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To easily multiply any 2-digit numbers together a simple algorithm is as follows (where a is the tens digit of the first number, b is the ones digit of the first number, c is the tens digit of the second number and d is the ones digit of the second number): (+) (+)
Note that only M 1, M 5, M 7, and M 11 give a one-to-one mapping (a complete set of 12 unique tones). This is because each of these numbers is relatively prime to 12. Also interesting is that the chromatic scale is mapped to the circle of fourths with M 5, or fifths with M 7, and more generally under M 7 all even numbers stay the same while odd numbers are transposed by a tritone.
Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit, essentially only keeping the middle digit of the result. By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held. Example:
In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.
Numerical sight singing is not the same as integer notation derived from musical set theory and used primarily for sight singing atonal music. Nor is it the same as " count singing ", a technique popularized by Robert Shaw in which the numbers sung represent the rhythms of a piece in accordance with the beat of a measure.
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The numbered musical notation (simplified Chinese: 简谱; traditional Chinese: 簡譜; pinyin: jiǎnpǔ; lit. 'simplified notation', not to be confused with the integer notation) is a cipher notation system used in mainland China, Taiwan, Hong Kong, and to some extent in Japan, Indonesia (in a slightly different format called "not angka"), Malaysia, Australia, Ireland, the United Kingdom ...
"Living by Numbers" is a song by the English synthpop group New Musik. It was the band's biggest hit worldwide, peaking at No. 13 in January 1980 in the UK and No. 12 in Ireland. The song appeared on the band's debut album, From A to B. It was used, with reworked lyrics, for a Casio advert. [1] The B-side of the single was "Sad Films ...