Tuning recommendations for beginners

This article contains lists of various users' recommendations for general-purpose tuning systems and beginner-friendly explanations. It is recommended to pick a tuning early and focus on it so that tuning theory does not become more important than composition. 12edo is the perfect tuning for people who don't want to have to think about tuning theory, but there are some close options.

To provide a simple overview, consonance of a musical interval is based on approximating simple frequency ratios, where you multiply the frequency of one note by the ratio to get the frequency of the other note. "Subgroups" are used to categorize intervals, where for example 2.3.5 describes intervals that can be made by multiplying and dividing the prime numbers 2, 3, and 5. Arbitrary intervals may be achieved with a complex enough ratio, but this article focuses on the simplest ones as they are the most clearly audible. The perfect fifth is 3/2.

• 2.3.5: Known as "pental", widely considered the default rational interpretation of Western harmony. The simple thirds are around 6/5 and 5/4.
• 2.3.7: Known as "septal", more xenharmonic with a narrower semitone. The simple thirds are around 7/6 and 9/7.
• 2.3.5.7 (2...7): Known as "septimal", the combination of the two, describing some Western forms of music like blues, jazz, and barbershop. A common subgroup for basic xenharmonic analysis.
• 2.3.5.7.11.13 (2...13): Known as "tridecimal", an extension that contains intervals further from diatonic. Its novel third-like intervals are the 11/9 and 16/13 neutral thirds approximated in some Middle-Eastern music, 15/13 semifourth (second-third), and 13/10 semisixth (third-fourth).

The diatonic perfect fifth is the most important interval in 12edo theory after the octave, as it generates the diatonic scale. Scales in the middle of the diatonic range can be split into three camps:

• Meantone (M): The diatonic scale is 2.3.5 with a flat 3, used in Renaissance and (especially earlier) Baroque music. Intervals involving 7 are small alterations of diatonic.
• Archy (A): The diatonic scale is 2.3.7 with a sharp 3, equally useful but with little historical precedent. Intervals involving 5 are small alterations of diatonic.
• Pythagorean (P): The diatonic scale is 2.3 with an especially accurate 3, the most common interpretation of popular 12edo music. In a sufficiently large edo, accurately tuned intervals involving both 5 and 7 are alterations of diatonic.

Ground's list

g_

This section is written from the perspective of User:Ground and may feature proposed concepts.

I specialize in edos, tuning systems with a pure octave split into equally sized steps. I categorize the difficulty of them based on their size (more notes is more difficult to handle) and size-independent difficulty, which is based on how easily structures and desirable intervals translate from 12edo and the number of concepts required to understand them (1 is easy and 3 is hard).

My favorite edos are not my best edos. 25edo is one of my favorites, but I can't reasonably recommend it to most people. This is an optimization of several specific tuning properties I'm interested in, being 7+18, 9+16, and 10+15 (summing them combines the properties they have in common). If I want to write an antidiatonic piece, I use 25edo. If I just want to write a piece, I use 37edo, because that's my favorite of the following. This is the philosophical distinction that I have to make in order to stop thinking so much about tuning theory.

This is my list of the most versatile edo tunings, split into two tiers. Both of these categories are diatonic to have a baseline level of harmonic stability:

• Absolute best: 12edo (M/P 0), 19edo (M 1), 22edo (A 2), 24edo (M/P 2), 31edo (M 1), 41edo (P 1).
• Second best: 17edo (A/P 1), 26edo (M 2), 27edo (A 2), 29edo (P 1), 37edo (A 3).

I intend to add sound examples to make the selection process easier.

The list contains all diatonic edos up to 41, with the exception of 32, 33, 34, 36, 38, and 39. These can be understood in pairs of a sharp 3 and about equally flat 3: [32, 33] have an especially inaccurate 3, and the best 5 is tuned in the opposite direction, giving pental chords an unstable sound. [34, 36] are great for 2.3.5 and 2.3.7 repectively, but are too large not to have the full 2.3.5.7. [39, 38] are fine, but nothing special for their size.

