Ch. 4 – Scales

Our ears are accustomed to melody and melodic movement that borrows from the various scales.

Major, Minor, Pentatonic, Heptatonic, Blues, Modal Scales

These are the scales we are most familiar with. All scales rely on the fact that pitches that double in frequency are the beginning and ending points of the scale. “A” 440 is the name given to the “A” above middle “C” and it vibrates at 440 vibrations per second. That pitch is called “A” or “la”. “A” also is the note that an orchestra starts their tuning. “A” is also the starting note of the natural A Minor scale. It is also the bottom note of an 88 key piano. All of the “A” notes occur at multiples of 55 Hz (vibrations per second) which is the 2nd lowest A on the piano. All the A’s from lowest to highest, left to right, are 27.5, 55, 110, 220, 440, 880, 1760, 3520

Those who don’t know “middle C” need to understand the significance of Middle C. The middle C on a piano is almost always very close to the middle of the keyboard. Other musical facts is that C happens to be a pitch that sits in a range that anybody can sing. It also is the horizontal line below the treble clef and the horizontal line above the bass clef. Middle C is a reference point and coincides with what many view as the simplest key and the first key that is formally taught to all beginners. Why? Because the scale has no black notes. That theoretically makes learning notation easier. The C Major scale consists of C D E F G A B C. All other Major scales have at least one black note. The natural A Minor is another kind of scale that has only white notes. The same notes but a different starting and finishing note. A B C D E F G A. The scales C Major and A Minor are both heptatonic. That simply means it uses seven notes
   C   D   E   F   G   A   B   C
   1   2   3   4   5   6   7   1
   A   B   C   D   E   F   G   A
   1   2   3   4   5   6   7   1

The notes that are most sympathetic or most consonant are the first and last note called the octave.

The scales are reducible to simple ratios and can be explained by fractions
1/2 is an octave, 2/3 is a perfect fifth, 3/4 is a perfect fourth, 4/5 is a major third, 5/6 is a minor third and not so predictable 8/9 is a major second a whole tone and 24/25 is a minor second
When the root is played with the interval they become more dissonant as the fractions become more complex.

In western music the smallest interval is a semi-tone which is easily seen by consecutive notes on the piano, white to black or white to white as long as no other notes are in between. On a guitar a semi-tone is just one fret from another and because the string length changes the pitch changes. Some cultures use quarter tones and they are smaller intervals and our ears find it strange to the ear.