TAMNAMS: Difference between revisions

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! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology

|-

| [[1L 4s]] || pedal || ped- || ped || |~~| [[#Pedal (1L 4s)~~|one big toe and four small toes]]

| [[1L 4s]] || pedal || ped- || ped || || one big toe and four small toes

|-

| [[2L 3s]] || pentic || pent- || pt || || common pentatonic; from penta- for 5

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! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

|-

| [[1L 6s]] || onyx || on- || on || |~~| [[#Onyx (1L 6s)~~|from a ''lot'' of naming puns]]

| [[1L 6s]] || onyx || on- || on || || from a ''lot'' of naming puns

|-

| [[2L 5s]] || antidiatonic || pel- || pel || || pel- is from pelog

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| [[9L 1s]] || sinatonic || sina- || si || || from [[sinaic]]

|}

<references/>For the reasoning for these names, see [[TAMNAMS/Appendix|TAMNAMS/Appendix#Reasoning for mos pattern names]].

~~=== Reasoning for the names ===~~

~~The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.~~

All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.

All names for mosses with five or less notes - excluding (mono)wood and biwood (which like all n-wood mosses are specific to octave tuning) - require that some small integer multiple of the period is equal to an octave, under the reasoning that mosses with five or less notes are common and broad in tuning enough that they are much more likely to find interest in non-octave contexts. Because of this, their names were chosen to be extremely general, both to avoid bias/being too flavorful and (correspondingly) so that the terms could validly be reused for ~~any mos for which the period is not equal to a (potentially tempered) octave.~~

~~Any multiperiod mos with more than five notes was given a name that wasn't reliant on the name of a mos with five or less notes as such~~ names ~~were based on those mos names formerly requiring an octave tuning (which is to say some small integer multiple of their period must be equal to a (potentially slightly tempered) octave).~~

Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings did not cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".

The inclusion of mos names for "multiperiod" mosses was from a desire to have all ten-note-and-under mosses named for completeness, which is also what prompted some of the reconsiderations mentioned earlier. Similarly, the inclusion of mosses of the form 1L ns using the "anti-" prefix (or an- for less-than-six-note mosses) was also for a practical consideration; although the tuning range is very unhelpful for knowing what such a mos will sound, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name, especially given that in such situations the tuning will likely be specified somewhere already. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (and for consistency with that their parent MOSS, 4L2s, is named citric).

The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is also not as trivial as it may sound. In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence the original reason for omitting such mosses), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range. In the case of mosses with five or less notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.

~~=== Name-specific reasonings ===~~

~~==== Pedal (1L 4s) ====~~

Pedals are operated with feet, which have one large toe and four small toes. Also comes from words like "bipedal", where in TAMNAMS, "bipedal" would literally mean a pedal scale with a period equal to half of some chosen interval, although such a scale would have either two right feet or two left feet depending on orientation chosen. If you think "car"/"vehicle" when you think "pedal" and don't think (or want to think) much about feet then you can think about "[[beep]]ing" (as [[beep]] is the 7-limit 4&5 exotemperament). Because this name relies so heavily and fundamentally on there being 1 large and 4 small steps per period, it is appropriate to generalise for any size of period you would want. In that regard, same goes for manual, pentic and anpentic.

~~==== Malic (2L 4s) and citric (4L 2s) ====~~

Malic derives from Latin ''malus'' 'apple'. An apple has two concave ends, and large steps in a scale with more small steps are hole-like, hence the two large steps in malic. Citric (4L 2s) is named after the child mosses of citric, namely lemon (6L 4s) and lime (4L 6s). Unlike apples, lemons have two convex pointy ends, and small steps in a scale with more large steps are pointy, hence the two small steps. Malic and citric acids are both ubiquitous in food and biology, thus justifying their use for fairly small mos scales.

~~==== Machinoid (5L 1s) ====~~

~~[[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64~~/~~63 and 99/98.~~

~~This temperament is supported by {{Optimal ET sequence~~| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28 and 33 }} equal divisions, with non-patent val tunings including 5+5=10e, 5+10e+12=21be, 5+5+5+5+6=26qe, which are mentioned here for demonstrating virtual completeness of the tuning range, and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.

