Twelfth root of two

<p>The twelfth root of two or 
  
    
      
        
          
            2
            
              12
            
          
        
      
    
    {\displaystyle {\sqrt[{12}]{2}}}
  
 (or <a href="/facts/Nth_root/XrRjtJGe">equivalently</a> 
  
    
      
        
          2
          
            1
            
              /
            
            12
          
        
      
    
    {\displaystyle 2^{1/12}}
  
) is an <a href="/facts/Algebraic_number/MkH1PzTK">algebraic</a> <a href="/facts/Irrational_number/Psv19TET">irrational number</a>, approximately equal to 1.0594631. It is most important in Western <a href="/facts/Music_theory/BoekvflP">music theory</a>, where it represents the <a href="/facts/Frequency/QUSbPaW8">frequency</a> <a href="/facts/Ratio/mFmhQt7T">ratio</a> (<a href="/facts/Musical_interval/aFwkkgpY">musical interval</a>) of a <a href="/facts/Semitone/lVBsLYSA">semitone</a> (Playⓘ) in <a href="/facts/Twelve-tone_equal_temperament/89BK2lpj">twelve-tone equal temperament</a>. This number was proposed for the first time in relationship to <a href="/facts/Musical_tuning/v5Q1kYxC">musical tuning</a> in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth is 7 semitones). A semitone itself is divided into 100 <a href="/facts/Cent_(music)/lsm8TJgX">cents</a> (1 cent = 
  
    
      
        
          
            2
            
              1200
            
          
        
        =
        
          2
          
            1
            
              /
            
            1200
          
        
      
    
    {\displaystyle {\sqrt[{1200}]{2}}=2^{1/1200}}
  
).
</p>

Twelfth root of two open-in-new

Twelfth root of two