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.

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 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).

I draw a distinction between my favorite edos and the best edos. 25edo is one of my favorites because it has a lot of tuning properties I'm interested in, but I can't reasonably recommend it to most people. 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 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. Requires an understanding of straddling the fifth to be used on the same level as the others.
• 41edo: Excellent 2...11. Like 31edo, but more complex and accurate.

Main types of scale-based composition theory required for the list, according to me:

• 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
• Aberrismic: 22+

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.

Aberrismic is a broad category because blackdye theory can be synthesized from diatonic + dicoid, diasem from diatonic + semiquartal, and so on.

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.

I have a pro-13edo bias.

On the edo side, I recommend 11edo, 13edo, and 18edo for melodic familiarity and harmonic unfamiliarity. 18edo in particular provides a straddle-fifth 12edo approximation and 4L3s and 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).

On the JI side, I recommend

• 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)
• 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.