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What is Scale
In music, a scale is an ascending or descending series of notes or pitches, as opposed to a series of intervals, which is a musical mode. Each note in a scale is referred to as a scale degree. Though the scales from musical traditions around the world are often quite different, the pitches of the notes in any given scale are usually related by a mathematical rule. Scales are theoretical constructs which may be used to control a composition, but much music is written without any scale in mind. Scales may be described as tonal, modal, diatonic, derived or synthetic, and by the number of tones included.
The Major Scale
A Scale is a succession of notes in upward or downward steps and based around a type of scale. Scales types may be major, minor, chromatic, diatonic, or pentatonic … and there are many many more.
The musical scale is based on octaves. Moving up one octave is defined as doubling the frequency. The octave appears to be an important musical interval in all cultures. To a human ear there is an obvious "sameness" about the two notes. But why do they sound similar? The ears can't know about the mathematical relationship. Possibly this is connected with the way the brain processes sound, but as far as I know, no one knows for sure.
Audio Clip (MIDI): Major Scale on C by us. Simple major scale
Audio Clip (MIDI): Major Scale on C# by us. Another simple major scale
Audio Clip (MIDI): Study on a C Major Scale by us. Using the C major scale tones
Now, we've neglected to mention some important aspects of the major scale. Not only does the scale define the key of the piece, but the notes in the scale are not variable. In other words, a composer cannot make up anything he or she wants and call it a scale. Instead, all major scales sound very similar and are all based on the same scale. For example, if you took the basic C major scale and bumped it up a few steps, you'd still have a major scale.
The Minor ScaleAudio Clip (MIDI): Harmonic Minor Scale on 'C' by us. Simple minor scale
Hopefully, you now have some understanding on what a major scale is. Later on, we will go into more depth onto what the notes are that make up the major scale. First, though, we'd like to look into another type of scale: the minor scale. Again, don't worry too much about what the notes in this scale are; just play our simple harmonic minor scale starting (and ending) on C. What's a harmonic minor scale, you ask? There are three different types of minor scales: natural, melodic, and harmonic. They all sound very similar but are slightly different.
Audio Clip (MIDI): Study on a 'c' Minor Scale by us. Using the 'c' minor scale tones
Now we know a little bit about how scales and keys work. There's still a whole lot more that we need to learn about music, though. Remember that music is more than just notes put together, there are also many different other components of music, including complex rhythms. Speaking of rhythms, continue to the next page for a lesson on rhythm.
Three Western Musical Scales
Scales in traditional Western music consist of seven notes, made up of a root
note and six other scale degrees whose pitches lie between the root and its
first octave. Notes in the scale are separated by whole and half step intervals
of tones and semitones.
The octave must then be divided into notes. This is where it gets complicated. There are two issues: 1 how many notes per octave, and (2) the "tuning," meaning the frequency ratios from note to note. Standard western scales have 12 notes per octave. There does not seem to be a consensus on the reason for this choice. Three of the possible guitar tuning for the 12 notes are given below. The frequency change from one note to the next is called a "half-step."
Finally a reference tone is required - a "standard of pitch." For most western music "A4," the fourth A from the bottom of the piano keyboard is set to 440 Hz. The one-octave step in the .wav file above is from A4 to A5.
The "Just" tuning is based on ratios of small integers so that harmonics of complex tones will tend to coincide. This avoids beats that occur between two tones of nearly the same frequency. This tuning was used in Europe in the 1600's.
The "Pythagorean" tuning is based on increasing the frequency of a note 7 half-steps higher by a factor of 3/2. The notes at octaves above and below the new note are then also determined. The process is then iterated. This scale dates back to the Greek philosopher, and supposedly relates to the perfect harmony of the heavens. (Unfortunately, if the process is extended to create the original note, the frequency is different than the initial original note, upsetting the perfection).
The "Equal Temperament" tuning ratios are identical from one note to the next. That is, the frequency is increased by a factor of 21/12 for each step. For the other two tunings above, the frequency of the notes differs when the starting notes differ, so each key has a different set of frequencies. For the equal tempered scale the frequencies are the same for all keys.
With A4 at 440 Hz, the frequencies of three notes of a major chord are shown in the table below. The frequencies of the three tunings are quite close. So close that the largest differences are barely perceptible to the human ear.
A chord containing only the three fundamental tones sounds the same, to my ears, for the three tunings. But when harmonics are added, then the tunings sound different. With amplitudes (picked out of the air) of 1/3, 1/5, 1/7, and 1/9 for the first four harmonics, played in the order of Just, Pythagorean, and Equal Temperament.
According to the Encarta encyclopedia, one of the most important duties of the first emperor of each new Chinese dynasty was to search out and establish that dynasty's true standard of pitch. Most Chinese music is based on the five-tone, or pentatonic, scale, but the seven-tone, or heptatonic, scale, is also used, often as an expansion of a pentatonic core. The pentatonic scale was much used in older music. The heptatonic scale is often encountered in northern Chinese folk music.
Arab melodies use tones half-way between western notes, leading to 24 notes. Scales of 22 steps are used in India. At the other extreme, Australian aborigines chant to a 2 note scale.
The distribution of notes within the octave also varies. Music of India theoretically offers 35 tunings. The tunings of the 5 notes of the gamelan music of Bali and Java are intentionally different for each orchestra, so that each has its own harmonic personality.
According to the Native American Flute music site, American Indians use pentatonic scales, which "are the most widely used musical scales in the world. They are found in China, Tibet, Mongolia, Oceania, India, Russia, and Africa, in the folk songs and hymns of Europe and the United States, and among Native Americans." The site defines a pentatonic scale based on the following criteria:
The pentatonic scale was also used by Incas, and in Africa. Finally it is also used by western composers such as Debussy, and Dvorák.
A Little History
Jourdain states that a recreation of Egyptian flutes found in Pharaoh's tombs produce tones very similar to the modern scales. The Pythagorean tuning was used for almost 2000 years. The problem was that music only sounded good in the key from which the scale notes are derived. By the 17th century the equally tempered scale was being adopted.
At the time of Beethoven and before the reference note A4 was lower - around 420 Hz. Therefore all of the music written in that period is now being played in a different key than for which it was composed! Some Stradivarius violins had to be reinforced to take the tighter strings a 440 Hz A4 requires. A higher tuning leads to a "brighter" sound, and tunings based on an A4 up to 465 Hz have been used in the 20th century.
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