Temperament Tier List

This list is of the 15 rank-2 temperaments in 31edo, and is just based on how useful I think they generally are. It shouldn't be taken too seriously, all of these temperaments produce scales that are useful in certain ways for composition (except maybe slender). This also serves as a good place for me to give my thoughts on each temperament.

S+:

Meantone - Meantone is the defining temperament of 31, so much so that one could easily never venture outside of it and still find too much new material and opportunity to require stopping. The basic pentatonic and diatonic scales are useful and filled with consonance, due to the perfect fifth generator, and pental triads are generated very simply. One small issue may be the wider semitones being less useful for direction, though the 12-note provides a solution through subsets that replace the leading tone with a supermajor one. These subsets may only use major and sub pitches, or just minor and super, emphasizing this idea. Beyond this, septimal triads and tetrads are represented relatively very simply, especially harmonic structures such as 4:5:6:7 and 9/7/6/5, and these chords are placed in a way such that their tritones may resolve in a sensible way. Septimal subsets of the 12-note also manage to avoid the traditional wolf fifths except when ideal by replacing pitches, specifically the second and sixth, with the appropriate alternative that is also part of the mother scale. Harmonic series structures such as 4:5:6:7:9 also exist, and the 4:5:6:9 especially is abundant in the 7-note. Meantone[19] additionally acts as a 19-WT, splitting the interseptimal intervals into purer septimal ratios.

S:

Squares - The world of Squares is interesting, as dieses aren’t generated until the 17-note MOS, so the full melodic potential of each scale is usable, and scales such as the 8-note and 11-note have characteristics that make them fantastic for alternative types of resolution. The small semitones in the scales resolve to tones used in perfect intervals, meaning that neutral sixths, sevenths, and thirds, as well as some superfourths and subfifths, resolve to the most consonant “perfect” intervals. Specifically, every perfect fifth in a Squares MOS can be resolved to by a neutral sixth, closing in by a chromatone on each side, with the fifths containing any desired tonality and extensions. These include sub and super triads, with super sevenths and sub sixths being most common, and the softer super sixth and sub seventh found in the 11-note. Pairs of small semitones can be replaced with neutral seconds to reduce long “chromatic” strings, an example being the Xenosquare Cradle. Two modes of the 8-note contain both subminor and supermajor root chords, with possible extensions for either. Other characteristic chords include the squares triad, which is a 7:9:11, neutral triads and tetrads, and 6:7:9:11 chords, all of which have the ability to resolve to the aforementioned simple consonances. Harmonic series chords found include the 4:6:7:9:11, one of which exists in the 11-note, and 5:6:7:9:11, two of which exist in the 14-note. The sound of squares tends to feel very dramatic and jagged, though not overly so as may be the case with harder scales.

Orwell - Built around orwell tetrads, the temperament both produces harmonics simply and includes useful chords, such as sub 7 and super 6 tetrads. Orwell[9] is useful for its soft sound and useful harmonic structures, including 4:6:7:11 and 4:5:11 chords. The principle and second modes include subminor and supermajor roots, allowing a switch between tonalities within the same mode, with the mode switch changing the extension from a sub seventh to super sixth respectively. The 13-note expands on this, as while the dieses may be generally avoided, the harmony becomes more complex, further simple triads and tetrads are available, and a 9-note MODMOS such as Graham Orwell is available, including more perfect fifths and a 4:5:6:7:11, while retaining the same general melodic feel due to the softness.

A:

Mohajira - Neutral[7] is a simple scale, introducing the neutral sound and providing harmonic useful structures. This sound, however, is greatly expanded on through MODMOSes and Mohajira[10], the first of which includes scales like Rast and Bayati, and is an entire important class of fantastic melodic scales, while the latter introduces 4:5:6:9:11 chords and includes certain important tetrachords and MODMOSes. Neutral triads are the defining sound of Mohajira, though harmonic series chords and the occasional major or minor triad are very important options. Overall, the scales are mainly known for their melodic features as opposed to harmonic, like the maqamat they share similarities with.

Tutone - Similar to the 12edo whole tone scale, the 6-note MOS forms the basis of what Tutone can do, with a 4:5:7:9 shell chord in the principle mode. The 7-note adds another, as well as a diesis for some mild direction, while the 13-note includes a vast depth of chords. Four modes include a 4:5:7:9:11, while four more just have a 4:5:7:9, and three more can choose between 4:5:9 with access to augmented fourths and fifths for color, a dominant seventh, or a 13/8. Despite not having fifths, the harmonic potential of Tutone is extremely vast, though the melodic side can be difficult to work with, as the whole time scale can feel limiting, but the small semitone in the 13-note adds to the possibilities, with the neutral intervals adding color. A 6-note MODMOS can bring some of this neutral flavor to a smaller scale, with Harmonic Whole Tone being a clear example, outlining the Tutone Harmonic chord.

Mothra - Mothra’s simple 4:6:7 chords are a key part of the sound, though subminor and supermajor triads are quite important as well, with four of each in Mothra[11]. They also have the addition of the fourth and major second respectively. Melodic material mainly comes from the equipentatonic scale, which can already outline perfect fifths with super sixths or sub sevenths on top. Mothra also supports barbados type chords, with the augmented and diminished 3&7 chords being represented very simply. Parent chords for modes of the 5- and 6-note MOSes can be used due to the fairly equal distance between pitches, with a warped but very interesting sound. Dieses in the 11-note MOS give it a very unbalanced feel, though the one small semitone preserves a useful sense of direction. Both the 11- and 16- note MOSes can be used in a Blackwood fashion, with alternating subminor and supermajor triads or tetrads falling from the subfourth in the principle modes. These subminor triads can add either a perfect fourth or harmonic seventh and possibly sub eleventh, and the supermajor can add either a major second/ninth or super sixth, with the principle root having a super seventh, which pairs well with the ninth.

