How to count music bars

Determine intervals

by Ulrich Kaiser



Tones and intervals

A single note in music can be thought of as a single color in painting. When the sound c for example red the sound could be e = green and the sound G = blue be. If the tones are used one after the other like individual colors, we hear a melody:

Each note is played with a key on the piano. However, there are more than three tones, and there are many more keys / tones on the keyboard above. If the arrangement of the keys is repeated on the keyboard, the 7 tones are also repeated in a higher or lower register. The 8th tone above would therefore be on again c (or a red tone with a slightly lighter color), which is very similar to the 1st tone. Complete the missing note names on the keyboard:

Two notes that are played one after the other or together are called: interval (from Latin intervallum = space in between). The name of an interval can be derived from the number of tones that the interval comprises. The smallest interval comprises only one tone (i.e. the distance of one tone to itself). This interval is called Prime (from Latin primus = the first). The interval of the second includes two tones (from Latin secundus = the second), the third three tones (from Latin tertius = the third) etc. The following table shows the spacing of the tones and the corresponding interval names:

You can determine an interval using the tone names and fingers: If you are from d E.g. if you want to calculate a fifth upwards, you count from d = 1 off (= Prime). Of this d calculated five tones upwards with the help of the fingers (d = 1, e = 2, f = 3, G = 4 and a = 5) leads to a awho have favourited fifth over d is therefore called a:

Another example: If you put the fourth (›the fourth‹) under G want to know, you have to count back four tones: G = 1, f = 2, e = 3 and d = 4. The fourth below G called d.
Instead of note names and fingers, the intervals can also be determined by counting the keys on a keyboard:

For calculating a fifth up from the tone f off you start with the key f = 1. The fifth over f is therefore called c:

For calculating a sixth down from the note f off you start again with the key f = 1. The sixth below f is therefore called a:

And for calculating a seventh up from the tone e off you start with the key e as 1. The seventh above e is therefore called d:

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Pure, small, large, diminished, and excessive intervals

With the so-called diatonic or natural intervals - i.e. the intervals that can be formed with the white keys of the piano - a distinction is made between pure, small and large as well as reduced and excessive intervals.

pure intervalssmall and large intervalsdecreased intervalexcessive interval
Prime, fourth and fifthSecond, third, sixth and seventhFifthFourth
3 x8 x1 x1 x

In the table you can see that there are only three of the white keys pure intervals let play: Prime, Fourth and Fifth.
However, there are eight options for large and small intervals: small and large second, small and large third, small and large Sixth as well as small and large Seventh.
There is only one at a time diminished or excessive interval: the diminished fifth and the excessive fourths.

The calculation of primes, fourths, fifths, seconds and sevenths is very easy:

  • From all levels of the scale (c, d, e, f, G, a and H) primes, fourths and fifths are pure. Exceptions are the fourth above and the fifth below f (i.e. the fourth above and the fifth below the fourth scale degree).
  • At all levels of the scale, seconds are major and sevenths are minor. Exceptions are seconds and sevenths, which correspond to the tones e-f and H-c, so can be formed with the ›natural‹ semitone steps (These are the scale levels 3-4 and 7-8 in major and 2-3 and 5-6 in minor). The seconds formed by natural semitones are small, sevenths are large.

The above cases are quite simple because you can remember rules (prime, fourth, fifth are pure / seconds large and sevenths small) and deviations can be understood as exceptions (fourths above and fifths below the 4th tone and intervals with natural semitones ). It is sometimes more difficult to determine the exact size of thirds and sixths. Which thirds and sixths are major and which are minor can be remembered with an aid, the ›interval beetle‹:

Memory rules

  • From the sounds f, G and c off (= 1st, 4th and 5th scale level) all thirds and sixths upwards are major.
  • From the sounds e, a and H off, all thirds and sixths upwards are small.
  • From the sound d off, the sixth upwards is large and the third upwards is small.

And what do you have to do if you want to determine thirds or sixths downwards? Then the knowledge of the so-called helps Complementary intervals. Complementary intervals are two intervals that add up to an octave, such as fifths and fourths, minor thirds and major sixths or minor sixths and major thirds. The following diagram illustrates the situation:

So if you want the sixth below e know, you simply calculate the third e. With the help of the interval beetle one knows that this third is small (right side of the beetle) and can conclude from this that the sixth is below e is great.
Or you want the third under f knowledge. Then you simply overdetermine the sixth fthat is large (left side of the beetle) and then knows that the third is below f is small.

Summary

The following diagram summarizes the procedure for determining diatonic intervals (i.e. the intervals that can be formed with the white keys or the tones of a scale):

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Creation of the article: November 12, 2018
Last change of the post on November 12, 2018