TAMNAMS: Difference between revisions

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The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. ''Major'', ''minor'', ''perfect'', etc. would apply as established~~. The modifier ''neutral'' is used for intervals exactly halfway between major and minor k-steps in a given tuning~~. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.

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== Naming mos degrees ==

To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major~~'', ''neutral~~'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.

To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.

To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal: Naming mos modes|below]] for the convention we have used to name the mode).

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| [[6L 4s]] || lemon || lem- || lem || anpentic mos with 2 periods per octave || from [[lemba]] temperament

|-

| [[7L 3s]] || ~~zaltertic~~ || ~~zal~~- || ~~zal~~ || || ~~From the term "Zalzalian third" for neutral thirds~~

| [[7L 3s]] || dicoid /'daɪkɔɪd/ || dico- || dico || || from exotemperaments [[Dicot family#Dichotic|dichotic]] and [[dicot]]

|-

| [[8L 2s]] || taric || tara- || tar || manual mos with 2 periods per octave || from Hindi ''aṭhārah'' '[[#Taric (8L 2s)|18]]'

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(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.~~<!--~~

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:

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Its list of patent val EDO tunings is {{ val list | 7, 10, 17 }} 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 associate the exotemperament with the range of vaguely saner tunings. ~~-->~~

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

==== 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 ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.

@@ Line 139: / Line 139: @@
 The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.
-Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. ''Major'', ''minor'', ''perfect'', etc. would apply as established. The modifier ''neutral'' is used for intervals exactly halfway between major and minor k-steps in a given tuning. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
+Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
 In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.
@@ Line 236: / Line 236: @@
 == Naming mos degrees ==
-To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''neutral'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.
+To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.
 To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal: Naming mos modes|below]] for the convention we have used to name the mode).
@@ Line 374: / Line 374: @@
 | [[6L 4s]] || lemon || lem- || lem || anpentic mos with 2 periods per octave || from [[lemba]] temperament
 |-
-| [[7L 3s]] || zaltertic || zal- || zal || || From the term "Zalzalian third" for neutral thirds
+| [[7L 3s]] || dicoid /'daɪkɔɪd/ || dico- || dico || || from exotemperaments [[Dicot family#Dichotic|dichotic]] and [[dicot]]
 |-
 | [[8L 2s]] || taric || tara- || tar || manual mos with 2 periods per octave || from Hindi ''aṭhārah'' '[[#Taric (8L 2s)|18]]'
@@ Line 424: / Line 424: @@
 (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.<!--
+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:
@@ Line 430: / Line 430: @@
 Its list of patent val EDO tunings is {{ val list | 7, 10, 17 }} 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 associate the exotemperament with the range of vaguely saner tunings. -->
+Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to associate the exotemperament with the range of vaguely saner tunings.
 ==== 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 ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.