XenReference:Tuning system article format
This page is an extension of XenReference:Guidelines. It is expected that that page has been read first.
Articles about tuning systems are some of the most important on this wiki. According to the wiki's mission statement, the ultimate purpose of such an article is to serve as a basic guide to using that tuning system for composition. An individual tuning system must, therefore, be presented as a coherent structure with unique rules and particularities that govern the flow of composition in that system. Not all tuning systems have independent value for composition, despite whatever value they might have in relation to other structures or in their theoretical properties; these should not receive dedicated individual articles.
Further, in xenharmonic music, the choice of a tuning system to use or focus on, out of the vast array that exist and the variety of approaches to tuning, is itself one of the most important compositional choices. When a tuning system is explicated, then, it must be stated what situations or preferences would justify using that particular tuning system in comparison to others.
With that in mind, and for the further sake of consistency, format specifications and recommendations for presenting different types of tuning systems are described below.
In general
All articles should begin with an introduction section. In the case of tuning systems, the introduction needs to include an overview of the basic harmonic and melodic structures of the tuning system. Verbally explaining the way harmonies interact within the tuning and how melodic movement is induced in the tuning's scaleforms is a minimum, but the more can be succinctly stated about how these might dictate compositional practice, the better. In other words, listing out commas or cent values is not a serviceable introduction.
Regular temperaments
As mentioned, temperament articles must begin with an introduction section. As far as a temperament's structure is explained, it should generally be phrased in terms of what equivalences it makes between stacks of intervals (e.g. "Slendric is the basic harmonic interpretation of the structure where the perfect fifth (~3/2) is split into three equal parts, each representing the interval 8/7.") Proceeding along the generator chain is also a good way to make sense of rank-2 temperament structures in particular, and many useful rank-3 temperaments also consist of rank-2 spines with an additional offset interval. Referencing EDOs which the temperament covers is also helpful for intuitizing the temperament as an object. Introductions should also include an infobox, which includes more compact information (such as the comma basis and mapping).
Outline of the article
Following an introduction, an article follows roughly this fixed structure, following that of xen.wiki:
- Structural theory
- General theory (incl. notation systems and basic harmonies)
- Interval chains
- Extensions and related objects
- Scales and compositional theory
- Tunings
- Tuning considerations (incl. optimal tunings)
- Tuning spectrum
- Other sections (instruments/existing music, history, etc.)
Format and content of tables
Rank-2 temperament articles should contain two tables, and these constitute the bare minimum of content beyond the introduction. These tables are the interval chain and the tuning spectrum.
The interval chain includes a list of basic harmonic interpretations of the intervals along the temperament's generator chain, and cent values for these intervals in some good tuning for the temperament. It may sometimes be convenient to include interval chains for different (strong) extended mappings within the same table; in some cases, these need separate tunings listed. Interval chains should include most of the harmonic content of the temperament but not be of extreme length; for this reason, it is discouraged to include both positive and negative generators in such a table, but this can be excused if the chain is short enough and for multiperiod/non-octave temperaments where complements are not as obvious.
The tuning spectrum should follow a discussion about different tuning ranges of the temperament's generator, being the tradeoffs made using either a flat or sharp tuning and what they induce harmonically, including the matter of which extensions are reasonable in such a tuning range. Proceeding along the tuning spectrum of the generator, notable EDO tunings should be highlighted, as well as certain tunings with an unchanged interval along the positive chain of generators. Odd-limit monotonicity bounds should be included as properties of EDO tunings. Keep in mind the spectrum is a chance to make detailed comments about specific tunings, not just a formulaic table. Also highly recommended to go along with the spectrum is a diagram showing the tuning error of the odd harmonics depending on the generator, with notable tunings marked on the graph.
Equal tunings
Multiples of an equal tuning may go in the same article as long as they aren't notable enough to have their own article or otherwise show up in multiple places. They should be placed in the Multiples section. For example, if enough information on 50edo can be provided separately from 25edo, then 50edo would merit its own article, but if 100edo is mainly being treated as a multiple of 50, it should be discussed in the 50edo article.
[TBD]
