TAMNAMS: Difference between revisions

'''TAMNAMS''' (read "tame names"; from '''''T'''emperament-'''A'''gnostic '''M'''OS '''NAM'''ing '''S'''ystem''), devised by the XA Discord, is a system of temperament-agnostic names for octave-[[MOS]] scales and their associated generator ranges, taking into account the relative sizes of large and small steps.

The TAMNAMS system names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the MOS scale.

For example, the 5L2s (diatonic) scale of 19edo has a step ratio of 3:2, which is "soft". We call the 19edo diatonic scale "soft diatonic". Tunings of a MOS with L:s larger are "harder", and tunings with L:s smaller are "softer".

The two extremes, equalized and paucitonic, are degenerate cases. An equalized MOS has L equal to s, so the MOS pattern is no longer apparent. A paucitonic MOS has s = 0, merging adjacent tones s apart into a single tone. In both cases, the MOS structure is no longer valid.

In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying MOS tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Note that the soft-of-basic range is always strictly proper while the hard-of-basic range is often improper but is always proper in the case that there is 1 small step per period in the MOS pattern.

== Naming MOS intervals ==

To denote interval classes within the MOS, TAMNAMS uses the generic prefix ''mos-'', or the specific prefixes and abbreviations listed under "MOS pattern names". Usage example: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''  

TAMNAMS uses the following modifiers to denote different interval sizes within a MOS interval class:

== MOS pattern names ==

The following names are suggested for certain octave-period MOSes of sizes between 6 and 10. These names are optional; interval size names and step ratio names can be combined with conventional "xL ys" names. For example: ''21edo is the soft [[5L 3s]] tuning and its major mosthird is a neutral third of size 342.9 cents.'' (Pattern names are the least important part of TAMNAMS.)

Some of these come from temperament-agnostic MOS names coined by [[Igliashon Jones]] and others, as well as some of the names (such as "mosh") from [[Graham Breed]]'s [[MOS naming#Graham_Breed.27s_naming_scheme|MOS names]]. Some are named by taking an arbitrary temperament that generates the scale (preferably in the MOS's [[proper]] range) and suffixing ''-oid''. These names have been coined so that MOSes can be discussed more independently of RTT temperaments (while drawing on an established RTT tradition in the xen community which may help make the names more meaningful to more people).

1L ns names are not given because the generator can be anywhere from the octave to to 1\(n+1) and can better be viewed as subsets of larger MOSes, for example [[1L 6s]] as a subset of [[7L 1s]].

|+ TAMNAMS MOS names

!colspan=5| 6-note MOSes

!colspan=5| 7-note MOSes

!colspan=5| 8-note MOSes

!colspan=5| 9-note MOSes

!colspan=5| 10-note MOSes

Extending the spectrum builds on the central spectrum and relies on a few key observations. Firstly, as periods and MOSSes come in wildly different shapes and sizes, and as we want to represent a somewhat representative variety of "simple" tunings for the step ratio for a given MOS pattern and period, the notion of "simple" used will correspond to the number of equally-spaced tones per period required. This is expressed as [number of large steps in pattern]*L + [number of small steps in pattern]*s, where L and s are from the step ratio itself, L/s, and are assumed to be coprime. Then, in order to not introduce bias to MOS patterns with more L's or more s's, we should assume that both are equally likely and thus weight both equally, which means that the resulting minimum number of tones per period for a ratio L/s is L+s. The next observation is that the large values of L/s can be a lot more consequential than the ones close to 1/1 due to the fact that small steps are guaranteed to be smaller than large steps and that we don't know how many small steps there are compared to large steps, and therefore the "hard" end of the spectrum is more vast, and analogously, L/s values close to 1/1 will tend to be inconsequential and for very close values likely impractical to distinguish - in the extremes only serving small tuning adjustments rather than melodic properties. This leads to another observation: MOS patterns with periods tuned to step ratios, while related to temperaments, ''are not'' temperaments - instead forming a sort of amalgamative superset of temperaments if you want to force a temperament interpretation, and thus their main function is in melodic structure, with temperaments informing potential harmonies and microtunings. Thus, the spectrum should be kept minimal and simple so that it is both generally hearable and not too specific.

Note that often the central spectrum will be sufficient for exploring a MOS pattern-period combination, and the extended spectrum is intended more for (literally) edge cases where it may be useful. Often if a temperament interpretation doesn't seem to show up for a MOS pattern-period combination, it just means the temperament needs a more complex MOS pattern to narrow down the generator range. An example of this phenomena is the highly complex MOS pattern of [[12L 17s]] represents near-Pythagorean tunings well due to having a generator of a fourth or a fifth bounded between those of [[12edo]] and those of [[29edo]], which are roughly equally off but in opposite directions, and many important near-Pythagorean systems show up in just the ratios of the central spectrum alone.

[[Category:MOS]]