Pythagorean tuning
Pythagorean intervals

Number of semitones
Generic names
Generic names
Generic names
Generic names
Specific names
Specific names
Specific names
Number of semitones
Quality and number
Quality and number
Other naming conventions
Other naming conventions
Pythagorean tuning
5-limit tuning
1/4-comma meantone
Number of semitones
Full
Short
Other naming conventions
Other naming conventions
Pythagorean tuning
5-limit tuning
1/4-comma meantone
0
-
-
comma
comma
Pythagorean comma (524288:531441)
-
diesis (128:125)
0
diminished second
d2
(531441:524288)
-
-
-
diesis (128:125)
1
minor second
m2
semitone, half tone, half step
diatonic semitone, minor semitone
limma (256:243)
-
-
1
augmented unison
A1
semitone, half tone, half step
chromatic semitone, major semitone
apotome (2187:2048)
-
-
2
diminished third
d3
tone, whole tone, whole step
tone, whole tone, whole step
-
-
-
2
major second
M2
tone, whole tone, whole step
tone, whole tone, whole step
sesquioctavum (9:8)
sesquioctavum (9:8)
-
3
minor third
m3
-
-
semiditone (32:27)
sesquiquintum (6:5)
-
4
major third
M3
-
-
ditone (81:64)
sesquiquartum (5:4)
sesquiquartum (5:4)
5
perfect fourth
P4
diatessaron
diatessaron
sesquitertium (4:3)
sesquitertium (4:3)
-
6
diminished fifth
d5
tritone
tritone
-
-
-
6
augmented fourth
A4
tritone
tritone
-
-
-
7
perfect fifth
P5
diapente
diapente
sesquialterum (3:2)
sesquialterum (3:2)
-
12
(perfect) octave
P8
diapason
diapason
duplex (2:1)
duplex (2:1)
duplex (2:1)

Question: What is the quality number for this equation?
Answer: The Pythagorean comma's size (524288:531441) is the reciprocal of the Pythagorean diminished second's size (531441:524288).