Interval (music) - Alternative Interval Naming Conventions

Alternative Interval Naming Conventions

As shown below, some of the above mentioned intervals have alternative names, and some of them take a specific alternative name in Pythagorean tuning, five-limit tuning, or meantone temperament tuning systems such as quarter-comma meantone. Notice that ditone and semiditone are specific for Pythagorean tuning, while tone and tritone are used generically for all tuning systems. Interestingly, 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 justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave.

The diminished second is a comma, but some commas are not diminished seconds. For instance, the Pythagorean comma (531441:524288) is the opposite of a diminished second. 5-limit tuning defines four kinds of comma, three of which meet the definition of diminished second, and hence are listed in the table below. The fourth one, called syntonic comma (81:80) can neither be regarded as a diminished second, nor as its opposite. See Five-limit tuning#Diminished seconds for further details.

Number of
semitones
Generic names Specific names
Quality and number Other naming conventions Pythagorean tuning 5-limit tuning 1/4-comma
meantone
Full Short
0 diminished second d2 descending
Pythagorean comma
(524288:531441)
lesser diesis (128:125)
diaschisma (2048:2025)
greater diesis (648:625)
1 minor second m2 semitone,
half tone,
half step
diatonic semitone,
minor semitone
limma (256:243)
augmented unison A1 chromatic semitone,
major semitone
apotome (2187:2048)
2 diminished third d3 tone, whole tone, whole step
major second M2 sesquioctavum (9:8)
3 minor third m3 semiditone (32:27) sesquiquintum (6:5)
4 major third M3 ditone (81:64) sesquiquartum (5:4)
5 perfect fourth P4 diatessaron sesquitertium (4:3)
6 diminished fifth d5 tritone (TT)
6 augmented fourth A4
7 perfect fifth P5 diapente sesquialterum (3:2)
12 (perfect) octave P8 diapason duplex (2:1)

Additionally, some cultures around the world have their own names for intervals found in their music. For instance, 22 kinds of intervals, called shrutis, are canonically defined in Indian classical music.

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