Xenharmonic Wiki

User:Ganaram inukshuk/TAMNAMS: Difference between revisions

← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
appendix -> faq
 
(9 intermediate revisions by the same user not shown)
Line 210: Line 210:


=== Expanded spectrum and other terminology ===
=== Expanded spectrum and other terminology ===
For a derivation of these ratio ranges, see <link>.


==Naming mos intervals==
==Naming mos intervals==
Line 223: Line 224:
**The large size of the dark generator is '''augmented''', and the small size is '''perfect'''.
**The large size of the dark generator is '''augmented''', and the small size is '''perfect'''.
*For all other intervals, the large size is '''major''' and the small size is '''minor'''.
*For all other intervals, the large size is '''major''' and the small size is '''minor'''.
There is one exception to the above rules: the designations of augmented, perfect, and diminished don't apply for the generators for mosses of the form ''n''L ''n''s. Instead, major and minor is used. This is to prevent ambiguity over calling every interval perfect.
There is one exception to the above rules: the designations of augmented, perfect, and diminished don't apply for the generators for ''n''L ''n''s mosses. Instead, major and minor is used, so as to prevent ambiguity over calling every interval perfect.


Mosstep intervals can exceed the octave as they do in standard music theory (eg, a diatonic 9th is a diatonic 2nd raised one octave). For a single-period mos, any interval that is raised by an octave will be the same interval quality that it was before raising. Likewise, for a multi-period mos, any interval raised by the period, where the period is a fraction of the octave, will be the same interval quality that it was before raising.
Mosstep intervals can exceed the octave as they do in standard music theory (eg, a diatonic 9th is a diatonic 2nd raised one octave). For a single-period mos, any interval that is raised by an octave will be the same interval quality that it was before raising. Likewise, for a multi-period mos, any interval raised by the period, where the period is some fraction of the octave, will be the same interval quality that it was before raising.


Examples using 5L 2s and 4L 4s are provided below. Note that 5L 2s interval names are identical to that of standard music theory, apart from the 0-indexed interval names. To differentiate intervals of a specific mos, a prefix can be used in place of "mos-", outlined <link>. For a detailed derivation of these intervals, see <link>.
Examples using 5L 2s and 4L 4s interval names are provided below. Note that 5L 2s interval names are identical to that of standard music theory, apart from the 0-indexed interval names. To differentiate intervals of a specific mos, the mos's corresponding prefix can be used in place of "mos-", outlined <link>. For a detailed derivation of these intervals, see <link>.
<table>
<table>
<tr>
<tr>
Line 235: Line 236:


===Alterations by a chroma===
===Alterations by a chroma===
The terms ''augmented'' and ''diminished'' are also used to describe intervals that are further lowered or raised by an interval called a ''moschroma'' (or simply ''chroma'' if context allows), a generalized sharp or flat. The rules for alteration are the same as with conventional music theory:
The terms ''augmented'' and ''diminished'' are also used to describe intervals that are further lowered or raised by an interval called a ''moschroma'' (or simply ''chroma'' if context allows), a generalized sharp or flat. The rules for alteration are the same as with conventional music theory.


