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I am working through a music theory workbook and one interval question is giving me trouble. The question shows a treble clef in C major with a G and F above it. I am asked to name the interval and indicate if it is perfect major or minor.

I count the lines and spaces and come up with a major 7th. The answer key says it is a minor 7th.

I'd like to know what the rule is to deal with this and what other situations counting lines and spaces doesn't work.

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    If G to F is a major seventh in your calculation, what would G to F# be then? A supermassive seventh? What would be a minor seventh from G? – piiperi Reinstate Monica Jan 12 at 23:07
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    @piiperiReinstateMonica F lieutenant colonel? – Sam Jan 12 at 23:51
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    Lines and spaces do not distinguish major from minor intervals. (This is a fundamental bug in the modern notation system and will probably never be fixed.) You must keep track of the exact intervals on every intermediate tone to get the right answer. – Kilian Foth Jan 13 at 8:07
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    @KilianFoth it is a fundamental feature of the notation system. It works on a certain level of abstraction, a scale, so the reader and writer can concentrate on what’s relevant. Only changes to the default scale are notated with accidentals, which is good. Removing this essential feature would break the system and make it much less suitable for working with western music. – piiperi Reinstate Monica Jan 13 at 9:34
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    "I count the lines and spaces and come up with a major 7th." – You correctly determined that it was a 7th, but how did you determine that it was major? – Tanner Swett Jan 13 at 16:22
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The common way of approaching this is determining whether the upper pitch is in the major scale of the lower pitch.

From the standpoint of intervals, it doesn't matter that we're in C major; we're only looking at G up to F.

Since G is the lowest pitch, let's think of the G-major scale, which has an F♯. G up to F♯ would be a major seventh, because the latter pitch is in the major scale of the former. But if we lower this F♯ to an F♮, it then creates a minor seventh interval.

Slightly different rule for 4ths 5ths and unisons/octaves. The interval that fits the major scale of the lower note is called Perfect, one semitone smaller is called Diminished.

  • What if you have a fixed noted above and need to find the note for a given interval (for example writing counterpoint with treble CF)? – Sam Jan 12 at 23:29
  • @Sam You can approach it in one of two ways. First, you can find the note name itself (without accidentals) and then add accidentals to change the interval quality. Imagine you want a major 7th below G: the 7th below is some type of A, but A–G is a minor seventh. Since a major 7th is larger than a minor 7th, we need to make this interval larger, so we lower the A to A♭. The second approach is intervallic inversion, which I discuss in my answer here. In short, a major 7th down is the same as a minor 2nd up, just transferred by octave. – Richard Jan 12 at 23:33
  • Thanks for the answer, very helpful. – Sam Jan 13 at 0:06
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    The reason it doesn't work for the perfect intervals, it should be noted, is that perfect intervals cannot be major nor minor, so determining whether such an interval is major or minor is meaningless. The reason it doesn't work for seconds is rather different. – phoog Jan 13 at 2:34
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    With all respect, that first sentence could be misleading. True, it works for some intervals, but 'in maj/min scale' isn't a good criterion. Obviously 2nds aren't in that equation, nor are 4ths and 5ths, for good (or even perfect) reasons. 6ths and 7ths will be the questionable ones, depending on which minor scale one considers. That pretty well leaves 3rds - which happily do get defined through their respective scales! – Tim Jan 13 at 9:10
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Many people seem to think that the minor third is called that because it is found in minor keys, minor scales, or minor chords. But it's the other way around: these things are called minor because they are characterized by the minor third. The theoretical concept of minor and major intervals arose centuries before the minor and major keys existed and before minor and major scales were called by those names.

The answer to your question, therefore, is that the minor seventh is so called because it is smaller than the major seventh. In Latin, minor means smaller, and major means bigger.

To find whether an interval is minor or major, the general solution is to look at this table, or the equivalent:

Imperfect interval  semitones, minor  semitones, major
------------------  ----------------  ----------------
2nd                  1                 2
3rd                  3                 4
6th                  8                 9
7th                 10                11

To derive intervals greater than an octave, add seven to the first column and 12 to the second and third.

To determine whether an interval is a second, third, etc., count the letters between one note and the other, inclusively. So, for example, the interval between D (or D flat or D sharp) and F (or F flat or F sharp) is going to be some sort of third, because counting D, E, and F yields three.

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    Small point: in Latin, "minor" means smaller and "major" means bigger. – psmears Jan 13 at 12:05
  • Within a diatonic scale, there are two sizes of each kind of interval (seconds, thirds, fourths, etc.), but seconds and sevenths split 2-5 or 5-2 between the smaller and larger kinds, thirds and sixths split 3-4 or 4-3, while fourths and fifths split 1-6 or 6-1. The last two are sufficiently skewed that one kind is "perfect" rather than being "minor" or "major"; the oddball is then "augmented" or "diminished". – supercat Jan 13 at 21:59
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    @psmears It is an excellent point, small or otherwise. The names make even more sense in that light. I've edited the answer; thanks for pointing it out. – phoog Jan 13 at 22:12
  • @supercat indeed, the tritone was definitely a second-class citizen or worse. It also does not exist within the hexachord, although that's also true of the minor sixth. In the hexachord the seconds are 4-1, the thirds are 2-2, and there are three perfect fourths, two perfect fifths, and one major sixth. If you want to start talking about inversions of these intervals then it's only fair to introduce one of the other two hexachords to fill in the missing notes, and then you have a C major scale or an F major scale (or actually one of the relative modes), and you end up with your analysis. – phoog Jan 13 at 22:21
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You ask about the interval made between G and the next F up. It matters not what key any intervals are found in, it's purely down to the actual notes themselves.

