scaling

Examples of scaling in the following topics:

• Other Scales

  • Some, like pentatonic and octatonic scales, have fewer or more notes per octave, but many have seven tones, just as a major scale does.
  • For example, one class of scales that intrigues some composers is symmetrical scales.
  • The chromatic scale and whole tone scales fall into this category, but other symmetrical scales can also be constructed.
  • Often the name of a scale simply reflects what it sounds like to the person using it, and the same name may be applied to different scales, or different names to the same scale.
  • Like chromatic and whole tone scales, a diminished scale is "symmetrical".

• The Blues Scale

  • Blues scales are closely related to pentatonic scales.
  • (Some versions are pentatonic. ) Rearrange the pentatonic scale in Figure 4.68 above so that it begins on the C, and add an F sharp in between the F and G, and you have a commonly used version of the blues scale.
  • Listen to this blues scale: http://cnx.org/content/m11636/latest/BlueScale.mid.

• Economies and Diseconomies of Scale

  • In economics, returns to scale describes what happens when the scale of production increases over the long run when all input levels are variable (chosen by the firm).
  • There are three stages in the returns to scale: increasing returns to scale (IRS), constant returns to scale (CRS), and diminishing returns to scale (DRS).
  • Returns to scale vary between industries, but typically a firm will have increasing returns to scale at low levels of production, decreasing returns to scale at high levels of production, and constant returns to scale at some point in the middle .
  • This graph shows that as the output (production) increases, long run average total cost curve decreases in economies of scale, constant in constant returns to scale, and increases in diseconomies of scale.
  • Identify the three types of returns to scale and describe how they occur

• Harmonic and Melodic Minor Scales

  • All of the scales above are natural minor scales.
  • The harmonic minor scale raises the seventh note of the scale by one half step, whether you are going up or down the scale.
  • (Please see Beginning Harmonic Analysis for more about this. ) In the melodic minor scale, the sixth and seventh notes of the scale are each raised by one half step when going up the scale, but return to the natural minor when going down the scale.
  • Rewrite each scale from Figure 4.23 as an ascending harmonic minor scale.
  • Rewrite each scale from Figure 4.23 as an ascending and descending melodic minor scale.

• Pentatonic Scales

  • Listen to the black key pentatonic scale.
  • Like other scales, this pentatonic scale is transposable; you can move the entire scale up or down by a half step or a major third or any interval you like.
  • For more on patterns of intervals within scales, see Major Scales and Minor Scales. ) Now listen to a transposed pentatonic scale: http://cnx.org/content/m11636/latest/pentatonic2.mid.
  • Any scale that uses only five notes within one octave is a pentatonic scale.
  • You may use more than one octave of each scale, but use only one scale for each piece.

• Minor Scales

  • Minor scales sound different from major scales because they are based on a different pattern of intervals.
  • Just as it did in major scales, starting the minor scale pattern on a different note will give you a different key signature, a different set of sharps or flats.
  • The scale that is created by playing all the notes in a minor key signature is a natural minor scale.
  • To create a natural minor scale, start on the tonic note and go up the scale using the interval pattern: whole step, half step, whole step, whole step, half step, whole step, whole step.
  • For each note below, write a natural minor scale, one octave, ascending (going up) beginning on that note.

• Scales and Scale Degrees

  • The first pitch of the scale, called the tonic, is the pitch upon which the rest of the scale is based.
  • Here is the D major scale.
  • It is called the "D major scale" because the pitch D is the tonic and is heard at both ends of the scale.
  • Another scale with which you are likely very familiar is the minor scale.
  • There are several scales that one might describe as minor, all of which have a characteristic third scale degree that is lower than the one found in the major scale.

• Farenheit Scale

  • The Fahrenheit scale measures temperature.
  • The unit of this scale is the degree Fahrenheit (°F).
  • The Fahrenheit scale was replaced by the Celsius scale in most countries in the mid- to late-20th century, though Canada retains it as a supplementary scale that can be used alongside the Celsius scale.
  • The Fahrenheit scale remains the official scale of the United States, the Cayman Islands, Palau, the Bahamas, and Belize.
  • Explain how the Fahrenheit scale is defined and convert between it and Celsius

• Scales and Western Music

  • In the chromatic scale, every interval is a half step.
  • In a whole tone scale, every interval is a whole step.
  • Because of this, most traditional and popular Western music uses major or minor scales rather than the chromatic or whole tone scales.
  • There are basically two possible whole tone scales.
  • Now write a whole tone scale beginning on an a flat.

• Solving Problems with Logarithmic Graphs

  • Here are some examples of functions graphed on a linear scale, semi-log and logarithmic scales.
  • The top left is a linear scale.
  • The bottom right is a logarithmic scale.
  • The top right and bottom left are called semi-log scales because one axis is scaled linearly while the other is scaled using logarithms.
  • Top Left is a linear scale, top right and bottom left are semi-log scales and bottom right is a logarithmic scale.