29edo/Unque's compositional approach
Note: This page is currently under construction, and will be subject to major expansion in the near future. Come back soon!
29edo is far from the most common tuning system advertised to newcomers; instead, the face of microtonality for many beginners are simple enharmonic distinctions (such as those found in 17edo), extended Meantone tunings (such as 31edo), or even further divisions of the familiar 12-tone chromatic scale (such as 24edo). However, I believe that 29edo is one of the best starting places to transition from 12-tone logic into the more expansive xenharmonic colors, and on this page I plan to present not only my experience and approach with 29edo, but my reasoning for why I believe that it should compete with, if not replace, those aforementioned tunings for the role of the introduction to microtonal colors.
Intervals and Notation
29edo's highly accurate 3/2 provides a very familiar Circle of Fifths, which means that the interval categories from the 12-tone chromatic scale remain intact and recognizable, while also introducing a plethora of new categories and finer distinctions that were not present at the broader range of 12edo. Additionally, 29edo introduced one interval to fulfill each of the four interordinal functions, allowing for newcomers to explore the application of these unfamiliar intervals by using them in conjunction with the more familiar diatonic categories.
| Degree | Cents | Category | Notation | Notes |
|---|---|---|---|---|
| 0 | 0.000 | P1 | C | |
| 1 | 41.379 | A7 | B♯ | Distinct from the octave. Three major thirds reach this augmented seventh. |
| 2 | 82.759 | m2 | D♭ | |
| 3 | 124.138 | A1 | C♯ | Distinct from the minor second. This distinction nullifies the familiar enharmonic equivalences. |
| 4 | 165.517 | d3 | B𝄪, E𝄫 | |
| 5 | 206.897 | M2 | D | |
| 6 | 248.276 | Chthonic | C𝄪, F𝄫 | New region in between M2 and m3; two of them make a perfect fourth. |
| 7 | 289.655 | m3 | E♭ | |
| 8 | 331.034 | A2 | D♯ | Distinct from the minor third, as can be seen in the Harmonic Minor modes. |
| 9 | 372.414 | d4 | F♭ | |
| 10 | 413.793 | M3 | E | |
| 11 | 455.172 | Naiadic | D𝄪, G𝄫 | New region in between M3 and P4; two of them make a major sixth. |
| 12 | 496.552 | P4 | F | Just barely flatter than the fourth of 12edo, and closer to justly-tuned 4/3. |
| 13 | 537.931 | A3 | E♯ | |
| 14 | 579.310 | d5 | G♭ | Distinct from the augmented fourth. Two minor thirds reach this diminished fifth. |
| 15 | 620.690 | A4 | F♯ | Distinct from the diminished fifth. Three whole tones reach this augmented fourth. |
| 16 | 662.069 | d6 | E𝄪, A𝄫 | |
| 17 | 703.448 | P5 | G | Just barely sharper than the fifth of 12edo, and closer to justly-tuned 3/2. |
| 18 | 744.828 | Cocytic | F𝄪 | New region between P5 and m6; two of them reduce to a minor third. |
| 19 | 786.207 | m6 | A♭ | |
| 20 | 827.586 | A5 | G♯ | Distinct from the minor sixth. Two major thirds reach this augmented fifth. |
| 21 | 868.966 | d7 | B𝄫 | Distinct from the major sixth. Three minor thirds reach this diminished seventh. |
| 22 | 910.345 | M6 | A | |
| 23 | 951.724 | Ouranic | G𝄪, C𝄫 | New region between M6 and m7; two of them reduce to a perfect fifth. |
| 24 | 993.103 | m7 | B♭ | |
| 25 | 1034.483 | A6 | A♯ | Augmented Sixth chords use this interval, not the typical minor seventh. |
| 26 | 1075.862 | d8 | C♭ | |
| 27 | 1117.241 | M7 | B | |
| 28 | 1158.621 | d2 | A𝄪, D𝄫 | Distinct from the octave. Four minor thirds reach this diminished ninth. |
| 29 | 1200.000 | P8 | C |
As can be seen here, the familiar diatonic categories allow composers to root themselves in established structures, permitting them to fall back onto comprehensible harmony while still allowing for the interordinals and other new colors to be utilized alongside them.
In some cases, using ups and downs notation may be more convenient than the plain circle of fifths. In this notation, the ^ accidental represents raising an interval by a single step of 29edo; 3\29, for instance, may be notated enharmonically as an upminor second rather than an augmented unison in certain scales to avoid accidentals that may be difficult to parse, or alternatively to preserve interval arithmetic.
