Editing Enharmonic equivalence (section)

===Pythagorean===
{{Main|Pythagorean tuning}}

In Pythagorean tuning, all pitches are generated from a series of [[Just intonation|justly tuned]] [[perfect fifth]]s, each with a frequency ratio of 3 to 2. If the first note in the series is an A{{music|b}}, the thirteenth note in the series, G{{music|#}} is ''higher'' than the seventh octave (1&nbsp;octave = frequency ratio of {{nobr|{{math| 2 to 1 {{=}} 2}} ;}} 7&nbsp;octaves is {{nobr|{{math| 2{{sup|7}} to 1 {{=}} 128}} )}} of the A{{music|b}} by a small interval called a [[Pythagorean comma]]. This interval is expressed mathematically as:

:<math>\frac{\ \hbox{twelve fifths}\ }{\ \hbox{seven octaves}\ } 
~=~ \frac{ 1 }{\ 2^7}\left(\frac{ 3 }{\ 2\ }\right)^{12}
~=~ \frac{\ 3^{12} }{\ 2^{19} }
~=~ \frac{\ 531\ 441\ }{\ 524\ 288\ }
~=~ 1.013\ 643\ 264\ \ldots
~\approx~ 23.460\ 010 \hbox{ cents} 
~.</math>