Equiheptatonic
An equiheptatonic scale is a scale with 7 approximately equally spaced notes within the octave. A tuning system that generates an equiheptatonic scale may be conceptualized with the 7-form.
The basic equiheptatonic is 7edo, where all the steps are tuned to be precisely equal. It features steps of (1200/7) ~= 171.4 cents. Below are several other examples of equipentatonic scales.
Equitetrachordal scale
The equitetrachordal scale is the scale sssLsss where L represents 9/8, and s represents the cube root of 4/3. If s is taken to be 11/10 and s+s to be 6/5, the result is Porcupine temperament, the most common temperament interpretation of the equitetrachordal scale. It is tuned close to just in 29edo.
Just equiheptatonic scale
This is Ptolemy's equable diatonic, the otonal or utonal series 18:20:22:24:27:30:36, which has steps of 10/9, 11/10, and 12/11 in each tetrachord and 9/8 separating them.
Other equiheptatonic scales
Any heptatonic MOS has a range of equiheptatonic tunings. The following is a table of equiheptatonic MOSes with related temperaments, expressed here as temperaments of the 2.3.5 subgroup (though often, other more accurate interpretations are available). Unlike equipentatonic systems, the scale is usually not tuned quite as equally, so extensions to 7 are more common.
| MOS | Pattern | Temperament [2.3.5] | Temperament [2.3.11] | Temperament [2.3.13] | EDO |
|---|---|---|---|---|---|
| 6L 1s | LLLLLLs | Tetracot | 7 & 27 | find 2.3.13 interpretation cuz sintel temper is not cooperating | 27 |
| 5L 2s | LLsLLLs | Meantone | Alpharabian flattone | Deeptone | 26 |
| 4L 3s | LLsLsLs | Sixix | 7 & 25 | 25 | |
| 3L 4s | LssLsLs | Dicot | Rastmic | Intertridecimal | 24 |
| 2L 5s | LssLsss | Mavila | 7 & 23 | 2 & 7 (sets 13/8 to the major sixth) | 23 |
| 1L 6s | Lssssss | Porcupine | Alpharabian porcupine | 7 & 22 | 22 |
Table of equiheptatonic intervals
| # | Name | Tuning range | Just intonation | Equal-tempered | Equitetrachordal | Equable diatonic | Soft antidiatonic | Soft diatonic | Soft mosh |
|---|---|---|---|---|---|---|---|---|---|
| 0 | Unison | 0c | 1/1 | 0c | 0c | 0c | 0c | 0c | 0c |
| 1 | Second | 130-210c | 10/9, 11/10, 12/11, 16/15, 9/8 | 171c | 166c | 182c, 151c | 157-208c | 138-185c | 150-200c |
| 2 | Third | 310-380c | 5/4, 6/5, 11/9 | 343c | 332c | 351c, 316c | 313-365c | 323-369c | 343-350c |
| 3 | Fourth | 480-550c | 11/8, 4/3 | 514c | 498c | 498c | 514-522c | 508-514c | 500-550c |
| 4 | Fifth | 650-720c | 3/2, 16/11 | 686c | 702c | 702c | 678-686c | 686-692c | 650-700c |
| 5 | Sixth | 820-890c | 5/3, 8/5, 18/11 | 857c | 868c | 884c, 849c | 835-887c | 831-877c | 850-857c |
| 6 | Seventh | 990-1070c | 20/11, 9/5, 16/9, 11/6, 15/8 | 1029c | 1034c | 1018c, 1049c | 992-1043c | 1015-1062c | 1000-1050c |
| 7 | Octave | 1200c | 2/1 | 1200c | 1200c | 1200c | 1200c | 1200c | 1200c |