Tuning descriptions (incomplete):

• 19edo: Good 2.3.5 with debatable 7. The best when it comes to simple practical composition. Clearly audibly xenharmonic, but not extreme. Like a smaller 31edo.
• 22edo: Good 2...11. About as xenharmonic as 19edo in a different way.
• 24edo: Contains all of 12edo as a subset, making familiar sounds trivial to access while adding the most xenharmonic intervals possible. Despite this, the difficulty is higher because the additional intervals don't fit into a 12edo-like framework at all. The easiest to play on 12edo instruments, which I have not factored into the difficulty score.
• 26edo: Debatable 2...13.
• 27edo: Good 2...7.13, all tuned sharp.
• 29edo: Excellent 2.3 with critically poor 5...13, meaning that ratios like 7/5 cancel out the errors and become accurate. Translates popular 12edo music well because it has a perfect fifth very close to 3/2. Most composers will be fine using a different tuning though.
• 31edo: Excellent 2...7 with debatable 11. Something of a standard. Easy to use and full of consonant intervals, but on the larger side.
• 37edo: Excellent 2.5...13, which makes it a huge outlier in the list. It has a highly efficient and interesting array of intervals, but a barely usable diatonic fifth, so the other intervals have to carry the harmonic stability. I had to invent straddle theory and the trackdye scale structure (aberrated compressed diatonic) just to be satisfied with it. I classify it as straddle-3, and the only edos I've found to be even more confusing are straddle-3-5 (42, 57).
• 41edo: Excellent 2...11. Like 31edo, but more complex and accurate.

These are the main types of MOS-based (rank-2) composition theory that I recommend for the edos on this list:

• Diatonic: Already known from 12edo, affects everything
• Dicoid: 17, 24, 27, 31, 37, 41
• Slendric: 26, 31, 41
• Semiquartal: 19, 24, 29
• Porcupine: 22, 29, 37

I add rank-3 aberrismic theory for all edos above 19. Aberrismic is a broad category where other scale theories combine. For example, blackdye theory can be synthesized from diatonic + dicoid, diasem from diatonic + semiquartal, and so on. 37 is the only edo on this list that I think requires an understanding of straddle theory to be used effectively.

I was not expecting dicoid to be so prevalent, but this list implies that it's the most broadly applicable MOS theory after Diatonic. This is because it splits the diatonic fifth in half while semiquartal (specifically the 5L9s superset) splits the diatonic fourth in half, but their nearby LCJI intervals are not equal. 6/5 and 5/4 are about twice as far apart as 8/7 and 7/6, meaning that a semiquartal edo has to be about twice the size to represent all of these intervals accurately without equating those in each pair.

Dicoid is LLLsLLsLLs, generated by a neutral third in the range (2\7, 3\10), half of a diatonic fifth. Its subset mosh is LsLsLss is more melodically useful, but has a wider generator range. The non-dicoid part is unusual and not represented here. I suggest writing composition theory based on two categories of the tuning range, just like we do for diatonic xen theory: ~11/9 and ~16/13, with 17edo about in the middle. Tunings near the middle of the range melodically resemble 12edo depictions of Middle Eastern scales, which new xen composers should basically know what to do with.

Small non-diatonic edos

I would not use these to write a piece anymore, but I recommend them to beginners at least because they force experimentation with more extreme xenharmony. My expectations for the stability and versatility of these are much lower.

This is every edo between 5 and 19 that I haven't listed yet:

• 5edo (2), 7edo (1): Toy-like in their simplicity, an equalized pentatonic and diatonic scale. 5edo's lack of tertian chords makes it more difficult.
• 6edo (2): A 12edo subset, not technically xenharmonic, but still unusual and underrepresented.
• 8edo (3), 9edo (3), 10edo (3): 9 and 10 are systems comparable to 12edo in their own right. Constructing 12edo-like melodies is virtually impossible. 9edo is the smallest to have recognizable minor and major chords, but 8 and 9 nothing even resembling a whole tone. 10edo has no minor third besides the dubious semifourth found in 5edo, which splits into two wide semitones.
• 11edo (1), 13edo (1): Wildly xenharmonic harmony but familiar melodic intervals (whole tones and semitones). My first ever xenharmonic song was in 11edo because I could retune the 12 available notes to it.
• 14edo (2), 15edo (2): Supersets of 7 and 5edo with a crude approximation of 2...7.
• 16edo (1), 18edo (1): Structurally similar to 8, 9, 11, and 13, but with more notes and more options to melodically approximate 12edo.

