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Showing posts with the label Pythagorean

26-TET and mixolydian mode - sound ancient with modern method

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 Mixolydian mode is often referred to as a medieval church mode and can be traced to ancient Greece. For composing, to bring out the taste of the mode, the melody should accent the flat-seven note in the mode. Thus, the tunning of the note flat-seven is critical. I have discussed the 53-TET is great for perfect 5th. This 26 TET is great for minor 7th. Harmonic series again, the just intonation of minor 7th is way flatter than the 12-TET that we normally use, -31 cent, about a quarter semitone. Finding an alternative temperament is needed. In the harmonic series, the 7th harmonics is the minor 7th interval to the fundamental. The 4th and 7th are the interval of minor 7th in the same octave. The ratio of 7:4 sounds harmonious in just intonation, as the ratio is from the harmonic series. There are also other ratios of minor 7th in the harmonic series, e.g. 9:5, 16:9, etc. Harmonic series in C Borrowing the same method by Pytheogoen, but we stack in 7:4 minor 7th interval instead. Aft...

Pythagorean - Music of the Spheres vs Guan Zi - Music of earths

Pythagoras discovered musical pitches are ways of vibration. Different intervals of pitches correspond to different ratios of vibration, for example, 1:2 ratios produced an “octave”, 2:3 as fifth, etc. He found new pitches with the ratio of fifth (2:3). Pythagoras saw sound as vibration and motion, to project it to the larger scale planets moving in orbit should also produce a sound. The relative speed of planets response to the certain interval as well. For more info, please visit this article . Similarly, in ancient Chinese philosophy, Guan Zi (c. 720–645 BC) has a view of musical tones related to geography and agriculture in his Diyuen chapter. The way ancient Chinese found pitches was based on a series of adding 1/3 and subtracting 1/3, called subtracting and adding a third method (Sān fēn sǔnyì fǎ).  The starting length is 81 (3^4) namely as "Gong( 宮 )" (do), the soil of Huangtang  黃唐土 The next pitch is 81x4/3= 108 as "Zhi( 微 )" (so), the soil of Heizhi...