~~==== Onyx (1L 6s) ====~~

"1Ln-ic's" and "nL1-ic's (like, the -ic suffix applied to MOSS names, collectivised for 1Lns and nL1s) sounds like "one-el-en-ics" or "en-el-one-ics" which abbreviated sort of sounds like "one-ics" => "onyx". Then "onyx" sounds sort of like "one-six". Furthermore the onyx mineral comes in many colours and types, which seems fitting given this is the parent scale for a wide variety of MOSSes; specifically of interest being 7L 1s (pine), 8L 1s (subneutralic) and 9L 1s (sinatonic). Finally, the name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and other than that, the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part (depending partially on your pronounciation).

~~==== Subaric (2L 6s), jaric (2L 8s), and taric (8L 2s) ====~~

~~The name "subaric" alludes to the fact that 2L 6s is the largest proper '''sub'''set mos of both j'''aric''' (2L 8s) and t'''aric''' (8L 2s).~~

The name "jaric" alludes to a few highly notable and generally inaccurate (with the exception of diaschismic) temperaments that exist in the tuning range of this MOSS. Specifically, notice how the letters and sound of "jaric" has (or is intended to have) a lot of overlap with [[pajara|pa'''jar'''a]], [[diaschismic|diaschism'''ic''']] and [[injera|in'''jer'''a]] (listed in order of increasingly sharp fourths; note that diatonic fourths and 4-jarasteps are equated in jaric, a notable property).

~~The name "taric" was named based on it being the only octave-tuned~~ TAMNAMS pattern with a [[#Simple step ratios|basic]] tuning of [[18edo]] (because [[7L 4s]] has more than 10 notes so is out of the scope of TAMNAMS, although not necessarily out of the scope of extensions) and it was also named based on rhyming with jaric (as they share the parent mos [[2L 6s]]).

~~==== Sephiroid (3L 7s) ====~~

~~[[Sephiroth]] is the 3&10 temperament in the 2.5.11.13.17.21 subgroup with commas including 65/64, 85/84, 105/104, 169/168, 170/169, 221/220, 273/272, 275~~/~~273.~~

~~This temperament is supported by {{Optimal ET sequence| 3, 10, 13, 16, 23 and 26 }} equal divisions, with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.~~

~~<nowiki>*</nowiki> Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.~~

~~(Note that ''q'' in the above is a placeholder symbol meaning that the generator 21 is warted.)~~

~~Note therefore how practically a full range of tunings is covered both in breadth and depth.~~

~~==== Dicoid (7L 3s) ====~~

~~[[Dicot family~~#Dichotic|Dichotic]] is the 7&10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for ~~the name, note that:~~

~~This temperament is supported by {{Optimal ET sequence| 7, 10 and 17 }} equal divisions, with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).~~

~~Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to loosely associate the exotemperament with the range of vaguely saner tunings.~~

~~==== Superdiatonic/armotonic (7L 2s) ====~~

~~Though the term has seen some use in other contexts, the name "superdiatonic" has seen some precedent of use on the Xenwiki to refer to the~~ mos pattern 7L 2s. This mos is part of a series of mos patterns (5+2k)L 2s, which starts with diatonic (5L 2s, k=0) and superdiatonic (7L 2s, k=1). Like 5L 2s, 7L 2s is also a fifth-generated scale and has a structure similar to diatonic in some ways, but with more large steps. In contexts where the term "superdiatonic" conveys a different meaning (other than referring to 7L 2s), the name "armotonic", in reference to Armodue theory, can be used as an alternative name.

~~==== On the term ''diatonic'' ====~~

In TAMNAMS, ''diatonic'' exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized/detuned'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''quasi-diatonic'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.

(The choice of how to define ''diatonic'' isn't bound by history, since many other terms have different meanings depending on the historical musical system referred to, for example the ''enharmonic scale'' may refer to a chain-of-fifths-based scale with 12edo enharmonics not equated, or to an ancient Greek genus.)

