Though Heinz Bohlen proposed the non-octave-repeating 833 cents scale based on combination tones, the tuning features relations based on the golden ratio.
12.
Combination tones can also be produced electronically by combining two signals in a circuit that has nonlinear distortion, such as an amplifier subject to clipping or a ring modulator.
13.
Note that the lowest combination tone ( 100 Hz ) is a 17th ( 2 octaves and a major third ) below the lower ( actual sounding ) note of the tritone.
14.
The rest of the combination tones are octaves of 100 Hz so the 7 : 5 interval actually contains 4 notes : 100 Hz ( and its octaves ), 300 Hz, 500 Hz and 700 Hz.
15.
In music, they are most commonly known by the name of'combination tones','difference tones', and sometimes'Tartini tones'( after the violinist Giuseppe Tartini, who is credited with discovering them ).
16.
When one contrasts this with a dissonant interval such as a tritone ( not tempered ) with a frequency ratio of 7 : 5 one gets, for example, 700 500 = 200 ( 1st order combination tone ) and 500 200 = 300 ( 2nd order ).
17.
For example, a perfect fifth, say 200 and 300 Hz ( cycles per second ), causes a listener to perceive a combination tone of 100 Hz ( the difference between 300 Hz and 200 Hz ); that is, an octave below the lower ( actual sounding ) note.
18.
A "'combination tone "'( also called "'resultant "'or "'subjective "'tone ) is a psychoacoustic phenomenon of an additional tone or tones that are artificially perceived when two real tones are sounded at the same time.
19.
This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order combination tones of 200 ( 300 100 ) and 100 ( 200 100 ) Hz and all further nth-order combination tones are all the same, being formed from various subtraction of 100, 200, and 300.
20.
This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order combination tones of 200 ( 300 100 ) and 100 ( 200 100 ) Hz and all further nth-order combination tones are all the same, being formed from various subtraction of 100, 200, and 300.
