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

lesson31.mid

Audio Clip (MIDI): Major Scale on C# by us. Another simple major scale

lesson32.mid

Let's move on to one of the basic building blocks of music: the scale. First, play a simple major scale starting on C. Perhaps you've heard this before, perhaps not, but this is what a basic major scale sounds like. What is a scale ? it's a series of notes like the one you just heard. Of course, it doesn't have to start on C. For example, we have another simple major scale starting on C#. This sounds slightly different, but you can tell that the scales are really the same thing. Hopefully, you've noticed that the note that the scales start and end on sound the same. This is an important point because a scale spans an octave, which is just two notes that are 12 notes apart.

Audio Clip (MIDI): Study on a C Major Scale by us. Using the C major scale tones

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What is a major scale? we've heard two of them, but that might not necessarily make it clear. Let's come up with an official definition: a major scale is a set of notes that defines the key of a piece. Wow, there are a lot of new terms in that. Rather than attempt to explain that, we'll give you an audio demonstration. Notice how all the notes in this demo are also notes in the C major scale? that's a technique used by composers to create music. This makes the major scale extremely useful in composing pieces. The scale that composers take their notes from is called the key of the piece. Of course composers are not limited by any means to using only certain tones. Composers are free to write whatever notes they wish to make their pieces sound good. For example, composers often quickly change from key to key, utilizing different scales.

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 Scale

Audio Clip (MIDI): Harmonic Minor Scale on 'C' by us. Simple minor scale

lesson34.mid

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

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Hopefully you were able to hear the harmonic minor scale. Notice anything different between it and the major scale? That's right; the minor scale sounded much "sadder". Like the major scale, the minor scale can be utilized by composers to create music. We've put together another little demonstration in the key of C minor. This means that the notes used in this demonstration were in that C minor scale. By the way, when a key is in a minor key, the general practice is to write the key of the piece in lower case. So, the key of this demonstration is c whereas the key of the demonstration before was C.

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.
There are a number of different types of scales used commonly in Western music, including:

  • The major scale
  • The minor scales
  • The chromatic scale
  • The modal scales
  • The whole tone scale
  • The pentatonic scale


Synthetic scales:

  • The diminished scales
  • The altered scale
  • The octatonic scales

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 tunings 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.

Tuning C4 E4 G4
Just 264 330 396
Pythagorean 260.741 330 391.11
Equal Temperament 261.625 329.63 392.00

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.

Non-Western Scales

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 basically 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 Forum, 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 scale must consist of five tones between the root tone and its octave
  • there must be at least two half-steps and no more than three half-steps between adjacent tones of the scale, which means,
  • given twelve half-steps in an octave, that the scale will have two tones separated by three half-steps and three tones separated by two half-steps
  • the two intervals of three half-steps cannot be adjacent to each other.

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 really 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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