== Naming mos modes ==

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== Appendix ==

~~=== Derivation of the step ratio names ===~~

~~The idea is to start with the simplest ratios (L/s = 1/0 and L/s = 1/1) and derive more complex ratios through repeated application of the [[mediant]] (aka Farey addition) to adjacent fractions.~~

* Applying the mediant to the starting intervals 1/0 and 1/1 gives (1+1)/(1+0) = 2/1, and as this is the simplest possible ratio where the large and small step are distinguished and nonzero, it is called the ''basic'' tuning. (Note that if applying the mediant to 1/0 seems confusing, think of it as equivalent to applying the mediant to 0/1 and 1/1 and the ratios as flipped, thus representing s/L rather than L/s when written this way.)

* As L/s = 1/1 represents L and s being equal in size, it is called ''equalized''.

* As L/s = 1/0 represents s = 0, it is called ''collapsed'', as the small scale steps collapse to zero cents and disappear.

* The mediant of 1/1 and 2/1 is 3/2, thus making the scale sound mellower/softer, and as this is the simplest (in the sense of lowest [[Odd limit#Relationship_to_other_limits|integer limit]]) ratio to represent such a property, it is simply called the ''soft'' tuning.

* Analogously, the mediant of 2/1 and 1/0, 3/1, is called the ''hard'' tuning. Thus you can say that a step ratio tuning is ''hard of'' or ''soft of'' another step ratio tuning.

* To get something between soft and basic we take the mediant again and get 5/3 for ''semisoft'', and analogously 5/2 for ''semihard''. To get something more extreme we take the mediant of 1/0 with 3/1 for a harder-than-hard tuning, giving us 4/1 for ''superhard'' and analogously 4/3 for ''supersoft''.

~~There are~~ also ~~tertiary names beyond the above:~~

* Anything softer than supersoft is ''ultrasoft,'' and anything harder than superhard is ''ultrahard''. Something between soft and supersoft is ''parasoft'', as ''para-'' means both ''beyond'' and ''next to''. Something between hard and superhard is ''parahard''.

* Something between soft and basic is ''hyposoft'' as it is less soft than soft. Something between hard and basic is ''hypohard'' for the same reason. Between semisoft and basic is ''minisoft'' and between semihard and basic is ''minihard''.

* Finally, between soft and semisoft is ''quasisoft'' as such scales may potentially be mistaken for soft or semisoft while not being either - hence the use of the prefix ''quasi-'', and between hard and semihard is ''quasihard'' for the same reason.

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'' - 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.

The most obvious adjustment to the edges is to draw a distinction between ''ultrasoft'' and ''pseudoequalized'' by adding a step ratio corresponding to ''semiequalized'', and between ''ultrahard'' and ''pseudocollapsed'' by adding a step ratio corresponding to ''semicollapsed''. Thus:

~~'''Ultrasoft''' is between '''supersoft''' and '''semiequalized''' and '''pseudoequalized''' is between '''semiequalized''' and '''equalized'''.~~

~~'''Ultrahard''' is between '''superhard''' and '''semicollapsed''', and '''pseudocollapsed''' is between '''semicollapsed''' and '''collapsed'''.~~

Then all that's left is to decide what the step ratios for semicollapsed and semiequalized should be. In order to keep the spacing (of the s/L ratios when graphed, or to a lesser extent the L/s ratios if you see the roughly gradual increase in spacing in that form) roughly consistent with all the other ratios, '''semiequalized''' should be L/s = 6/5 rather than L/s = 5/4. Then note the complexity of L/s = 6/5 is 6+5=11, so to find the corresponding complexity for '''semicollapsed''' we use L/s = 10/1 as 10+1=11 too. Then finally, to preserve some of the symmetry, we include L/s = 6/1 as '''extrahard'''. Although L/s = 10/1 for '''semicollapsed''' may seem a little extreme of a boundary, L/s = 12/1 would actually be what is the most ''equally spaced'' continuing on from 6/1 for the same reason that L/s = 6/5 is the most ''equally spaced''. Note that while the range from '''superhard''' to '''semicollapsed''' is '''ultrahard''', the region may be split into two sub-ranges:

~~'''superhard''' (L/s=4/1) to '''extrahard''' (L/s=6/1) is '''hyperhard''' (4 < L/s < 6).~~

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

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

~~=== Extended spectrum ===~~

~~'''Equalized''': L/s = 1/1 (trivial/pathological)~~

~~::: ('''Pseudoequalized''' range here.)~~

~~:: '''Semiequalized''': L/s = 6/5~~

~~::: ('''Ultrasoft''' range here.)~~

~~:: '''Supersoft''': L/s = 4/3~~

~~(4/3 < L/s < 4/1 range here, called the '''nonextreme''' range, detailed by central spectrum.)~~

~~:: '''Superhard''': L/s = 4/1~~

~~::: (Beginning of '''ultrahard''' range here.)~~

~~::: ('''Hyperhard''' range here.)~~

~~:: '''Extrahard''': L/s = 6/1~~

~~::: ('''Clustered''' range here.)~~

~~::: (End of '''ultrahard''' range here.)~~

~~::'''Semicollapsed''': L/s = 10/1~~

~~::: ('''Pseudocollapsed''' range here.)~~

~~'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)~~

~~=== Terminology and final notes ===~~

A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or ''pentasoft'', the simplest hyperhard tuning is 5-hard or ''pentahard'', the simplest clustered tuning is 7-hard or ''heptahard'', 8-hard is ''octahard'', 9-hard is ''nonahard'', and finally, the characteristic simple ultrahard tuning is 6-hard or ''extrahard'', as previously discussed, which can be seen to be similar to ''hexahard'' - hopefully helping with memorisation.

~~A perhaps useful (or otherwise mildly amusing) mnemonic is ''2-soft is too soft to be hard and 2-hard is too hard to be soft'', representing that 2-soft = 2-hard = 2~~/~~1 = '''basic'''.~~

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 scale]]