* Raising a minor interval by a chroma makes it minor.
* Raising a minor interval by a chroma makes it minor.
Line 249: Line 250:
|+Table of alterations, with abbreviations
|+Table of alterations, with abbreviations
|-
|-
!Number of chromas
! rowspan="2" |Chromas
!Perfectable intervals
! colspan="2" |Perfectable intervals
! Major/minor intervals
! colspan="2" | Non-perfectable intervals
|-
|-
| +4 chromas
!Interval quality
|Quadruply-augmented (A<sup>4</sup> or A^4)
!Abbrev.
|Quadruply-augmented (A<sup>4</sup> or A^4)
!Interval quality
!Abbrev.
|-
|-
|  +3 chromas
|  +4
|Triply-augmented (AAA, A<sup>3</sup>, or A^3)
|Quadruply-augmented
|Triply-augmented (AAA, A<sup>3</sup>, or A^3)
|A<sup>4</sup> or A^4
|Quadruply-augmented
|A<sup>4</sup> or A^4
|-
|-
|  +2 chromas
|  +3
|Doubly-augmented (AA)
|Triply-augmented
|Doubly-augmented (AA)
|AAA, A<sup>3</sup>, or A^3
|Triply-augmented
|AAA, A<sup>3</sup>, or A^3
|-
|-
|  +1 chroma
|  +2
|Augmented (A)
|Doubly-augmented
|Augmented (A)
|AA
|Doubly-augmented
|AA
|-
|-
| rowspan="2" |0 chromas (unaltered)
| +1
| rowspan="2" |Perfect (P)
|Augmented
|Major (M)
|A
|Augmented
|A
|-
|-
|Minor (m)
| rowspan="2" |0
| rowspan="2" |Perfect
| rowspan="2" |P
|Major
|M
|-
|-
| -1 chroma
|Minor
|Diminished (d)
|m
|Diminished (d)
|-
|-
|  -2 chromas
|  -1
|Doubly-diminished (dd)
|Diminished
|Doubly-diminished (dd)
|d
|Diminished
|d
|-
|-
| -3 chromas
| -2
|Triply-diminished (ddd, d<sup>3</sup>, or d^3)
|Doubly-diminished
|Triply-diminished (ddd, d<sup>3</sup>, or d^3)
|dd
|Doubly-diminished
|dd
|-
|-
|  -4 chromas
|  -3
|Quadruply-diminished (d<sup>4</sup> or d^4)
|Triply-diminished
|Quadruply-diminished (d<sup>4</sup> or d^4)
|ddd, d<sup>3</sup>, or d^3
|Triply-diminished
|ddd, d<sup>3</sup>, or d^3
|-
|  -4
|Quadruply-diminished
|d<sup>4</sup> or d^4
|Quadruply-diminished
|d<sup>4</sup> or d^4
|}
 
=== Intervals smaller than a chroma ===
{| class="wikitable"
!Interval name
! Absolute value of a...
|-
|Moschroma (generalized [[chroma]], provided for reference)
|Large step minus a small step
|-
| Mosdiesis (generalized [[Diesis (scale theory)|diesis]])
|Large step minus two small steps
|-
| Moskleisma (generalized [[kleisma]])
|Mosdiesis minus a moschroma
|-
| Mosgothma (generalized gothma)
|Mosdiesis minus a small step
|}
|}
===Other terminology and other intervals===
===Other terminology and intervals===
Intervals that have a perfect variety (the unison, period intervals, and generators) are called ''perfectable intervals'', whereas intervals that do not have a perfect variety are called ''non-perfectable intervals''. Intervals corresponding to the generators may be called ''imperfect intervals'' since, unlike the period and unison, they have two varieties instead of one.
Intervals that have a perfect variety (the unison, period intervals, and generators) are called ''perfectable intervals'', whereas intervals that do not have a perfect variety are called ''non-perfectable intervals''. Intervals corresponding to the generators may be called ''imperfect intervals'' since, unlike the period and unison, they have two varieties instead of one.


Line 320: Line 363:
''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''
''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''


TAMNAMS uses the following names for octave-equivalent (or tempered-octave) mosses with step counts between 6 and 10, called the ''named range''. These names are optional, and conventional ''xL ys'' names can be used instead in discussions regarding mosses, its intervals, scale degrees, and modes.
TAMNAMS primarily uses the following names for octave-equivalent (or tempered-octave) mosses with step counts between 6 and 10. These names are optional, and conventional ''xL ys'' names can be used instead in discussions regarding mosses, its intervals, scale degrees, and modes.


