Equipentatonic: Difference between revisions
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== Equal trichordal scale == | == 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 [[Polychordal scale|trichord]]. It | 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 [[Polychordal scale|trichord]]. It is tuned close to just in [[24edo]]. | ||
=== Semaphore === | |||
Semaphore is a possible temperament interpretation of the equal trichordal scale, also supported by 24edo. Semaphore equalizes 6:7:8 (that is, tempers 7/6 and 8/7 together, or tempers out 49/48), turning the just equipentatonic scale into the equal trichordal one. It is sometimes considered an exotemperament due to the fact that doing so requires tuning 7/4 to 950 cents assuming a just fourth. The fourth can be flattened (bringing the generator closer to 8/7 at the cost of 7/6, at which point the natural next step is [[blackwood]] temperament), or sharpened (bringing the generator closer to 7/6 at the cost of 8/7). | |||
== Just equipentatonic scale == | == Just equipentatonic scale == | ||
Latest revision as of 09:03, 27 March 2026
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 is tuned close to just in 24edo.
Semaphore
Semaphore is a possible temperament interpretation of the equal trichordal scale, also supported by 24edo. Semaphore equalizes 6:7:8 (that is, tempers 7/6 and 8/7 together, or tempers out 49/48), turning the just equipentatonic scale into the equal trichordal one. It is sometimes considered an exotemperament due to the fact that doing so requires tuning 7/4 to 950 cents assuming a just fourth. The fourth can be flattened (bringing the generator closer to 8/7 at the cost of 7/6, at which point the natural next step is blackwood temperament), or sharpened (bringing the generator closer to 7/6 at the cost of 8/7).
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 |