@@ Line 482: / Line 482: @@
 ! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology
 |-
-| [[1L 4s]] || pedal || ped- || ped || || [[#Pedal (1L 4s)|one big toe and four small toes]]
+| [[1L 4s]] || pedal || ped- || ped || || one big toe and four small toes
 |-
 | [[2L 3s]] || pentic || pent- || pt || || common pentatonic; from penta- for 5
@@ Line 508: / Line 508: @@
 ! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology
 |-
-| [[1L 6s]] || onyx || on- || on || || [[#Onyx (1L 6s)|from a ''lot'' of naming puns]]
+| [[1L 6s]] || onyx || on- || on || || from a ''lot'' of naming puns
 |-
 | [[2L 5s]] || antidiatonic || pel- || pel || || pel- is from pelog
@@ Line 580: / Line 580: @@
 | [[9L 1s]] || sinatonic || sina- || si || || from [[sinaic]]
 |}
-<references/>
+<references/>For the reasoning for these names, see [[TAMNAMS/Appendix|TAMNAMS/Appendix#Reasoning for mos pattern names]].
-=== Reasoning for the names ===
-The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.
-All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.
-All names for mosses with five or less notes - excluding (mono)wood and biwood (which like all n-wood mosses are specific to octave tuning) - require that some small integer multiple of the period is equal to an octave, under the reasoning that mosses with five or less notes are common and broad in tuning enough that they are much more likely to find interest in non-octave contexts. Because of this, their names were chosen to be extremely general, both to avoid bias/being too flavorful and (correspondingly) so that the terms could validly be reused for any mos for which the period is not equal to a (potentially tempered) octave.
-Any multiperiod mos with more than five notes was given a name that wasn't reliant on the name of a mos with five or less notes as such names were based on those mos names formerly requiring an octave tuning (which is to say some small integer multiple of their period must be equal to a (potentially slightly tempered) octave).
-Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings did not cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".
-The inclusion of mos names for "multiperiod" mosses was from a desire to have all ten-note-and-under mosses named for completeness, which is also what prompted some of the reconsiderations mentioned earlier. Similarly, the inclusion of mosses of the form 1L ns using the "anti-" prefix (or an- for less-than-six-note mosses) was also for a practical consideration; although the tuning range is very unhelpful for knowing what such a mos will sound, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name, especially given that in such situations the tuning will likely be specified somewhere already. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (and for consistency with that their parent MOSS, 4L2s, is named citric).
-The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is also not as trivial as it may sound. In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence the original reason for omitting such mosses), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range. In the case of mosses with five or less notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.
-=== Name-specific reasonings ===
-==== Pedal (1L 4s) ====
-Pedals are operated with feet, which have one large toe and four small toes. Also comes from words like "bipedal", where in TAMNAMS, "bipedal" would literally mean a pedal scale with a period equal to half of some chosen interval, although such a scale would have either two right feet or two left feet depending on orientation chosen. If you think "car"/"vehicle" when you think "pedal" and don't think (or want to think) much about feet then you can think about "[[beep]]ing" (as [[beep]] is the 7-limit 4&5 exotemperament). Because this name relies so heavily and fundamentally on there being 1 large and 4 small steps per period, it is appropriate to generalise for any size of period you would want. In that regard, same goes for manual, pentic and anpentic.
-==== Malic (2L 4s) and citric (4L 2s) ====
-Malic derives from Latin ''malus'' 'apple'. An apple has two concave ends, and large steps in a scale with more small steps are hole-like, hence the two large steps in malic. Citric (4L 2s) is named after the child mosses of citric, namely lemon (6L 4s) and lime (4L 6s). Unlike apples, lemons have two convex pointy ends, and small steps in a scale with more large steps are pointy, hence the two small steps. Malic and citric acids are both ubiquitous in food and biology, thus justifying their use for fairly small mos scales.
-==== Machinoid (5L 1s) ====
-[[Machine]] is the 5&amp;6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98.
-This temperament is supported by {{Optimal ET sequence| 5, 6, 11, 12, 16, 17, 22, 23, 27, 28 and 33 }} equal divisions, with non-patent val tunings including 5+5=10e, 5+10e+12=21be, 5+5+5+5+6=26qe, which are mentioned here for demonstrating virtual completeness of the tuning range, and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.
