Editing Pythagorean tuning (section)

== Pythagorean intervals ==
{{Main|Pythagorean interval|Interval (music)}}
Four of the above-mentioned intervals take a specific name in Pythagorean tuning. In the following table, these specific names are provided, together with alternative names used generically for some other intervals. The Pythagorean comma does not coincide with the diminished second, as its size (524288:531441) is the reciprocal of the Pythagorean diminished second (531441:524288). Also ''ditone'' and ''semiditone'' are specific for Pythagorean tuning, while ''tone'' and ''tritone'' are used generically for all tuning systems. Despite its name, a semiditone (3 semitones, or about 300 cents) can hardly be viewed as half of a ditone (4 semitones, or about 400 cents). All the intervals with prefix ''sesqui-'' are [[just intonation|justly]] tuned, and their [[Interval ratio|frequency ratio]], shown in the table, is a [[superparticular number]] (or epimoric ratio). The same is true for the octave.

:{| class="wikitable"
! rowspan="3"| Number of<br>semitones!! colspan="4"|Generic names !! colspan="3"|Specific names
|-
! colspan="2"| [[Interval (music)#Interval number and quality|Quality and number]] !! colspan="2" rowspan="2"|Other naming conventions !! rowspan="2"|Pythagorean tuning <br> (pitch ratio names)!! rowspan="2"|[[5-limit tuning]] !! rowspan="2"|[[Quarter-comma meantone|1/4-comma<br>meantone]]
|-
! Full !! Short
|-
| 0 || || || colspan="2"| [[comma (music)|comma]] || [[Pythagorean comma]]&nbsp;(524288:531441) || rowspan="2"| ||rowspan="2"| [[diesis]] (128:125)
|-
| 0 || [[diminished second]] || d2 || colspan="2"| || (531441:524288)
|-
| 1 || [[minor second]] || m2  || rowspan="2"| semitone,<br>half tone,<br>half step || diatonic semitone,<br>minor semitone || [[Pythagorean limma|limma]] (λείμμα) (256:243) || ||
|-
| 1 || [[augmented unison]] || A1 || chromatic semitone,<br>major semitone || [[Pythagorean apotome|apotome]] (αποτομή) (2187:2048) || ||
|-
| 2 || [[major second]] || M2 
| colspan="2" | tone, whole tone, whole step
| colspan="2" style="text-align: center" | [[epogdoon|epogdoön]] (επόγδοον), [[sesquioctavum]] (9:8) ||
|-
| 3 || [[minor third]] || m3 || colspan="2"| || [[semiditone]] (32:27) || [[sesquiquintum]] (6:5) ||
|-
| 4 || [[major third]] || M3 || colspan="2"| || [[ditone]] (δίτονον) (81:64) || colspan="2" style="text-align: center"| [[sesquiquartum]] (5:4)
|-
| 5 || [[perfect fourth]] || P4 || colspan="2" | diatessaron (διατεσσάρων)
| colspan="2" style="text-align: center" | epitrite (επίτριτος), [[sesquitertium]] (4:3) ||
|-
| 6 || [[diminished fifth]] || d5 
| colspan="2" rowspan="2"|   
||   || ||
|-
| 6 || [[augmented fourth]]|| A4 
|| tritone (τρίτονον) (729:512) || ||
|-
| 7 || [[perfect fifth]]|| P5 
| colspan="2" |  diapente (διαπέντε)
| colspan="2" style="text-align: center" | hemiolion (ημιόλιον), [[Perfect fifth|sesquialterum]] (3:2) ||
|-
| 12 || (perfect) [[octave]] || P8 
| colspan="2" | diapason (διαπασών)   
| colspan="3" style="text-align: center" | duplex (2:1)
|}