Prefixes and abbreviations for each name are also provided, and can used in place of the prefix ''mos-'' and its abbreviation of ''m-'', as seen in mos-related terms, such as ''mosstep'' and ''mosdegree'', and their abbreviations of ''ms'' and ''md'', respectively. For example, discussion of the intervals and scale degrees of ''oneirotonic'' uses the terms ''oneirosteps'' and ''oneirodegrees'', abbreviated as ''oneis'' and ''oneid'', respectively.
Prefixes and abbreviations for each name are also provided, and can used in place of the prefix ''mos-'' and its abbreviation of ''m-'', as seen in mos-related terms, such as ''mosstep'' and ''mosdegree'', and their abbreviations of ''ms'' and ''md'', respectively. For example, discussion of the intervals and scale degrees of ''oneirotonic'' uses the terms ''oneirosteps'' and ''oneirodegrees'', abbreviated as ''oneis'' and ''oneid'', respectively.
Line 333: Line 376:
|-
|-
|[[1L 5s]]|| selenite||sel-||sel||References [[luna]] temperament (selenite is named after the moon); also called ''antimachinoid<ref name="anti-name">Alternate name based on the name of its sister mos, with anti- prefix added.</ref>''.
|[[1L 5s]]|| selenite||sel-||sel||References [[luna]] temperament (selenite is named after the moon); also called ''antimachinoid<ref name="anti-name">Alternate name based on the name of its sister mos, with anti- prefix added.</ref>''.
(Provided for lack of a better name)
|-
|-
|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
Line 341: Line 383:
|[[4L 2s]]||citric||citro-||cit||Parent (or subset) mos of 4L 6s and 6L 4s.
|[[4L 2s]]||citric||citro-||cit||Parent (or subset) mos of 4L 6s and 6L 4s.
|-
|-
|[[5L 1s]]||machinoid||mech-||mech||From [[machine]] temperament.
|[[5L 1s]]||machinoid||mech-||mk||From [[machine]] temperament.
|-
|-
! colspan="5" |7-note mosses
! colspan="5" |7-note mosses
Line 357: Line 399:
|[[5L 2s]]|| diatonic||dia-||dia||
|[[5L 2s]]|| diatonic||dia-||dia||
|-
|-
|[[6L 1s]]||archaeotonic ||arch- || arch||Originally a name for 13edo's 6L 1s scale; also called ''archæotonic/archeotonic<ref name="spelling">Spelling variant.</ref>''.
|[[6L 1s]]||archaeotonic ||arch- || arc||Originally a name for 13edo's 6L 1s scale; also called ''archæotonic/archeotonic<ref name="spelling">Spelling variant.</ref>''.
|-
|-
! colspan="5" |8-note mosses
! colspan="5" |8-note mosses
Line 371: Line 413:
|[[4L 4s]]|| tetrawood||tetrawd- ||ttw||Blackwood[10] and whitewood[14] generalized to 4 periods; also called ''diminished<ref name="unofficial">Common name no longer recommend by TAMNAMS due to risk of ambiguity. Provided for reference.</ref>.''
|[[4L 4s]]|| tetrawood||tetrawd- ||ttw||Blackwood[10] and whitewood[14] generalized to 4 periods; also called ''diminished<ref name="unofficial">Common name no longer recommend by TAMNAMS due to risk of ambiguity. Provided for reference.</ref>.''
|-
|-
|[[5L 3s]]||oneirotonic ||oneiro-||onei|| Originally a name for 13edo's 5L 3s scale; also called ''oneiro''<ref>Shortened form of name.</ref>.
|[[5L 3s]]||oneirotonic ||oneiro-||or|| Originally a name for 13edo's 5L 3s scale; also called ''oneiro''<ref>Shortened form of name.</ref>.
|-
|-
|[[6L 2s]]||ekic||ek- ||ek||From [[echidna]] and [[hedgehog]] temperaments.
|[[6L 2s]]||ekic||ek- ||ek||From [[echidna]] and [[hedgehog]] temperaments.
|-
|-
|[[7L 1s]]||pine||pine-||pine||From [[porcupine]] temperament.
|[[7L 1s]]||pine||pine-||p||From [[porcupine]] temperament.
|-
|-
! colspan="5" | 9-note mosses
! colspan="5" | 9-note mosses
Line 383: Line 425:
|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''
|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''
|-
|-
|[[2L 7s]]||balzano||bal-||bal||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
|[[2L 7s]]||balzano||bal-||bz||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
|-
|-
|[[3L 6s]]||tcheretonic||cher-||ch|| In reference to Tcherepnin's 9-note scale in 12edo. Also called ''cheretonic<ref name="spelling" />''.
|[[3L 6s]]||tcherepnin||cher-||ch|| In reference to Tcherepnin's 9-note scale in 12edo.
|-
|-
|[[4L 5s]]|| gramitonic||gram-||gram||From "grave minor third".
|[[4L 5s]]|| gramitonic||gram-||gm||From "grave minor third".
|-
|-
|[[5L 4s]]||semiquartal||cthon-||cth||From "half fourth"; cthon- is from "chthonic".
|[[5L 4s]]||semiquartal||cthon-||ct||From "half fourth"; cthon- is from "chthonic".
|-
|-
|[[6L 3s]]||hyrulic||hyru-||hy||References [[triforce]] temperament.
|[[6L 3s]]||hyrulic||hyru-||hy||References [[triforce]] temperament.
|-
|-
|[[7L 2s]]||armotonic||arm-||arm||From [[Armodue]] theory; also called ''superdiatonic<ref name="unofficial" />.''
|[[7L 2s]]||armotonic||arm-||am||From [[Armodue]] theory; also called ''superdiatonic<ref name="unofficial" />.''
|-
|-
|[[8L 1s]]||subneutralic||blu-|| blu||Derived from the generator being between supraminor and neutral quality; blu- is from [[bleu]] temperament.
|[[8L 1s]]||subneutralic||blu-|| bl||Derived from the generator being between supraminor and neutral quality; blu- is from [[bleu]] temperament.
|-
|-
! colspan="5" |10-note mosses
! colspan="5" |10-note mosses
Line 401: Line 443:
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 9s]]||olivnie ||oli- ||oli||Rhymes with "nine", depending on one's pronunciation; also called ''antisinatonic<ref name="anti-name" />.''
|[[1L 9s]]||olivnie ||oli- ||ol||Rhymes with "nine", depending on one's pronunciation; also called ''antisinatonic<ref name="anti-name" />.''
|-
|-
|[[2L 8s]]||jaric||jara-||jar||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.
|[[2L 8s]]||jaric||jara-||ja||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.
|-
|-
|[[3L 7s]]||sephiroid||seph-|| seph||From [[sephiroth]] temperament.
|[[3L 7s]]||sephiroid||seph-|| sp||From [[sephiroth]] temperament.
|-
|-
|[[4L 6s]]||lime ||lime-||lim||Sister mos of 6L 4s; limes are smaller than lemons, as are 4L 6s's step sizes compared to 6L 4s.
|[[4L 6s]]||lime ||lime-||lm||Sister mos of 6L 4s; limes are smaller than lemons, as are 4L 6s's step sizes compared to 6L 4s.
|-
|-
|[[5L 5s]]||pentawood||pentawd-||pw||Blackwood[10] and whitewood[14] generalized to 5 periods.
|[[5L 5s]]||pentawood||pentawd-||pw||Blackwood[10] and whitewood[14] generalized to 5 periods.
|-
|-
|[[6L 4s]]||lemon||lem- ||lem||From [[lemba]] temperament.
|[[6L 4s]]||lemon||lem- ||le||From [[lemba]] temperament. Also sister mos of 4L 6s.
|-
|-
|[[7L 3s]]||dicoid||dico-||dico ||From [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
|[[7L 3s]]||dicoid||dico-||di ||From [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
|-
|-
|[[8L 2s]]||taric||tara-||tar||Sister mos of 2L 8s; based off of [[wikipedia:Hindustani_numerals|Hindi]] word for 18 (aṭhārah), since 18edo contains basic 8L 2s.
|[[8L 2s]]||taric||tara-||ta||Sister mos of 2L 8s; based off of [[wikipedia:Hindustani_numerals|Hindi]] word for 18 (aṭhārah), since 18edo contains basic 8L 2s.
|-
|-
|[[9L 1s]]|| sinatonic||sina-||si|| Derived from the generator being within the range of a [[sinaic]].
|[[9L 1s]]|| sinatonic||sina-||si|| Derived from the generator being within the range of a [[sinaic]].
Line 421: Line 463:
<references />
<references />


