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===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.
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|}
|}


=== Interval arithmetic ===
=== Intervals smaller than a chroma ===
A discussion on how to perform interval arithmetic can be found at <link>.
{| 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 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.
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|-
|-
|[[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.
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|[[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
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|[[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
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|[[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
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|[[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
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!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]].
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|-
|-
!Pattern!!Name!!Prefix!!Abbr.
!Pattern!!Name!!Prefix!!Abbr.
!Must be octave-equivalent?!!Etymology
!Must be 2/1-equivalent?!!Etymology
|-
|-
| rowspan="2" |[[1L 1s]]|| trivial|| triv-||trv
| rowspan="2" |[[1L 1s]]|| trivial|| triv-||tw
|No||The simplest valid mos pattern.
|No||The simplest valid mos pattern.
|-
|-
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|-
|-
!Pattern!!Name!! Prefix!!Abbr.
!Pattern!!Name!! Prefix!!Abbr.
!Must be octave-equivalent?!! Etymology
!Must be 2/1-equivalent?!! Etymology
|-
|-
|[[1L 2s]]||antrial|| atri-||atri
|[[1L 2s]]||antrial|| atri-||at
|No ||Opposite pattern of 2L 1s, with broader range. Shortening of ''anti-trial''.
|No ||Opposite pattern of 2L 1s, with broader range. Shortening of ''anti-trial''.
|-
|-
|[[2L 1s]]||trial||tri-||tri
|[[2L 1s]]||trial||tri-||t
|No ||From tri- for 3.
|No ||From tri- for 3.
|-
|-
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|-
|-
!Pattern!! Name!!Prefix!! Abbr.
!Pattern!! Name!!Prefix!! Abbr.
!Must be octave-equivalent?!!Etymology
!Must be 2/1-equivalent?!!Etymology
|-
|-
|[[1L 3s]]|| antetric|| atetra-||att
|[[1L 3s]]|| antetric|| atetra-||att
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|-
|-
!Pattern!!Name!!Prefix !! Abbr.
!Pattern!!Name!!Prefix !! Abbr.
!Must be octave-equivalent?!!Etymology
!Must be 2/1-equivalent?!!Etymology
|-
|-
|[[1L 4s]]||pedal||ped-||ped
|[[1L 4s]]||pedal||ped-||pd
|No ||From Latin ''ped'', for ''foot''; one big toe and four small toes.
|No ||From Latin ''ped'', for ''foot''; one big toe and four small toes.
|-
|-
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| No||Opposite pattern of 2L 3s.
| No||Opposite pattern of 2L 3s.
|-
|-
|[[4L 1s]]||manual ||manu-|| manu
|[[4L 1s]]||manual ||manu-|| mn
|No||From Latin ''manus'', for ''hand''; one thumb and four longer fingers.
|No||From Latin ''manus'', for ''hand''; one thumb and four longer fingers.
|}
|}
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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}}
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