B:

Joan - Despite a near complete lack of perfect fifths, MOSes of Joan are characterized by an abundance of harmonics, even in Joan[5], where 4:7:11:15 is an available chord. Harmonics 9, 13, and 19 are found in higher number MOSes, and the 11-note uses a 17 as an extension to the chords, allowing very interesting harmonic options, all with a structure characterized by antidiatonic and superdiatonic type patterns, with Joan[7] able to be used as an extreme mavila. The duality of 4:7:9:11:15 and 4:7:13:17:19 chords is part of what makes Joan interesting, especially with no 3s or 5s and yet very meantone chromatic-like melodic structures.

Valentine - Valentine[15] and [16] are the two main scales of the temperament that can be used, and they exist partly as a way to recolor meantone harmonies with fresh exotic melodies. There exist many nonoctave scales based on these melodic steps, these being the small semitone, neutral second, and large tone. Examples include nonoctave Blackwood and Mavila, both being common microtonal scales with more in-tune harmonies in exchange for the octave. Valentine's steps are often much more colorful than the simple whole tones and semitones found in diatonic modes, allowing us to "recolor" more standard scales by roughly translating them into a form that uses these steps. The 16-note MOS, Semi-Equalized Armodue, specifically can utilize Mavila-type ideas.

C:

Myna - Myna is defined by diminished chords and structures, with 5:6:7 chords and Orwell triads being some of the lowest complexity triads in the temperament. The principal mode of Myna[11] is especially useful, however, as it makes use of a superfourth to perfect fifth resolution, with a harmonic seventh root chord. The abundance of dissonance from the diminished chords in Myna is what makes this root chord feel so stable, and there is another option for the root chord, that being the utonal tetrad. These split roots are a defining feature of the sound, and they provide an avenue for melodic material, despite the disjointed feeling of such a hard scale.

Würschmidt - Würschmidt is defined by augmented chords and structures, with 8:10:13 chords and Squares triads being some of the lowest complexity triads in the temperament. The principal mode of Würschmidt[10] is especially useful, however, as it makes use of a neutral sixth to perfect fifth resolution, with a major seventh root chord, as well as other augmented chord types as possible roots. Split roots also exist in this mode, allowing the balancing of two different sounds, and the second mode leans into this minor sound with a b6. There are also two major sevenths, with the standard being more useful harmonically and the larger being a good option for resolution, retained in the ‘minor’ second mode. Most melodic material will come from either the smaller 7-note MOS, or by making use of notes two dieses apart to create some movement, like in the Augmented scale of P1 m3 M3 P5 s6 M7 P8, despite the very disjointed feeling of such a hard scale.

Miracle - Miracle is generally known for its simple generation of the 11-limit tonality diamond, though in 31, its main uses come in the form of combining Slendric and Neutral melodic ideas, as well as using its role as 6edf and a roughly chromatic scale to create disorienting runs on top of relatively simple chords, not as much for standalone scales. Miracle[11] contains 4:5:7:13:17 chords, as well as certain major-type shell voicings combining the major and subminor thirds and sevenths in latter modes, and some simple options from both slendric and neutral.

D:

A-team - A-Team has two main scales, Oneirotonic and A-Team[13], with a pentatonic scale that can be used for melodic material. Oneirotonic is an odd scale, as it has hardly any traditionally useful harmonic structures, outside of one 8:10:13 and two orwell tetrads, on opposite ends of the modes. However, the main chords used in Oneirotonic theory are known as Delta Rational chords, which use similar arithmetic distances between intervals, and are theoretically abundant in Oneirotonic. The sound of Oneirotonic can be described as a warped diatonic, with the extra semitone providing a very odd sense of melodic location to untrained ears. 13:17:19 chords are a common suspended chord option, closely matching the harmonic series. A-Team[13] contains 8:10:13:17:19 chords and Orwell pentads, though the complete lack of perfect fifths or traditional harmonic resources in these scales makes them difficult to approach.

Nusecond - Nusecond has two main scales for use, Greeley[8] and Nusecond[15]. The first is useful for its 6:7:10:11 chords, one of which has a 13/6 extension, while the other has a semitone over the root. The equioctatonic feel is what makes the scale interesting, and is why it’s used. The second scale makes use of how the generator is 11/10, 12/11, and 13/12 all in one, so when the 13 is generated, the others all follow. Melodic material mainly consists of the same quasioctatonic runs of Greeley, with more semitones as a possibility.

F:

Slender - The standard MOSes of Slender are quite useless, though they serve as a way to conceptualize “octave-stretched” 31, even on a pure octave, by stretching the generator of slender. A generator size of 39 cents makes fifths pure and some other intervals are optimized, while octaves can still be used. Regular Slender MOSes, however, are only ever used because theoretically they’re the same as subchromatic runs, as a piece solely using them would have to focus around the octave exclusively. In this specific case, 4:7:9:15 chords are an option, though they’re found starting in Slender[12].

Tritonic - The chord option that is most accessible in Tritonic MOSes is the 8:11:12, though these harmonics are found on opposite sides of the generator chain, so the chord isn’t available without a 9-tone MOS, and other harmonic resources are relatively lackluster. The possible resolution of superfourth to perfect fifth can be used, but using a superfourth as a dissonance is hard when it’s one of a few potential consonances in the scales. These scales feel very jagged as a whole, due to the large jumps generated from the tritones, and the dieses. Creating interesting music with a small Tritonic MOS would be quite a challenge.