Intervals are always calculated from bottom to top notes. So here we start at G, and count upwards. Including G, it's - G A B C D E F. 7 letter names, making it a 7th - of some sort.

Now, we can use the fact that in key G (that of the lower note - nothing to do with the key that interval was found in), any F note is basically F♯. It's in that key signature. So, G>F♯ is called a major 7th. Making that gap smaller by a semitone means that interval now gets called minor 7th. Actually, that could be achieved in two ways - changing the G to G♯, or, as in your case, making the F♯ into F♮. Here, major= larger, and minor= smaller.

Another criterion with intervals is the number of semitones between the two notes. Minor 7ths have 10 semitones, major 7ths have 11.

Care needs to be taken as only using the number of semitones gives half of the story. G>E♯ sounds exactly the same as G>F, but that needs a different name - it's an augmented 6th!

Counting lines and spaces just isn't enough! And there are minor intervals in major keys!

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The keyboard pattern of black and white keys is the best representation and demonstration of the western tone system.

enter image description here

You can see there is a black key between F and G (F-G is a major second = 2 semi tones) If you control the inversion of the intervals you will see that all minor intervals will become major when inverted. G-F down steps = major 2nd, G-F up steps = minor 7th.

(The staff system doesn't show the semitones and major 2nd but it is since we used note lines defined that the half steps of a tetrachord (4 note scale respectively 4 tone strings) are always between B - C and E - F. The clefs define where C and F are notated, so where ever they are, one step down will be a semitone.)

Btw:

Mind that the sum of all inverted intervals = 9 (=> 1+8,2+7,3+6,4+5,5+4,6+3,7+2,8+1)

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...I count the lines and spaces...

You can't answer the question completely just by counting the number of lines and spaces. That will only give you one part of two needed to answer the question.

You need to get the basic interval number first: third, fifth, sixth, etc. Then you need to determine the specific quality of the interval.

Counting lines and spaces - which is just going through the gamut of letters A to G - will give you the basic interval class. Given G A B C D E F we go up to the seventh position to get from G to F so it is a seventh of some quality.

Getting the specific quality is a bit tricky. Technically it is determined by the exact size of the interval in half steps. A minor seventh is 10 half steps. A major seventh is 11 half steps.


In practice I think people use a number of shortcut strategies to identify intervals rather than count half steps.

One way is to know the intervals within keys. In C major the given tones G and F are the dominant and subdominant and the interval between those two is a minor seventh. In fact all sevenths in a major key are minor except between the tonic and the leading tone above (Do and TI in solfege) and the subdominant and and mediant above (FA and MI).

There are other basic interval facts like: in a major key thirds on the tonal degrees (DO, FA, SOL) are major while all others are minor, or all fifths are perfect except between FA and TI.

Understanding inversion is a helpful aid. Third invert to sixth, fifths to fourths, etc. Inversion changes major to minor and visa versa, but perfect remains perfect. You can use that in connection with knowing the half step size of small intervals like minor seconds (one half step) and major seconds (two half steps.) If you invert G to F you have F to G a major second (two half steps) which upon inversion flips major to minor and second to seventh. It's a minor seventh.

Another trick is to work relative to some know interval. An octave shortened by one half step is a major seventh, shortened by two half steps it's a minor seventh. F natural is two steps down from the octave above therefore it's a minor seventh.

All that knowledge comes with time so just keep identifying intervals.

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On a staff(stave) the lines and spaces contain all the notes but not the accidentals(or notes between the lines and spaces). Counting the lines will tell you what type of interval it is in the sense that it is a 7th interval but if it is one half step away from the octave it is a major 7th if it is a whole step away it would be a minor 7th.

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    Haven't you missed the point that some notes are on spaces? – Tim Jan 13 at 11:07
  • @Tim yes you are right, I see how that is unclear, I have edited the answer. – Timinycricket Jan 13 at 17:12
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There are two types of intervals: Perfect (which comprise unisons, fourths, fifths and octaves) and non-perfect (2nds, 3rds, 6ths and 7ths).

Perfect intervals can be augmented (raised a semitone) or diminished (lowered a semitone). For example, C-G is a perfect 5th, C-G# is an augmented 5th, and C-Gb is a diminished 5th.

Non-perfect intervals can be either major or minor. The wider one is major and the narrower is minor. Example: C-D is a major 2nd and C-Db is a minor 2nd.

Inverting an interval (i.e. the top note is transposed below the bottom note) yields the following results:

  1. Unisons stay the same; 2nds become 7ths, 3rds become 6ths, 4ths become 5ths (and vice versa)
  2. Major intervals become minor and minor intervals become major
  3. Diminished intervals become augmented and augmented intervals become diminished
  4. Perfect intervals stay perfect

For sevenths (we're considering the particular case of G-F), we can think of it in two ways:

  1. We have two "sevenths" starting from G. The first one is G-F and the second one is G-F#. The fact that G-F is the narrower one means that G-F is a minor 7th, and as such G-F# is a major 7th.
  2. When inverting the interval, we have F-G. as F-G is a major second, the original interval (G-F) should be a minor 7th. Likewise, F#-G is a minor second, so G-F is a major 7th.
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    Imperfect intervals can also be diminished or augmented. The augmented second is a favorite of mine as a melodic interval. The diminished third is also a fairly common melodic interval. – phoog Jan 14 at 6:29
  • Never heard of 'imperfect' intervals! Your 2nd para is misleading. Intervals are not 'raised' or 'lowered' by a semitone. Did you mean the higher note. Check your last paragraph. And there are in fact 4 "sevenths", not two. – Tim Jan 15 at 6:49

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