Inthar's list

KC

This section is written from the perspective of User:Inthar and may feature proposed concepts.

Edos

Note: I specialized in oneirotonic and have a pro-13edo bias. This list is for those who are not content with the standard list of "beginner edos" 5, 7, 17, 19, 22, and 31:

1. Straddle-fifth edos: I particularly recommend 11edo, 13edo, and 18edo to beginners for melodic familiarity (whole tones and semitones) and harmonic unfamiliarity (lack of diatonic or low-complexity JI). 18edo in particular provides a straddle-fifth 12edo approximation and smitonic (4L3s) and oneirotonic (5L3s) MOS scales, both melodically familiar but warped. However, if you just want to specialize in one of 4L3s and 5L3s, you can't go wrong with 11edo (for 4L3s) or 13edo (for 5L3s).
   • Like diatonic, oneirotonic is also a segment of a "circle of fifths", albeit a very sharp fifth (between 720c and 750c). This leads to a somewhat familiar but warped form of functional harmony.
2. JI approximation: 41edo is the first structurally accurate 7-limit edo in that it observes both 81/80 and 64/63, and additionally approximates 11-limit intervals. 41edo has an advantage over the comparable 46edo and 53edo in size and in that it supports the Kite guitar. Smaller edos sacrifice approximation of either prime 5 or 7, or they temper at least one of 81/80 and 64/63.
   • 41 and 46 both have acceptable tunings of 11/8 and support Slendric and penslen. 53edo does none of these things but is extremely accurate in the 5-limit, has a sharp tuning of 7/4 and approximates 13/8 more accurately via the high-accuracy 2.3.5.13 temperament Kleismic.
3. Armotonic edos: Flat-of-7edo but sharp-of-9edo fifths generate the armotonic (7L2s) MOS scale, which contains easier-to-use tunings of the antidiatonic (2L5s) MOS scale compared to the balzano (2L7s) MOS which is generated by an even flatter fifth. The smallest armotonic edos are 16edo, 23edo, and 25edo. Somewhat familiar triads — major and minor triads are just swapped in the 2L5s armotonic MOS — but melodically more exotic. 9edo is a degenerate version of armotonic. See Ground's list above.
4. Multiples of 5 and 7: I recommend 15edo if crude 7-limit approximations and melodically challenging 160c and 240c "whole tones" are your thing. 21edo is a multiple of 7edo with conventional-sounding major and minor thirds like 15edo, but less challenging from a melodic perspective. 14edo has a semiquartal (5L4s) scale (which doesn't sound that "interordinal" unlike 19edo or 24edo's semiquartal but you might prefer it melodically due to its larger semitones). 10edo, like 7edo, has simplified neutral harmony but has more melodic variation, providing a 3L4s scale. 20edo and 28edo are not very commonly used; 20edo is the first edo with a balzano (2L7s) MOS scale.
5. 8edo: 8edo is the only edo between 7 and 23 I haven't mentioned. It is uniquely strange — it has no familiar melodic steps, and major/minor triadic harmony doesn't work the same way — though in my opinion that is all the more reason to be somewhat partial to 8edo. You might prefer Ammonite (e.g. 29edo) or Sensi (e.g. 19edo or 27edo) for quasi-8edo but more JI-interpretable harmonic structures.

