Editing Chromatic scale (section)

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

The most common conception of the chromatic scale before the 13th century was the [[Pythagorean tuning|Pythagorean chromatic scale]] ({{audio|Shí èr lǜ on C.mid|Play}}). Due to a different tuning technique, the twelve semitones in this scale have two slightly different sizes. Thus, the scale is not perfectly symmetric. Many other [[tuning system]]s, developed in the ensuing centuries, share a similar asymmetry.

In Pythagorean tuning (i.e. 3-limit [[just intonation]]) the chromatic scale is tuned as follows, in perfect fifths from G{{music|b}} to A{{music|#}} centered on D (in bold) (G{{music|b}}–D{{music|b}}–A{{music|b}}–E{{music|b}}–B{{music|b}}–F–C–G–'''D'''–A–E–B–F{{music|#}}–C{{music|#}}–G{{music|#}}–D{{music|#}}–A{{music|#}}), with sharps ''higher'' than their [[enharmonic]] flats (cents rounded to one decimal):

:{| class="wikitable" style="text-align: center"
|-
!width=4%|
!width=4%| C 
!width=4%| D{{music|flat}} 
!width=4%| C{{music|#}} 
!width=4%| D 
!width=4%| E{{music|flat}}
!width=4%| D{{music|#}} 
!width=4%| E 
!width=4%| F 
!width=4%| G{{music|flat}}
!width=4%| F{{music|#}}
!width=4%| G 
!width=4%| A{{music|flat}} 
!width=4%| G{{music|#}}
!width=4%| A 
!width=4%| B{{music|flat}}
!width=4%| A{{music|#}}
!width=4%| B
!width=4%| C
|-
!Pitch<br />ratio
| 1 || {{frac|256|243}} || {{frac|2187|2048}} || {{frac|9|8}} || {{frac|32|27}} || {{frac|19683|16384}} || {{frac|81|64}} || {{frac|4|3}} || {{frac|1024|729}} || {{frac|729|512}} || {{frac|3|2}} || {{frac|128|81}} || {{frac|6561|4096}} || {{frac|27|16}} || {{frac|16|9}} || {{frac|59049|32768}} || {{frac|243|128}} || 2
|-
!Cents
| 0 || 90.2 || 113.7 || 203.9 || 294.1 || 317.6 || 407.8 || 498 || 588.3 || 611.7 || 702 || 792.2 || 815.6 || 905.9 || 996.1 || 1019.6 || 1109.8 || 1200
|}
where {{frac|256|243}} is a diatonic semitone ([[Pythagorean limma]]) and {{frac|2187|2048}} is a chromatic semitone ([[Pythagorean apotome]]).

The chromatic scale in Pythagorean tuning can be tempered to the [[17 equal temperament|17-EDO tuning]] (P5 = 10 steps = 705.88 cents).