Scales of 29edo
5L 2s
The 5L 2s scale is generated by taking seven adjacent tones from the Circle of Fifths, just as it is in 12edo. Melodies and chords made using this scale will sound nearly identical to those that can be made using 12edo.
| Gens Up | Step Pattern | Notation | Name |
|---|---|---|---|
| 6 | LLLsLLs | C - D - E - F♯ - G - A - B - C | Lydian |
| 5 | LLsLLLs | C - D - E - F - G - A - B - C | Ionian |
| 4 | LLsLLsL | C - D - E - F - G - A - B♭ - C | Mixolydian |
| 3 | LsLLLsL | C - D - E♭ - F - G - A - B♭ - C | Dorian |
| 2 | LsLLsLL | C - D - E♭ - F - G - A♭ - B♭ - C | Aeolian |
| 1 | sLLLsLL | C - D♭ - E♭ - F - G - A♭ - B♭ - C | Phrygian |
| 0 | sLLsLLL | C - D♭ - E♭ - F - G♭ - A♭ - B♭ - C | Locrian |
5L 7s
The 5L 7s scale is an extension of 5L 2s created by continuing the generator sequence. Because the Circle of Fifths is bidirectional, the seven modes can be extended either by continuing the sequence upwards or downwards; those created by going up the chain are called grave modes, and those extended by going down the chain are called acute modes.
| Gens Up | Step Pattern | Notation | Name | Notes |
|---|---|---|---|---|
| 11 | LsLsLssLsLss | C - C♯ - D - D♯ - E - E♯ - F♯ - G - G♯ - A - A♯ - B - C | Grave Lydian | Like the seven-note Lydian, lacks a Perfect Fourth over the root. |
| 10 | LsLssLsLsLss | C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - A♯ - B - C | Grave Ionian | |
| 9 | LsLssLsLssLs | C - C♯ - D - D♯ - E - F - F♯ - G - G♯ - A - B♭ - B - C | Grave Mixolydian | |
| 8 | LssLsLsLssLs | C - C♯ - D - E♭ - E - F - F♯ - G - G♯ - A - B♭ - B - C | Grave Dorian | |
| 7 | LssLsLssLsLs | C - C♯ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C | Grave Aeolian | |
| 6 | sLsLsLssLsLs | C - D♭ - D - E♭ - E - F - F♯ - G - A♭ - A - B♭ - B - C | Grave Phrygian | Also accounts for Acute Lydian |
| 5 | sLsLssLsLsLs | C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - B - C | Acute Ionian | Also accounts for Grave Locrian |
| 4 | sLsLssLsLssL | C - D♭ - D - E♭ - E - F - G♭ - G - A♭ - A - B♭ - C♭ - C | Acute Mixolydian | |
| 3 | sLssLsLsLssL | C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - A - B♭ - C♭ - C | Acute Dorian | |
| 2 | sLssLsLssLsL | C - D♭ - D - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C | Acute Aeolian | |
| 1 | ssLsLsLssLsL | C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - G - A♭ - B𝄫 - B♭ - C♭ - C | Acute Phrygian | |
| 0 | ssLsLssLsLsL | C - D♭ - E𝄫 - E♭ - F♭ - F - G♭ - A𝄫 - A♭ - B𝄫 - B♭ - C♭ - C | Acute Locrian | Like the seven-note Locrian, lacks a Perfect Fifth over the root. |
4L 3s
The 4L 3s scale can be thought of as an alteration of the Harmonic Minor scale, which is unique to 29edo. If we notice that the augmented second is precisely three steps larger than a major second, we can distribute this error amongst the three semitones that occur in the scale, which reduces the scale to a maximum variety of two. We may also notice that this scale's pattern creates a circle of augmented seconds, which can be used to quantify the brightness of the seven modes.
The mode names for this scale are given by Ayceman.
| Gens Up | Step Pattern | Notation | Name (Ayceman) | Altered Diatonic Mode |
|---|---|---|---|---|
| 6 | LLsLsLs | C - D - E - ^F - ^G - vA - vB - C | Nerevarine | Major Augmented |
| 5 | LsLLsLs | C - D - ^E♭ - ^F - ^G - vA - vB - C | Vivecan | Harmonic Minor |
| 4 | LsLsLLs | C - D - ^E♭ - ^F - vG - vA - vB - C | Lorkhanic | Lydian #2 |
| 3 | LsLsLsL | C - D - ^E♭ - ^F - vG - vA - B♭ - C | Sothic | Dorian #4 |
| 2 | sLLsLsL | C - ^D♭ - ^E♭ - ^F - vG - vA - B♭ - C | Kagrenacan | Locrian #6 |
| 1 | sLsLLsL | C - ^D♭ - ^E♭ - vF - vG - vA - B♭ - C | Almalexian | Ultralocrian |
| 0 | sLsLsLL | C - ^D♭ - ^E♭ - vF - vG - A♭ - B♭ - C | Dagothic | Phrygian Dominant |
4L 5s
The 4L 5s scale takes the role of a diminished scale in 29edo. Since four minor thirds fall short of the octave, the chain of minor thirds can be extended into this enneatonic form. Note how the four bright modes resemble the pattern of the familiar octatonic scale, with one of the small steps duplicated, and the four darkest modes resemble the rotated variant of that scale; additionally, there is a symmetrical mode that is entirely new to 29edo.
