second note and that is the interval. C- to whatever E is a third because you have C (1) D (2) and then E (3).

It could not be simpler.

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I'll try to provide the same information, but hopefully clearer.

I'll start with the "perfect" intervals. They don't change when you go from, say, the key of C major to the key of C minor. The interval C - G (a perfect fifth) works in both keys.

However, the quality of the third depends on whether you are in C major or C minor. If you use the E flat, you are in C minor, and therefore we call that interval a "minor third." Which means, you could C = 1, D = 2, E flat = 3. Since you landed on 3, we'll call that interval a "third." What flavor of third? Minor. Because it fits with the minor scale.

I agree with you that "major second" and "minor second" are a little weird. I would just take those names as an extension of the naming convention I explained for thirds.

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