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The vibration rates per second of the vibrating bodies, strings, steel rods, etc., which produce those musical tones which are consonant, are in definite and small mathematical ratios to each other. Thus the rates of C-C' are as 1:2; of C-G, C-E, as 2:3, 4:5. In general, the simpler the fraction, the greater the consonance.
P-r C-g: Do not criticize people's noses unless you are sure they can't hear you, and don't criticize your best girl's great-aunt's nose in any case. C-y K-g: When my most intimate friend walks with another girl and exchanges lace patterns with her, what ought I to do? Ans. Adopt a dignified attitude.
F-y K-g: It is better not to wear your second best hat to church, but if your mother says you must it is not for me to question her decision. P-r C-g: Yes, it would be quite proper to say good evening to the family ghost if you met it. F-x K-g: No, it is not polite to sleep with your mouth open. What's more, it isn't safe. Something might fall into it.
We cannot avoid the observation that certain tones "go together," as the phrase is, while others do not. This peculiar impression of belonging together is known as consonance, or harmony. The intervals of the octave, the fifth, the third, for instance, that is, C-C', C-G, C-E, in the diatonic scale, are harmonious; while the interval of the second, C-D, is said to be dissonant.
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