Section 2: The progression and number of notes of musical intervals

The musical intervals are explained by the series of intervals and the number of notes, both of which are indispensable.

The number of lines and spaces contained in an interval on the staff is called the degree of the interval. Each line or space of the staff is called a degree. The interval formed by adjacent lines and spaces is called a second degree. The rest are deduced in sequence.

The degrees of musical intervals are marked with Arabic numerals. The number of semitones or whole tones contained in an interval is called the number of notes of the interval. The number of notes in musical intervals is marked by fractions, whole numbers, and mixed fractions.

In order to distinguish intervals with the same series but different numbers of notes, words must be used to explain them, such as major, minor, increasing, decreasing, doubling, doubling, pure, etc. (one degree, fourth degree, fifth degree, etc.) There are no great or small degrees in degrees and octaves, and there is no purity in second, third, sixth and seventh degrees). These descriptive words are written in front of the interval series, such as perfect fifth, major sixth, etc.

Section 3 Natural intervals and changed intervals

Pure intervals, major intervals, minor intervals, augmented fourths and diminished fifths are called natural intervals.

1. Pure one degree A degree with a note number of 0 is called a pure degree.

2. Minor second The second with a note number of 1/2 is called a minor second.

3. Major second The second with a note number of 1 is called a major second.

4. Minor third The third with a note number of 1 and 1/2 is called a minor third.

5. Major third The third with a note number of 2 is called the major third.

6. Perfect fourth A fourth with a note number of 2 and 1/2 is called a perfect fourth.

7. Augmented fourth A fourth with a note number of 3 is called an augmented fourth.

8. Diminished fifth A fifth with a note number of 3 is called a diminished fifth.

9. Perfect fifth A fifth with a note number of 3 and 1/2 is called a perfect fifth.

10. Minor sixth The sixth with a note number of 4 is called the minor sixth.

11. Major Sixth A sixth with a note number of 4 and 1/2 is called a major sixth.

12. Minor seventh The seventh with a note number of 5 is called the minor seventh.

13. Major Seventh A seventh with a note number of 5 and 1/2 is called a major seventh.

14. Pure octave An octave with a note number of 6 is called a pure octave.

In the staff, two adjacent lines or two spaces always form a third interval, and two lines separated by a line or two spaces separated by a space always form a fifth interval. The line that separates two lines and the space that separates two spaces always constitute a seventh.

The augmented fourth and diminished fifth, because they contain three whole tones, are also called three whole tones or three whole tones.

Diatonic intervals can begin at any level, upward or downward.

All increasing and decreasing intervals (except augmented fourths and diminished fifths) and doubling and doubling intervals are called changing intervals.

Various intervals are derived from natural intervals.

Raising the crown sound or lowering the root sound can increase the number of interval sounds; conversely, lowering the crown sound or raising the root sound can reduce the number of interval sounds.

Intervals with the same series but different numbers of notes have the following relationship:

When major intervals and pure intervals increase by half a step, they become augmented intervals.

When minor intervals and pure intervals are reduced by a semitone, they become diminished intervals. But it is impossible to reduce one degree, because no matter what changes are made to the one-degree interval, it can only increase the interval of the interval.

A minor interval increases by a semitone and becomes a major interval, and a major interval decreases by a semitone and becomes a minor interval.

The augmented interval increases and changes the interval into a doubled interval. The most commonly used doubled intervals are doubled by one degree, doubled by fourth, and doubled by octave.

Diminished intervals reduce the change by half a step and become doubled intervals. The most commonly used doubled intervals are doubled fifths and doubled octaves.

Section 4: Single interval and polyphonic interval

An interval of no more than an octave is called a single interval. Intervals exceeding an octave are called polyphonic intervals. Therefore, the name of a polyphonic interval is formed by adding a few octaves in front of the name of a monophonic interval. Such as the major second separated by one octave, the major second separated by two octaves

The transposition of the fifth interval

The root and crown of the interval are mutually exclusive Reversal is called interval transposition.

Interval inversions can be performed within one octave or beyond. When the interval is transposed, the root or crown can be moved, or the root and crown can be moved together.

The following rules apply when intervals are transposed:

1. All intervals are divided into two groups, and they can be reversed. The total number of intervals that can be reversed is 9, so if we want to know how many degrees a certain interval becomes after transposition, we can subtract the number of notes of the original interval from 9.

2. Except for pure intervals, other intervals become opposite intervals after transposition.

Section 6: Methods of forming and identifying intervals

The basic method of forming and identifying intervals is based on the number and progression of intervals. The second way to form and identify intervals is to use narrow intervals. The third method is to compare the intervals with the intervals between basic tone levels, and draw conclusions based on the interrelationships of various intervals with the same series but different note numbers.

Section 7 Equal Intervals

When two intervals are listened to in isolation, they have the same sound effect, but have different meanings and writing methods in the music. Such intervals are called equal intervals.

Equal intervals are produced by changes in equal notes. There are two types of equal intervals:

1. The two tones in the interval do not change the progression of the interval due to changes in equal notes.

2. Change the progression of musical intervals due to changes in equal pitch.

Equal intervals are mainly used in key changes.

Section 8 Consonant and Disconsonant Intervals

According to the auditory impression produced by the interval, the interval can be divided into consonant intervals and dissonant and dissonant intervals.

The intervals that sound pleasant and integrated are called consonant intervals.

Consonance intervals can be divided into three types:

1. Extremely perfect consonance intervals

That is, a pure degree in which the sounds are completely unified and a pure degree in which the sounds are almost completely unified. Octave.

2. Complete consonance interval

That is, the major and minor thirds and major and minor sixths in which the sounds are quite integrated.

3. Incomplete consonance intervals are minor and minor thirds and major and minor sixths that are not well integrated.

The characteristic of perfect consonance intervals and perfect consonance intervals is that the sound is a bit hollow, while the sound of imperfect consonance intervals is fuller.

Intervals that sound harsh and do not blend well with each other are called dissonant intervals. Major and minor 2nds, major and minor 7ths, and all increased and decreased intervals (including augmented 4ths and diminished 5ths) doubled and doubled intervals fall into this category.

The consonance and dissonance of sounds are not only determined by the physical complexity of the vibration number ratio of the sounds, but also the modal significance of each tone in the interval can seriously change the dissonance of the interval.

Consonant intervals are still consonant intervals after inversion. A dissonant interval remains a dissonant interval after inversion.

Section 9 Stable Intervals and Unstable Intervals

In the simultaneous combination of two tones, intervals can be divided into two types: consonant and dissonant. In terms of stability and instability, intervals can be divided into stable intervals and unstable intervals.

An interval composed of stable intervals is called a stable interval.

An interval composed of an unstable interval or a stable level and an unstable level is an unstable interval.