Perfect octave.
Perfect
perfect fourth
~ All relations can be reduced to number relations.~ Vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios can be extended to other instruments.~ At its deepest level, reality is mathematical in nature.~ Philosophy can be used for spiritual purification.~ The soul can rise to union with the divine.~ Certain symbols have a mystical significance.~ There is dependence of the dynamics of world structure on the interaction of contraries, or pairs of opposites.~ The soul is a self-moving number experiencing a form of metempsychosis, or successive reincarnation in different species until its eventual purification.~ All existing objects were fundamentally composed of form and not of material substance.~ The brain was the locus of the soul; he prescribed certain secret cult-like practices.Pythagorean Theorem(see link below)Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians 1000 years earlier, he might have been the first to prove it.
The factor strings for 12 is 6*2 , 2*2*3, 4*3 if you are doing a chart than you put the length is how long the problem.
-- There are 256 bit strings of length 8 . -- There are 4 bit strings of length 2, and you've restricted 2 of the 8 bits to 1 of those 4 . -- So you've restricted the whole byte to 1/4 of its possible values = 64 of them.
perfect fourth !
A perfect octave
Perfect
Perfect
Perfect
Perfect fourth
Pythagoras discovered the mathematical relationship between musical intervals, specifically the perfect fifth, by stretching out two strings to create the interval of a fifth. He found that the ratio of the lengths of the strings producing this interval was 3:2. This observation led to the understanding of how different string lengths produce harmonious sounds, influencing both music theory and mathematics.
perfect fourth
Pythagoras discovered that to create the interval of an octave, you need to play the second string at a frequency that is double that of the first string, resulting in a 2:1 ratio. This principle illustrates how harmonious sounds can be achieved through specific numerical relationships. The octave is fundamental in music theory, highlighting the connection between mathematics and musical intervals.
The Pythagorean interval, often referred to in music, can be represented by the ratio of string lengths. When two strings are stretched to create musical intervals, if one string is played at a length ratio of 2:1, it produces an octave. However, if you mentioned a ratio of 21, it could refer to a specific interval or tuning system. Generally, in the context of Pythagorean tuning, different ratios correspond to various musical intervals, with the most common ones being 3:2 for a perfect fifth and 4:3 for a perfect fourth.
Pythagoras discovered that the ratio for creating an interval of a perfect octave is 2:1. This means that when one string vibrates at a frequency of a certain pitch, the string that is an octave higher vibrates at double that frequency. By using two strings of the same tension and varying their lengths, he found that shortening the string to half its length produces this harmonious interval. This principle laid the foundation for understanding musical harmony and the mathematical relationships between musical notes.
Pythagoras is famously associated with the study of musical acoustics, particularly the relationship between the lengths of strings and the musical notes they produce. He discovered that vibrating strings produce harmonious sounds when their lengths are in simple ratios, such as 1:2, 2:3, and 3:4, which correspond to octaves and other musical intervals. This insight laid the foundation for the mathematical principles underlying music and demonstrated the connection between mathematics and art.