===Extending the named range===
===Names for smaller mosses===
For a discussion of names for mosses with fewer than 6 steps, see <link>. For a discussion of names for mosses with more than 10 steps, see <link>.
In addition to the names listed above are names for smaller mosses, provided for completeness. These names, with the exception of ''monowood'' and ''biwood'', are meant to be as general as possible so as to avoid flavor and to allow for valid reuse for non-octave mosses.
{| class="wikitable center-all"
! colspan="6" |2-note mosses
|-
!Pattern!!Name!!Prefix!!Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
| rowspan="2" |[[1L 1s]]|| trivial|| triv-||tw
|No||The simplest valid mos pattern.
|-
|monowood
| monowd-
| w
|Yes
| Blackwood[10] and whitewood[14] generalized to 1 period.
|-
! colspan="6" |3-note mosses
|-
!Pattern!!Name!! Prefix!!Abbr.
!Must be 2/1-equivalent?!! Etymology
|-
|[[1L 2s]]||antrial|| atri-||at
|No ||Opposite pattern of 2L 1s, with broader range. Shortening of ''anti-trial''.
|-
|[[2L 1s]]||trial||tri-||t
|No ||From tri- for 3.
|-
! colspan="6" |4-note mosses
|-
!Pattern!! Name!!Prefix!! Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
|[[1L 3s]]|| antetric|| atetra-||att
|No ||Opposite pattern of 3L 1s, with broader range. Shortening of ''anti-tetric''.
|-
|[[2L 2s]]||biwood||biwd-||bw
|Yes||Blackwood[10] and whitewood[14] generalized to 2 periods.
|-
|[[3L 1s]]||tetric|| tetra- ||tt
|No ||From tetra- for 4.
|-
! colspan="6" | 5-note mosses
|-
!Pattern!!Name!!Prefix !! Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
|[[1L 4s]]||pedal||ped-||pd
|No ||From Latin ''ped'', for ''foot''; one big toe and four small toes.
|-
|[[2L 3s]]||pentic||pent- ||pt
|No||Common pentatonic; from penta- for 5.
|-
|[[3L 2s]]||antipentic || apent-||apt
| No||Opposite pattern of 2L 3s.
|-
|[[4L 1s]]||manual ||manu-|| mn
|No||From Latin ''manus'', for ''hand''; one thumb and four longer fingers.
|}
=== Names for larger mosses ===
For a discussion of names for mosses with more than 10 steps, see <link>.