-==== Onyx (1L 6s) ====
-"1Ln-ic's" and "nL1-ic's (like, the -ic suffix applied to MOSS names, collectivised for 1Lns and nL1s) sounds like "one-el-en-ics" or "en-el-one-ics" which abbreviated sort of sounds like "one-ics" => "onyx". Then "onyx" sounds sort of like "one-six". Furthermore the onyx mineral comes in many colours and types, which seems fitting given this is the parent scale for a wide variety of MOSSes; specifically of interest being 7L 1s (pine), 8L 1s (subneutralic) and 9L 1s (sinatonic). Finally, the name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and other than that, the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part (depending partially on your pronounciation).
-==== Subaric (2L 6s), jaric (2L 8s), and taric (8L 2s) ====
-The name "subaric" alludes to the fact that 2L 6s is the largest proper '''sub'''set mos of both j'''aric''' (2L 8s) and t'''aric''' (8L 2s).
-The name "jaric" alludes to a few highly notable and generally inaccurate (with the exception of diaschismic) temperaments that exist in the tuning range of this MOSS. Specifically, notice how the letters and sound of "jaric" has (or is intended to have) a lot of overlap with [[pajara|pa'''jar'''a]], [[diaschismic|diaschism'''ic''']] and [[injera|in'''jer'''a]] (listed in order of increasingly sharp fourths; note that diatonic fourths and 4-jarasteps are equated in jaric, a notable property).
-The name "taric" was named based on it being the only octave-tuned TAMNAMS pattern with a [[#Simple step ratios|basic]] tuning of [[18edo]] (because [[7L 4s]] has more than 10 notes so is out of the scope of TAMNAMS, although not necessarily out of the scope of extensions) and it was also named based on rhyming with jaric (as they share the parent mos [[2L 6s]]).
-==== Sephiroid (3L 7s) ====
-[[Sephiroth]] is the 3&amp;10 temperament in the 2.5.11.13.17.21 subgroup with commas including 65/64, 85/84, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273.
-This temperament is supported by {{Optimal ET sequence| 3, 10, 13, 16, 23 and 26 }} equal divisions, with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.
-<nowiki>*</nowiki> Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.
-(Note that ''q'' in the above is a placeholder symbol meaning that the generator 21 is warted.)
-Note therefore how practically a full range of tunings is covered both in breadth and depth.
-==== Dicoid (7L 3s) ====
-[[Dicot family#Dichotic|Dichotic]] is the 7&amp;10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for the name, note that:
-This temperament is supported by {{Optimal ET sequence| 7, 10 and 17 }} equal divisions, with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).
-Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to loosely associate the exotemperament with the range of vaguely saner tunings.
-==== Superdiatonic/armotonic (7L 2s) ====
-Though the term has seen some use in other contexts, the name "superdiatonic" has seen some precedent of use on the Xenwiki to refer to the mos pattern 7L 2s. This mos is part of a series of mos patterns (5+2k)L 2s, which starts with diatonic (5L 2s, k=0) and superdiatonic (7L 2s, k=1). Like 5L 2s, 7L 2s is also a fifth-generated scale and has a structure similar to diatonic in some ways, but with more large steps. In contexts where the term "superdiatonic" conveys a different meaning (other than referring to 7L 2s), the name "armotonic", in reference to Armodue theory, can be used as an alternative name.
-==== On the term ''diatonic'' ====
-In TAMNAMS, ''diatonic'' exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized/detuned'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''quasi-diatonic'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.
-(The choice of how to define ''diatonic'' isn't bound by history, since many other terms have different meanings depending on the historical musical system referred to, for example the ''enharmonic scale'' may refer to a chain-of-fifths-based scale with 12edo enharmonics not equated, or to an ancient Greek genus.)
 == Naming mos modes ==
@@ Line 672: / Line 610: @@
 == Appendix ==
+{{See also|TAMNAMS/Appendix}}
-=== Derivation of the step ratio names ===
-The idea is to start with the simplest ratios (L/s = 1/0 and L/s = 1/1) and derive more complex ratios through repeated application of the [[mediant]] (aka Farey addition) to adjacent fractions.
-* Applying the mediant to the starting intervals 1/0 and 1/1 gives (1+1)/(1+0) = 2/1, and as this is the simplest possible ratio where the large and small step are distinguished and nonzero, it is called the ''basic'' tuning. (Note that if applying the mediant to 1/0 seems confusing, think of it as equivalent to applying the mediant to 0/1 and 1/1 and the ratios as flipped, thus representing s/L rather than L/s when written this way.)
-* As L/s = 1/1 represents L and s being equal in size, it is called ''equalized''.
-* As L/s = 1/0 represents s = 0, it is called ''collapsed'', as the small scale steps collapse to zero cents and disappear.
