127834/1: Difference between revisions
Created page with "{{Infobox Interval | Ratio = 127834/1 | Monzo = 2 0 0 7 0<sup>4</sup> 23 0<sup>68</sup> 397 | Cents = 20356.6945 | Name = 127834th harmonic, 29-wood major 119th }} 127834/1, t..." |
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| Name = 127834th harmonic, 29-wood major 119th | | Name = 127834th harmonic, 29-wood major 119th | ||
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127834/1, the '''127834th harmonic''', or '''29-wood | 127834/1, the '''127834th harmonic''', or '''29-wood supermajor 119th''', is 16 octaves above [[63917/32768]]. It is a part of 397-limit harmony, the 78th prime number. | ||
The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the two is 0.534 millicents, or 1 in 2.24 million parts of an octave. | The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the two is 0.534 millicents, or 1 in 2.24 million parts of an octave. | ||