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.
Read more about this topic: Interval (music)
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