JI scales

On the JI side, I recommend

1. modes of 8:9:10:11:12:13:14:16 or 8:9:10:11:12:13:15:16 if you want a simple harmonic series scale and you're okay with a modal approach with limited modulation (like maqam). Try various modes of these scales that have 3/2 perfect fifths, such as 12:13:14:16:18:20:22:24.
   • 16:18:20:21:24:27:28:32 is a JI quasi-diatonic scale, a mode of so-called "septimalydian". It is notably both 7-prime-limit and harmonic-series-oriented.
2. diasem if you want a scale rich in both fifths and 7-limit JI concordances not found in 12edo, allowing for a kind of functional harmony in 2.3.7 just intonation.

Vector's list

SS

This section is written from the perspective of User:Vector and may feature proposed concepts.

Edos

The set of three "beginner EDOs" provided by Leriendil are as follows:

- To retain a composite structure and JI-agnostic characteristic similar to 12edo, while changing the relationships between intervals: 15edo

Harmonic unfamiliarity: ★★★

Stylistic unfamiliarity: ★

- To retain a 5-limit heptatonic MOS with recognizable but inverted relationships between intervals, while using an unusual tuning: 16edo

Harmonic unfamiliarity: ★★

Stylistic unfamiliarity: ★★

- To retain diatonic and familiar interval categories, while approximating something that isn't the 5-limit and having a higher resolution including neutral intervals: 17edo

Harmonic unfamiliarity: ★

Stylistic unfamiliarity: ★★★

Additionally, 22edo and 24edo provide complementary ways of elaborating on 12edo's interval qualities: 22edo splits each quality into two, while 24edo adds new qualities in between each 12edo quality. (An edo that provides both, while large, is 34edo.) Thus they are good introductions to the more general variety of intervals found in xenharmonic music.

Unque's list

UQ

This section is written from the perspective of User:Unque and may feature proposed concepts.

While my user page contains more in-depth propaganda for the tuning systems listed here and more, I wanted to make this list more compact and perhaps more beginner-friendly. My list specifically caters to someone whose approach is focused on expanding the familiar tonal world into something more diverse and colorful; as such, I've prioritized a tuning's ability to integrate its new contents smoothly into familiar or conventional melodic and harmonic frameworks, rather than appending them on top or completely abandoning those frameworks.

• 15edo: The "Nicetone" scale from 15edo approximates a diatonic scale, but distinguishes two different types of wholetones, and thus contains "wolf" intervals. This Nicetone scale is also a subset of the ten-note Blackwood scale, which simplifies the scale to contain only one type of wholetone and one type of semitone; because the Blackwood scale is a mode of limited transposition, the diatonic scale it contains is repeated on every other step, and it can thus be used to smoothly transition between keys that in 12edo would seem rather unrelated. Finally, 15edo can split the perfect fourth into three equal parts, allowing you to construct a tetrachord where all intervals are the same size, and a scale made of these equal tetrachords can also be considered analogous to diatonic in a way.
• 17edo: This is one of the most common choices for a beginner tuning, and for good reason. 17edo adds neutral thirds on top of the regular diatonic paradigm, which means there are three types of tonalities available (major, neutral, and minor) rather than the classicalist two. The "neutral" or "Mosh" scale provides a contrast with the classic diatonic scale, as its small step is the diatonic chroma and vice versa; because of their close relationship, borrowing chords between these two scales or transitioning between them can be done much more cleanly than in tunings such as 24edo where diatonic is less closely tied to the neutral scale.
• 29edo: In spite of its larger size, I believe 29edo is the absolute best tuning in this category. Its perfect fifth is even closer to JI than 12edo's, and it contains a single exemplary interval of each interordinal space. Unlike in 24edo, these interordinals are placed on the chain of fifths, allowing them to be reached by an extension of conventional chromatic harmony. The perfect fourth is additionally highly divisible, making 29edo an excellent introduction to divisibility properties of important intervals.
• 36edo: The largest interval in this category, 36edo actually contains 12edo as a subset. In spite of this, the new content that it offers fit much more cleanly into the structure than in 24edo, and additionally offer excellent approximations of septal harmonies. 36edo contains a whopping six main types of tonalities: major and minor from 12edo, supermajor and subminor approximating the septal ratios, and submajor and supraminor representing the more complex 17/14 and 21/17.