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Notes and intervals

Notes

Before talking about complex terms and systems of music theory its basic units must be defined.

When we pick a string, say a word, or clap our hands we create energy that is transmitted through the particles of matter, the air, for example. When it reaches our eardrums, we hear a sound. This movement of energy has its moments of maximum air pressure - compression and minimum air pressure - rarefaction. Therefore, it is a wave.

Like other types of waves, the sound wave has characteristics such as wavelength, amplitude, and frequency. The wavelength defines the duration of a sound. The loudness of a sound depends on the amplitude of its wave. The frequency is the number of compression-rarefaction cycles that occur per second. It allows us to distinguish pitches from noise.

When we talk about musical pitches we have in mind sound waves with specific frequencies. A higher pitch has a greater frequency. Systematized pitches have names and symbols. They are called musical notes. Sometimes pitch, tone, and note are used as synonymous. However, you can think about these terms the next way: the pitch is a frequency that we hear, the tone is a set of sound characteristics that we mean, the note is what we write on the musical staff.


Octave

Naming

Musical notes have different naming systems. The traditional system is Do - Re - Mi - Fa - Sol - La - Si but English-speaking theorists use letters of the Latin alphabet: C - D - E - F - G - A - B. Similarly, the situation is with the designation of the octave from which the note was taken. In the conservative system, octaves have the following names and designations: sub-contra (AAA BBB), contra (CC BB), great (C B), small (c b), one-line (c1 b1), two-line (c2 b2), three-line (c3 b3), four-line (c4 b4), five-line (c5). In turn, the commonly used system offers to designate octaves with numbers: A0 B0, C1 B1, C2 B2, C3 B3, C4 B4, C5 B5, C6 B6, C7 B7, C8.

NoteAccidOctFreq
261.63 Hz

Note

Intervals

An interval is a relation between two musical pitches or, in other words, the ratio of their frequencies. We can also define an interval as the distance between two notes. Named intervals are the following: unison, second, third, fourth, fifth, sixth, seventh, and octave. When tones appear together, they form a harmonic interval which refers to vertical connections of these tones. Musical chords consist of harmonic intervals. When one tone appears after the other, the two form a melodic interval. It refers to horizontal connections. Musical scales consist of melodic intervals. When working with melodic intervals, it must be remembered that the interval is also defined relative to its lower pitch, as is the case with harmonic intervals.

The name of the octave interval is borrowed from the Latin language and represents a literal translation: the eighth. It implies a particular degree of the scale. Octave - the eighth degree of the scale. Within the octave, we can form eight original intervals from various tones of the diatonic and chromatic scales. Due to the alteration of one of the two notes, the interval does not change but the distance between both notes increases or decreases. That is why there is an auxiliary division of intervals into perfect, major, minor, diminished, and augmented. Any interval can be diminished or augmented. Second, third, sixth, and seventh can also be major or minor. When unison, octave, fifth, and fourth are not diminished or augmented they are perfect.

Inversion of intervals occurs by moving the upper note an octave down or the lower note an octave up. Inverted unison becomes octave; second - seventh; third - sixth; fourth - fifth; fifth - fourth; sixth - third; seventh - second; octave becomes unison. In this case, inverted major intervals become minor ones; minor - major; diminished – augmented; augmented - diminished; perfect intervals remain perfect.


Inversion

Distance

Intervals are measured in musical tones and semitones. A semitone is the closest distance between two different notes; one tone consists of two semitones. Minor intervals are one semitone less than major; diminished intervals are one semitone less than perfect and minor ones; augmented intervals are one semitone larger than perfect and major intervals.

Following this logic, diminished unison contains a paradoxical number of semitones - minus one semitone. Perfect unison has no distance between its notes at all. Augmented unison, as well as the minor second, contains one semitone. And finally, major second contains one whole tone; minor third – one tone and a semitone; major third – two tones; perfect fourth – two tones and a semitone; augmented fourth and diminished fifth contains three tones sometimes called tritone; perfect fifth – three tones and a semitone; minor sixth – four tones; major sixth – four tones and a semitone; minor seventh – five tones; major seventh – five tones and a semitone; perfect octave – six tones.

Intervals that extend beyond the octave represent repetitions of the relationships formed by the intervals within the octave. Such intervals are called a compound. Among them, only ninth has an independent meaning in harmony.

C
D
E
F
G
A
B
m2M2m3M3P4A4/d5P5m6M6m7M7
D♭DE♭EFF♯/G♭GA♭AB♭B
E♭EFF♯GG♯/A♭AB♭BCC♯
FF♯GG♯AA♯/B♭BCC♯DD♯
G♭GA♭AB♭B/C♭CD♭DE♭E
A♭AB♭BCC♯/D♭DE♭EFF♯
B♭BCC♯DD♯/E♭EFF♯GG♯
CC♯DD♯EE♯/FF♯GG♯AA♯
NoteAccid
to
from
QualIntDist
P10 T 0 s

Harmony

According to the impression they produce intervals are divided into consonances that sound stable and can exist independently and dissonances which are representing an element of movement that requires support and must be resolved in the interval following them. Consonant intervals are divided into perfect: unison (1:1), octave (2:1), perfect fifth (3:2); and imperfect: major sixth (5:3), major (5:4), and minor third (6:5), minor sixth (8:5). All other intervals are dissonances: major second (9:8), major seventh (15:8), minor seventh (16:9), minor second (16:15), diminished fifth (25:18), augmented fourth (45:32) and other possible diminished or augmented intervals. The perfect fourth (4:3) is a cross between consonance and dissonance. However, it relates more to dissonances. If we analyze the ratio of the frequencies of the tones involved in the interval we may notice some correlation between the determination of the consonance or dissonance of the interval and the value of the integers in the ratio. Thus from the above intervals, unison will be the most consonant and the augmented fourth will be the most dissonant interval.

Conclusion

Fundamental concepts of classical music theory are based on the laws of mathematics and physics. It is a mistake to think of the theory only as a combination of musical traditions of certain time in the cultural development of different nations or even personal preferences of theoreticians themselves. So-called rules are designed not to limit creativity but to talk about how various musical sounds interact in nature which in turn of course contributes to creative development. Theoretical knowledge directs a composer opens up new possibilities for him and provides means for their implementation. These laws existed before humanity discovered and described them and they will exist after. From here we can conclude that music theory is the physics of sound waves.