-* The mediant of 1/1 and 2/1 is 3/2, thus making the scale sound mellower/softer, and as this is the simplest (in the sense of lowest [[Odd limit#Relationship_to_other_limits|integer limit]]) ratio to represent such a property, it is simply called the ''soft'' tuning.
-* Analogously, the mediant of 2/1 and 1/0, 3/1, is called the ''hard'' tuning. Thus you can say that a step ratio tuning is ''hard of'' or ''soft of'' another step ratio tuning.
-* To get something between soft and basic we take the mediant again and get 5/3 for ''semisoft'', and analogously 5/2 for ''semihard''. To get something more extreme we take the mediant of 1/0 with 3/1 for a harder-than-hard tuning, giving us 4/1 for ''superhard'' and analogously 4/3 for ''supersoft''.
-There are also tertiary names beyond the above:
-* Anything softer than supersoft is ''ultrasoft,'' and anything harder than superhard is ''ultrahard''. Something between soft and supersoft is ''parasoft'', as ''para-'' means both ''beyond'' and ''next to''. Something between hard and superhard is ''parahard''.
-* Something between soft and basic is ''hyposoft'' as it is less soft than soft. Something between hard and basic is ''hypohard'' for the same reason. Between semisoft and basic is ''minisoft'' and between semihard and basic is ''minihard''.
-* Finally, between soft and semisoft is ''quasisoft'' as such scales may potentially be mistaken for soft or semisoft while not being either - hence the use of the prefix ''quasi-'', and between hard and semihard is ''quasihard'' for the same reason.
-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'' - 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.
-The most obvious adjustment to the edges is to draw a distinction between ''ultrasoft'' and ''pseudoequalized'' by adding a step ratio corresponding to ''semiequalized'', and between ''ultrahard'' and ''pseudocollapsed'' by adding a step ratio corresponding to ''semicollapsed''. Thus:
-'''Ultrasoft''' is between '''supersoft''' and '''semiequalized''' and '''pseudoequalized''' is between '''semiequalized''' and '''equalized'''.
-'''Ultrahard''' is between '''superhard''' and '''semicollapsed''', and '''pseudocollapsed''' is between '''semicollapsed''' and '''collapsed'''.
-Then all that's left is to decide what the step ratios for semicollapsed and semiequalized should be. In order to keep the spacing (of the s/L ratios when graphed, or to a lesser extent the L/s ratios if you see the roughly gradual increase in spacing in that form) roughly consistent with all the other ratios, '''semiequalized''' should be L/s = 6/5 rather than L/s = 5/4. Then note the complexity of L/s = 6/5 is 6+5=11, so to find the corresponding complexity for '''semicollapsed''' we use L/s = 10/1 as 10+1=11 too. Then finally, to preserve some of the symmetry, we include L/s = 6/1 as '''extrahard'''. Although L/s = 10/1 for '''semicollapsed''' may seem a little extreme of a boundary, L/s = 12/1 would actually be what is the most ''equally spaced'' continuing on from 6/1 for the same reason that L/s = 6/5 is the most ''equally spaced''. Note that while the range from '''superhard''' to '''semicollapsed''' is '''ultrahard''', the region may be split into two sub-ranges:
-'''superhard''' (L/s=4/1) to '''extrahard''' (L/s=6/1) is '''hyperhard''' (4 < L/s < 6).
-'''extrahard''' (L/s=6/1) to '''semicollapsed''' (L/s=10/1) is '''clustered''' (6 < L/s < 10).
-With the inclusion of these 3 new L/s ratios nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed above, just for the regions affected to avoid repetition.
-=== Extended spectrum ===
-'''Equalized''': L/s = 1/1 (trivial/pathological)
-::: ('''Pseudoequalized''' range here.)
-:: '''Semiequalized''': L/s = 6/5
-::: ('''Ultrasoft''' range here.)
-:: '''Supersoft''': L/s = 4/3
-(4/3 < L/s < 4/1 range here, called the '''nonextreme''' range, detailed by central spectrum.)
-:: '''Superhard''': L/s = 4/1
-::: (Beginning of '''ultrahard''' range here.)
-::: ('''Hyperhard''' range here.)
-:: '''Extrahard''': L/s = 6/1
-::: ('''Clustered''' range here.)
-::: (End of '''ultrahard''' range here.)
-::'''Semicollapsed''': L/s = 10/1
-::: ('''Pseudocollapsed''' range here.)
-'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)
-=== Terminology and final notes ===
-A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or ''pentasoft'', the simplest hyperhard tuning is 5-hard or ''pentahard'', the simplest clustered tuning is 7-hard or ''heptahard'', 8-hard is ''octahard'', 9-hard is ''nonahard'', and finally, the characteristic simple ultrahard tuning is 6-hard or ''extrahard'', as previously discussed, which can be seen to be similar to ''hexahard'' - hopefully helping with memorisation.
-A perhaps useful (or otherwise mildly amusing) mnemonic is ''2-soft is too soft to be hard and 2-hard is too hard to be soft'', representing that 2-soft = 2-hard = 2/1 = '''basic'''.
-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 scale]]

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