== Generalizations to non-mos scales ==
== Generalizations to non-mos scales ==
Line 429: Line 530:
The terminology for intervals and scale degrees can be applied to scales with arbitrary equivalence intervals, replacing the term ''octave'' with the term ''equave''.
The terminology for intervals and scale degrees can be applied to scales with arbitrary equivalence intervals, replacing the term ''octave'' with the term ''equave''.


The mos names provided in the previous section ''do not apply'' for non-octave mos patterns, unless the equave in question is seen as a tempered octave.
The mos names provided for step counts 6-10 ''do not apply'' for non-octave mos patterns, unless the equave in question is seen as a tempered octave.


=== Intervals for MV3 scales ===
=== Intervals for MV3 scales ===
Line 444: Line 545:
Zero-indexed interval and degrees can be used for arbitrary scales. However, instead of using the terms ''k-mosstep'' and ''k-mosdegree'', the terms ''k-scalestep'' and ''k-scaledegree'' are used. As with octave-equivalent mosses, these terms can be further shortened to ''k-step'' and ''k-degree'', if context allows.
Zero-indexed interval and degrees can be used for arbitrary scales. However, instead of using the terms ''k-mosstep'' and ''k-mosdegree'', the terms ''k-scalestep'' and ''k-scaledegree'' are used. As with octave-equivalent mosses, these terms can be further shortened to ''k-step'' and ''k-degree'', if context allows.


==Appendix==
==Frequently asked questions==
'''Do I need to use this system over temperament names?'''
 
'''Why are intervals zero-indexed?'''
 
'''What's the difference between mosdegrees and mosintervals?'''
 
===Reasoning for step ratio names===
===Reasoning for step ratio names===
{{Main|TAMNAMS/Appendix#Reasoning for step ratio names}}
{{Main|TAMNAMS/Appendix#Reasoning for step ratio names}}
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/TAMNAMS"