User:Unque

An updated version of the tier list in question

I am Uncreative Name, or Unque! I'm a music theorist, composer, performer, mathematician, worldbuilder, and linguist. Members of the community may know me as a vocal advocate for tunings of suboptimal popularity; an exotempering troll; a spewer of recreational mathematics; or even the author of a tier list which was used in a Tumblr post teasing the xen wiki.

I learned of the Arabic Maqamat several years ago when I was studying non-Western music traditions, and I was especially intrigued by the presence of the neutral intervals in Jins Rast and other scales. This kickstarted a weird rabbit hole where I learned about the harmonic series, Just Intonation, and various Equal Divisions of the [your name here].

Tuning Propaganda

There are several tuning systems for which I am a vocal advocate; while in-depth descriptions of my thoughts can be found on my Composition Theory pages, I will provide a short summary here of why I find them useful.

15edo

This was the first tuning system that I ever truly fell in love with in my xenharmonic journey. Whereas most popular tunings such as 17, 19, and 31 felt like simple extensions to the familiar, 15edo allowed for a framework that was beautifully alien in ways that those other systems failed to be.

While 15edo does not provide accurate representations of the harmonic series, it does provide extremely useful melodic frameworks. The Blackwood Decatonic scale, for instance, contains several copies of Nicetone over each degree, allowing for diatonic-like chord progressions to move smoothly between keys that may seem unrelated in systems with a more accurate chain of fifths.

Additionally, it can be noted that if one makes an Isodifferential chord with an interval of 400c (the familiar major third from 12edo) between the bottom two pitches, this chord will have a "fifth" which very closely resembles the "fifth" of 5edo. Thus, we can assume that a tuning which contains 3edo and 5edo as subsets has a close approximation of this chord. This can be seen as an alternative way to "fix" the lack of harmonic effect in the 12edo major triad, which detunes the fifth rather than the third.

30edt

There isn't too much to say about 30edt. Its most obvious application is as a stretched version of 19edo, which is desirable due to 19edo's consistent flat temperament of prime harmonics.

A proof of concept that I wrote for 30edt.

However, it can also be used on its own as a tritave-equivalent system. Because the tritave is significantly wider than the octave, using the semi-tritave as a period can be a good way to make scales more melodically coherent. The semi-tritave interval, unlike the semi-octave, is relatively consonant, and a very intuitive size for a period due to being precisely half way between the perfect fifth and the octave (the two most common spans for a scale).

29edo

I strongly believe that 29edo should be alongside systems such as 19edo and 31edo as introductions to xenharmonic tunings for beginners. Not only does it represent the third harmonic within less than two cents of error (making the diatonic scale roughly equivalent to its familiar representations in western music), but it additionally contains distinct, unambiguous representations for interordinal intervals. The ability to place these unfamiliar intervals onto the familiar circle of fifths is extremely beneficial, as it allows beginners to more clearly get a feel for how these intervals can be used to create sounds unavailable in 12edo. This provides a benefit over systems such as Meantone, in that the circle of fifths requires less relearning to account for the difference in intonation compared to 12edo, and in that the interordinals represented are distinct and unambiguous (compare to 31edo, where there is no clear representation for, say, the semifourth or the semisixth).

Additionally, 29edo finds the perfect fourth at 12 steps, a highly divisible size, supporting Porcupine, Tesseract, and Unicorn. This helps provide an introduction into systems that divide simple intervals into a certain number of steps, and how those divisions can apply to writing melodies and chord progressions.

Finally, for those who like microtemperaments, simple harmonics such as 5 and 7 are very easy to find in supersets such as 58edo and 87edo, since these harmonics have a relative error very close to simple fractions. The perfect fifth of 29edo is optimal for parapyth tuning, which makes supersets of 29edo extremely desirable if one seeks an extremely high accuracy equal temperament sequence.

36edo

I don't have too much to say regarding 36edo. It is a superset of 12edo, which provides a very accurate representation of prime 7. It is roughly the optimal tuning for Slendric temperament, as well as a good EDO representation for 2.3.7 JI scales such as Septimal Zarlino and Diasem.

