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Major 2nd: C-D
notice the pattern?
Octave: C-C
Major 7th: C-B
The pitch A4 is used in western music as a tuning and reference pitch. It is known as the central pitch with a frequency of 440Hz.
the formula for calculating the frequencies of the 12 pitches is:
fn = f0 x (a)^n
1) fo refers to the frequency of one set pitch (A4= 440Hz)
2) n refers to the number of half steps you are from the set pitch A4
* if you are at a higher note than A4, n is positive; if you are at a lower note than A4, n is negative*
3) a = 2^(1/12) this is about 1.059463
4) this formula is derived from the "equal tempered scale" which was created so that no matter what key something was played in, it could sound equally good or bad
using the frequency of A4, we can determine the frequency of all of the other 12 chromatic pitches used in western music
fn = f0 X (a)^n
1)find the freqency of C5
C5 is greater than A4 so n is positive
from A to C there are 3 half steps so n=3
Now set up equation
f3= 440hz(1.059463)^3
f3= 523.3Hz
the frequency of C5 is 523.3Hz
Conclusion:
To find the beat frequency between two notes, take the absolute value of the second frequency(f2) minus the first frequency(f1)
fbeat = |f2 – f1|
As a general rule of musical consonance and dissonance:
1) any beat frequency between 10Hz and 60Hz is considered dissonant
2)any beat frequency greater that 60Hz is considered consonant
In conclusion, musical tonality of dissonance/consonance can be determine using various methods as explained. The Beat Frequency, ratios, and sine graphs all serve as models of the relationship between intervals. All of the standards for consonance/dissonance are related to Western Music are not always defined the same way in Eastern or other cultural music studies.