The mode names for this scale are given by Lilly Flores.
| Gens Up | Step Pattern | Notation | Name (Flores) |
|---|---|---|---|
| 8 | LsLsLsLss | C - F𝄫 - E♭ - A𝄫♭ - G♭ - C𝄫♭ - B𝄫 - E𝄫𝄫 - D𝄫 - C | Roi |
| 7 | LsLsLssLs | C - F𝄫 - E♭ - A𝄫♭ - G♭ - C𝄫♭ - B𝄫 - A - D𝄫 - C | Steno |
| 6 | LsLssLsLs | C - F𝄫 - E♭ - A𝄫♭ - G♭ - F♯ - B𝄫 - A - D𝄫 - C | Limni |
| 5 | LssLsLsLs | C - F𝄫 - E♭ - D♯ - G♭ - F♯ - B𝄫 - A - D𝄫 - C | Telma |
| 4 | sLsLsLsLs | C - B♯ - E♭ - D♯ - G♭ - F♯ - B𝄫 - A - D𝄫 - C | Krini |
| 3 | sLsLsLssL | C - B♯ - E♭ - D♯ - G♭ - F♯ - B𝄫 - A - G𝄪 - C | Elos |
| 2 | sLsLssLsL | C - B♯ - E♭ - D♯ - G♭ - F♯ - E𝄪 - A - G𝄪 - C | Mychos |
| 1 | sLssLsLsL | C - B♯ - E♭ - D♯ - C𝄪♯ - F♯ - E𝄪 - A - G𝄪 - C | Akti |
| 0 | ssLsLsLsL | C - B♯ - A𝄪♯ - D♯ - C𝄪♯ - F♯ - E𝄪 - A - G𝄪 - C | Dini |
3L 5s
Similarly to the minor third, the major third of 29edo also does not close at the octave, allowing us to create an octatonic augmented scale. Just like the diminished scale, notice how the three brightest modes resemble the bright mode of the Tcherepnin scale, with one of the nine steps omitted; the three darkest modes similarly resemble the dark mode of that scale; and the remaining two modes both resemble the symmetrical mode of Tcherepnin.
The mode names for this scale are given by R-4981.
| Gens Up | Step Pattern | Notation | Name (R-4981) |
|---|---|---|---|
| 7 | LsLssLss | C - G𝄫♭ - F♭ - C𝄫♭ - B𝄫♭ - A♭ - E𝄫♭ - D𝄫 - C | King |
| 6 | LssLsLss | C - G𝄫♭ - F♭ - E - B𝄫♭ - A♭ - E𝄫𝄫 - D𝄫 - C | Queen |
| 5 | LssLssLs | C - G𝄫♭ - F♭ - E - B𝄫♭ - A♭ - G♯ - D𝄫 - C | Marshall |
| 4 | sLsLssLs | C - B♯ - F♭ - E - B𝄫♭ - A♭ - G♯ - D𝄫 - C | Cardinal |
| 3 | sLssLsLs | C - B♯ - F♭ - E - D𝄪 - A♭ - G♯ - D𝄫 - C | Rook |
| 2 | sLssLssL | C - B♯ - F♭ - E - D𝄪 - A♭ - G♯ - F𝄪♯ - C | Bishop |
| 1 | ssLsLssL | C - B♯ - A𝄪♯ - E - D𝄪 - A♭ - G♯ - F𝄪♯ - C | Knight |
| 0 | ssLssLsL | C - B♯ - A𝄪♯ - E - D𝄪 - C𝄪𝄪 - G♯ - F𝄪♯ - C | Pawn |
5L 1s
Just like the thirds, we can notice that the whole tones in 29edo do not close at the octave; instead, we see that five whole tones exceed the minor seventh by an edostep. However, the octave can still be closed by employing a diminished third to act as a "wolf" version of the whole tone; this leads to the scale having six distinct modes, rather than having an identical pattern on every degree as 12edo had.
The mode names for this scale are given by Lilly Flores.
| Gens Up | Step Pattern | Notation | Name (Flores) |
|---|---|---|---|
| 5 | LLLLLs | C-D-E-F♯-G♯-A♯-C | Erev |
| 4 | LLLLsL | C-D-E-F♯-G♯-B♭-C | Oplen |
| 3 | LLLsLL | C-D-E-F♯-A♭-B♭-C | Layla |
| 2 | LLsLLL | C-D-E-G♭-A♭-B♭-C | Shemesh |
| 1 | LsLLLL | C-D-F♭-G♭-A♭-B♭-C | Boqer |
| 0 | sLLLLL | C-E𝄫-F♭-G♭-A♭-B♭-C | Tsohorayim |