41edo

While a bit larger than the typical optimal size for practicality, physical instruments such as the Kite Guitar have made 41edo significantly more accessible than it may seem at first.

In terms of tone organization, 41edo is extremely accurate and efficient. The first fifteen harmonics are practically indistinguishable from JI (potentially excluding 13), and the edostep acts as an all-purpose formal comma, representing S10~S9~78/77~66/65~S8~S7~45/44. Additionally, 41edo is the unique intersection of Magic, Sensamagic, and Pentacircle, all extremely intuitive relationships that make it a perfect choice for composers who want to access strong low-complexity JI-like sound while retaining all the benefits of an equal temperament sequence.

Additionally, and perhaps more convincingly for practical composers, 41edo maps the perfect fifth to 24 steps. Just like with the perfect fourth of 29edo, this highly divisible interval allows for many useful melodic structures, including (but not limited to) Neutral, Slendric, Tetracot, and Miracle.

Music

A proof of concept that I wrote for Dhembrwood temperament.

Here are some of the pieces I've written:

• Spring (26-EDO): https://youtu.be/OjW8dgooG9Q_
• Isles of Despair (15-EDO): https://youtu.be/T49aXRutQxE
• Summer (17-EDO): https://youtu.be/UthDbDI31IY
• Nachtlandian Somersault (19-EDO): https://youtu.be/XZ3zB3EDKOM
• Bonetrousle Remix (22-EDO): https://youtu.be/wgyie6m7f5g
• Random Encounter Type Beat (2.3.7 JI): https://youtu.be/0OkCl2yfgBo
• Methane Lamentation (31-EDO): https://youtu.be/CBmYRoej2yQ
• Autumn (27-EDO): https://youtu.be/dcQe6ebpGFU
• Winter (37-EDO): https://youtu.be/rE9L56yZ1Kw

Main Space Contributions

Here are some of the contributions I've made to the wiki main space:

• The Octaphore comma and its related temperaments (I am sadly responsible for that name too)
  • Tempering out the Octaphore provides a highly accurate temperament that cleaves 4/3 into eight equal parts.
• The 131072/130321 comma
  • Tempering out this comma provides an interpretation of 4-EDO, much more accurate than Diminished.
• The Tesseract comma and its related temperaments
  • Tempering out this comma provides cleaves 4/3 into four equal parts; it's not quite as accurate as the Octaphore, but it's supported by more ET sequences at lower complexity, and quite frankly has a much better name.

User Space Contributions

Here are some other contributions I've made to theory on my personal user space:

• A convention for describing 15-EDO Chords
• Dhembrwood Temperament
• Redeye Scale
• A study on Imaginary Harmonics
• Chord Interlace Scales
• A naming convention for MV3 ternary scales (which is currently undergoing serious reconstruction)
• A system of nineteen functions to describe xenmelody
• A study on tuning theory as applied to Barbershop music
• The Dietic Minor scale

I confine many of my pages to my user space to contain idiosyncrasies, jokes, niche topics, subpar writing quality, and other stuff that I don't believe deserves to be put on the main wiki space. Some of these pages may be moved over to main space pages if they are deemed to be well-written pages about legitimately applicable ideas, but for now they remain here.

Composition Theory

When I was first getting into xenharmony, I was surprised to find that there was very little in-depth composition theory regarding specific tuning systems in the way that modern Western music has intricate descriptions of just about anything that can be done with 12-EDO.

So, over the next several months, I will be spending some time detailing my experience with some of my personal favorite tuning systems, and laying out a framework for a distinct composition theory in each of those systems.

For EDOs:

• 15-EDO
• 22-EDO
• 29-EDO
• 37-EDO (Under construction)

For scales:

• 5L 3s (Under construction)

Worldbuilding Projects

I've also used my user space as a place to document the music theory associated with several of my worldbuilding projects:

• The "Gense" traditions, which use 17-EDO pentachords
• The "Plagal" traditions, which use 22-EDO MOS scales

Just like the theory pages, these worldbuilding pages are not intended to enter the main wiki space, for obvious reasons.