Music

First, it can be defined as Loud or Soft which refers to change of pressure inside our body space.

Second, it can be defined as Pitch (High or Low) which refers to its frequency in Hz cycles i.e. during one second of time.

Click here for Chinese musicology, that mostly uses a pentatonic scale. These scales contain 5 tones, roughly equivalent to C, D, E, G, A and have been popular in other cultures from old times. Its most popular folk song in English is probably "I come from Ala-bam-a with my Banjo on my knee"

The following table based on the diatonic (7 note) and chromatic (12 note) scale, shows the frequencies in Hz for those 5 tones and those extra 7 semitones (half-tones) in their successive octaves. See too how each note doubles in frequency cycles as it steps through each octave.

In the pentatonic scale above, the G tone should be exactly 150% higher in frequency cycles to its lower C tone, a concept explored by Pythagoras in ancient Greece. It is often called a "Perfect Fifth" (i.e. as in C,D,E,F,G) as the sound in our ears is physically "present" whenever we play the lower tone, making the two notes inseparable. However in the twelve note chromatic scale where it is the 7th semitone relative to the others, it is 149.83% higher in frequencies from the 1st semitone, a fractionally lower percentage. (See 12√27). Why the difference? The scale is accounting for its lack of a "zero" semitone prior to the first note, one of the quirks that result from its living "inside" of space and time.

From https://en.wikipedia.org /wiki/ Pitch_(music)

Click here for more on the evolution of the pitch standard A (440 Hz) used by orchestras everywhere.

 
Note Contra Great Small One-lined Two-lined Three-lined
A 55.00 110.00 220.00 440.00 880.00 1760.00
A♯ 58.27 116.54 233.08 466.16 932.33 1864.66
B 61.74 123.47 246.94 493.88 987.77 1975.53
C 65.41 130.81 Middle C
261.63
523.25 1046.50 2093.00
C♯ 69.30 138.59 277.18 554.37 1108.73 2217.46
D 73.42 146.83 293.66 587.33 1174.66 2349.32
D♯ 77.78 155.56 311.13 622.25 1244.51 2489.02
E 82.41 164.81 329.63 659.26 1318.51 2637.02
F 87.31 174.61 349.23 698.46 1396.91 2793.83
F♯ 92.50 185.00 369.99 739.99 1479.98 2959.96
G 98.00 196.00 392.00 783.99 1567.99 3135.96
G♯ 103.83 207.65 415.30 830.61 1661.22 3322.44

The tuning of the 12 tone chromatic scale above, that uses the 149.83% ratio between 1st and 5th tones, that enables complex melody lines to be played more "pleasingly", in any key, is referred to as "Equal Temperament" (ET) tuning.

Where singers / orchestras desire the "ring" achieved in having that 150% ratio between 1st and 5th tones, that use simpler melody arrangements, in a fixed key, it is referred to as "Just Intonation" (JI), as Pure, or Harmonic tuning.

Click here for a list of the ratios in the two systems.

** End of article