User:Unque

From Xenharmonic Reference

I am Uncreative Name, or Unque! I'm a student at a music school and linguistics school; 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 mythical guy who asked.

After some chaos in the main Xenharmonic community, I've moved my base of operation to Xenreference. In my time here, I plan to take a music-first approach for sects of theory whose usefulness have been called into question due to the disproportionate amount of mathematical discussion and lack of musical composition. This primarily includes Regular Temperament Theory, a point of contention among xenharmonicists and a common punching bag for those musicians who dislike mathematically-heavy theory.

Some of my previous works can be found on the main xenharmonic wiki here.

Tuning Propaganda

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 triad 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.

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, Negri, Semaphore, and other similar structures. 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 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; additionally, 87edo supports Rodan temperament, an extremely efficient system which extends the harmonies of the chain of fifths by adding a formal chroma S9~S8~S7 at (8/7) ^ 5. Rodan also contains Slendric and Hemifamity as subset parts of its structure

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 composers who want to skip the frivolities and pick up and play with a tuning, 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.

43edo

By the size of 43edo, even rank-2 thinking is rather difficult for conceptualizing how the system fits together. However, 43edo can very intuitively be taken as a Septimal Meantone system with 45/44~56/55~100/99 as a secondary chroma to provide access to 11-limit intervals. Because the chromatic semitone of the diatonic scale is three of these undecimal chromata, any interval size in the system can be notated with no more than one accidental of each kind.

This threefold division of the chroma additionally allows the wholetone to be altered into a down-wholetone such that three of them make a perfect fourth instead of an augmented one; the structure begotten by these down-wholetones resembles Porcupine in its form, but does not contain the classical minor third.

Finally, 43edo offers a rather accurate tuning of Bleu, the temperament which cleaves the perfect fifth into five parts; two of these parts reaches 7/6, three reach 14/11, and four reach 11/8.

Music

Here are some of the pieces I've written:

Contributions

Scales and tunings

One important part of my mission on xenreference is to provide more concrete composition theory, especially when it comes to concepts like scales and temperaments whose utility may not be obvious. My primary goal in so doing is to rectify the poor reputation of these systems and hopefully to beget greater interest and understanding of these systems, and utilization of their novelty for practical composition.

Theory case studies

Another side goal of mine is to uncover writings of historical theorists that have application in tuning theory and further on practical xen composition. The Renaissance era in particular saw dozens of these writings, as musical tuning was a flourishing field of study at the time with many novel ideas yet to be explored.

User space

Just like back in Xen Wiki, I will be using my user space to contain any idiosyncrasies, jokes, niche topics, subpar writing quality, and other stuff I write that I don't believe deserves to be put on the main wiki space. Some 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.

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