Equipentatonic
An equipentatonic scale is a scale with 5 approximately equally spaced notes within the octave. A tuning system that generates an equipentatonic scale may be conceptualized with the 5-form.
The basic equipentatonic is 5edo, where all the steps are tuned to be precisely equal. It features steps of (1200/5) = 240 cents. Below are several other examples of equipentatonic scales.
Equal trichordal scale
The equal trichordal scale is the scale of the form and mode LLsLL, where s represents 9/8 and L represents sqrt(4/3). It is so named by Vector because it is constructed from the equally divided trichord. It can represent Semaphore temperament or simply an equally divided hemipythagorean subset. It is tuned close to just in 24edo.
Just equipentatonic scale
The just equipentatonic is the scale 12:14:16:18:21:24, either as an otonal or utonal chain. It has the pattern LMsLM, where L is 7/6, M is 8/7, and s is 9/8. It is a part of the reason why 5edo represents the structure of the 2.3.7 group so well.
Slendro
Slendro is an equipentatonic gamelan tuning used in Indonesian music. It is often approximated as 5edo, however its tuning varies. It is usually tuned with stretched octaves. One tuning in particular more closely resembles an extremely soft pentic (2L 3s) MOS than a perfect equipentatonic.[[citation needed]]
Other equipentatonic scales
Any pentatonic MOS has a range of equipentatonic tunings. The following is a table of equipentatonic MOSes with related temperaments, which all serve as basic temperaments of the 2.3.7 subgroup, though due to being 5-form their extensions to 5/4 are rather complex and sensitive to detuning.
| MOS | Pattern | Temperament | EDO |
|---|---|---|---|
| 4L 1s | LLsLL | Semaphore | 29edo |
| 3L 2s | LLsLs | Buzzard | 28edo |
| 2L 3s | LssLs | Archy | 27edo |
| 1L 4s | Lssss | Slendric | 26edo |
Table of equipentatonic intervals
| # | Name (ADIN) | Tuning range | Just intonation | Equal-tempered | Equitrichordal | Just equipentatonic | Soft pentic |
|---|---|---|---|---|---|---|---|
| 0 | Unison | 0c | 1/1 | 0c | 0c | 0c | 0c |
| 1 | Major second, minor third | 220-270c | 9/8, 8/7, 7/6 | 240c | 249c | 231c, 267c | 222-267c |
| 2 | Perfect fourth | 480-500c | 21/16, 4/3 | 480c | 498c | 498c | 480-489c |
| 3 | Perfect fifth | 700-720c | 3/2, 32/21 | 720c | 702c | 702c | 711-720c |
| 4 | Major sixth, minor seventh | 930-980c | 7/4, 12/7, 16/9 | 960c | 951c | 933c, 969c | 933-978c |
| 5 | Octave | 1200c | 2/1 | 1200c | 1200c | 1200c | 1200c |
