TAMNAMS: Difference between revisions

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The following names are suggested for octave-equivalent 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.''

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 names ~~below~~. 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).

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 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 intentionally unspecific 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]].

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The reasoning for the "para- super- ultra-" progression (note that "super-" is the odd one out as it refers to an exact ratio) is it mirrors naming for shades of musical intervals and because "parapythagorean" is between "pythagorean" and "superpythagorean".

This results in the "central spectrum" ~~below~~ - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.

This results in the "central spectrum" - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.

=== Extending the spectrum's edges ===

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.

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'''extrahard''' (L/s=6/1) to '''semipaucitonic''' (L/s=10/1) is '''clustered''' (6 < L/s < 10).

With the inclusion of these 3 new L/s rations nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed ~~below~~, just for the regions affected to avoid repetition.

With the inclusion of these 3 new L/s rations nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed, just for the regions affected to avoid repetition.

[[Category:MOS]]

@@ Line 181: / Line 181: @@
 The following names are suggested for octave-equivalent 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.''
-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 names below. 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).
+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 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).
 L ns names are intentionally unspecific 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]].
@@ Line 264: / Line 264: @@
 The reasoning for the "para- super- ultra-" progression (note that "super-" is the odd one out as it refers to an exact ratio) is it mirrors naming for shades of musical intervals and because "parapythagorean" is between "pythagorean" and "superpythagorean".
-This results in the "central spectrum" below - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.
+This results in the "central spectrum" - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.
 === Extending the spectrum's edges ===
 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.
@@ Line 280: / Line 280: @@
 '''extrahard''' (L/s=6/1) to '''semipaucitonic''' (L/s=10/1) is '''clustered''' (6 < L/s < 10).
-With the inclusion of these 3 new L/s rations nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed below, just for the regions affected to avoid repetition.
+With the inclusion of these 3 new L/s rations nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed, just for the regions affected to avoid repetition.
 [[Category:MOS]]