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{{Idiosyncratic terms|Many of the MOS pattern names are only found on this page.}}
{{Idiosyncratic terms|Many of the MOS pattern names are only found on this page.}}


This article is a mostly rewritten proposal for the [[Scale tree]] article, and more specifically, the scale tree pertaining to MOS scales with [[3/2|fifths]] as generators. Note that this article is full of idiosyncratic names, taken to be proposals to be considered. Acknowledgements to [[Kite Giedraitis]] for feedback and for designing the blueprint for the EiE ('''E'''do-'''i'''nter-'''E'''do) nomenclature.
This article is a mostly rewritten proposal for the [[Scale tree]] article, and more specifically, the scale tree pertaining to MOS scales with [[3/2|fifths]] as generators. Note that this article is full of idiosyncratic names, taken to be proposals to be considered. Acknowledgements to [[Kite Giedraitis]] for feedback.


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== MOS scales and fifth ranges. ==
== MOS scales and fifth ranges. ==
A single MOS scale explicitly defines the ranges of a fifth, and describes a number of related temperaments, however, the fifth ranges can also be described with the EiE nomenclature. There are more descendants that are less notable. Also described are the MOSes generated by Pythagorean tuning in bold.
A single MOS scale explicitly defines the ranges of a fifth, and describes a number of related temperaments, however, the fifth ranges can also be described with the EiE nomenclature. There are more descendants that are less notable. Also described are the MOSes generated by Pythagorean tuning in bold.
=== EiE nomenclature ===
Blueprinted by Kite, it is written as ~R AiB; where R is any interval, A and B are patent val approximations of edos, ~R of A > ~R of B. It describes a range of approximations of R, including A and B. Here, it is used to describe ranges of ~3/2, but without implicit knowledge, R has to be declared, Such as in ~5/4 28i41 or ~7/4 26i31. This would be read as "five over four twenty eight inter forty one" and "seven over four twenty six inter thirty one".


=== MOS-based adjectives ===
=== MOS-based adjectives ===
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! Diatonic<br>relationship
! Diatonic<br>relationship
! Scale<br>Signature
! Scale<br>Signature
!Fifth ranges
in edos
!Fifth ranges
in cents
! TAMNAMS<br>based name
! TAMNAMS<br>based name
! EiE (3/2)
! L:s describes
! L:s describes
! Notes on mappings
|-
|-
| self
| self
| '''5L 2s'''
| '''[[5L 2s]]'''
|5-7
|34.285
| '''diatonic'''
| '''diatonic'''
| 5i7
| M2:m2
| M2:m2
| M2 and m2 are the major and minor seconds;<br>A1 is the chroma, the apotome.
|-
|-
| rowspan="2" | daughter
| rowspan="2" | daughter
| '''5L 7s'''
| '''[[5L 7s]]'''
|5-12
|20.000
| '''<u>p-chromatic</u>'''
| '''<u>p-chromatic</u>'''
| 5i12
| A1:m2
| A1:m2
| rowspan="2" | d-2 is the chroma, the pythagorean comma.
|-
|-
| 7L 5s
| [[7L 5s]]
|7-12
|14.285
| m-chromatic
| m-chromatic
| 12i7
| m2:A1
| m2:A1
|-
|-
| rowspan="4" | granddaughter
| rowspan="4" | granddaughter
| 5L 12s
| [[5L 12s]]
|5-17
|14.117
| s-enharmonic
| s-enharmonic
| 5i17
| d-2:m2
| d-2:m2
| rowspan="2" | dd3 is the chroma, the ''gothic'' [[17-comma]].
|-
|-
| '''12L 5s'''
| '''[[12L 5s]]'''
|12-17
|5.882
| '''p-enharmonic'''
| '''p-enharmonic'''
| 17i12
| m2:d-2
| m2:d-2
|-
|-
| 12L 7s
| 12L 7s
|12-19
|5.263
| m-enharmonic
| m-enharmonic
| 12i19
| m2:d2
| m2:d2
| rowspan="2" | d2 is the meantone diesis; dd-2 is the chroma, <br>the meantone kleisma.
|-
|-
| 7L 12s
| 7L 12s
|7-19
|9.022
| f-enharmonic
| f-enharmonic
| 19i7
| d2:m2
| d2:m2
|-
|-
| rowspan="2" | 3rd-descendant
| rowspan="2" | 3rd-descendant
| '''12L 17s'''
| '''12L 17s'''
|12-29
|3.448
| '''pythagotonic'''
| '''pythagotonic'''
| 29i12
| dd3:d-2
| dd3:d-2
| rowspan="2" | 4d4 is the chroma, the ''mystery'' [[29-comma]].
|-
|-
| 17L 12s
| 17L 12s
|17-29
|2.434
| gothitonic
| gothitonic
| 29i17
| d-2:dd3
| d-2:dd3
|-
|-
| rowspan="2" | 4th-descendant
| rowspan="2" | 4th-descendant
| 12L 29s
| 12L 29s
|12-41
|2.439
| '''pythamystonic'''
| '''pythamystonic'''
| 41i12
| 4d4:d-2
| 4d4:d-2
| rowspan="2" | 6d5 is the chroma, <br>the ''countercomp'' [[41-comma]].
|-
|-
| 29L 12s
| 29L 12s
|29-41
|1.009
| ''countermystonic''
| ''countermystonic''
| 41i29
| d-2:4d4
| d-2:4d4
|-
|-
| rowspan="2" | 5th-descendant
| rowspan="2" | 5th-descendant
| '''41L 12s'''
| '''41L 12s'''
|41-53
|0.552
| '''<u>pythomerc</u>'''
| '''<u>pythomerc</u>'''
| 41i53
| d-2:6d5
| d-2:6d5
| rowspan="2" | 7d-6 is the chroma, the ''mercator'' [[53-comma]].
|-
|-
| 12L 41s
| 12L 41s
|12-53
|1.886
| ''comptomerc''
| ''comptomerc''
| 53i12
| 6d5:d-2
| 6d5:d-2
|-
|-
| rowspan="4" | 6th-descendant
| rowspan="4" | 6th-descendant
| 41L 53s
| 41L 53s
|41-94
|0.311
| ''garytonic''
| ''garytonic''
| 41i94
| 7d-6:6d5
| 7d-6:6d5
| rowspan="2" | 13d10 is the chroma, the [[94-comma]].
|-
|-
| '''53L 41s'''
| '''53L 41s'''
|53-94
|0.240
| '''''acupyth'''''
| '''''acupyth'''''
| 94i53
| 6d5:7d-6
| 6d5:7d-6
|-
|-
| 53L 12s
| 53L 12s
|53-65
|0.348
| ''pontiacitonic''
| ''pontiacitonic''
| 53i65
| d-2:7d6
| d-2:7d6
| rowspan="2" | 7d6 is the inverse mercator comma.<br>The chroma is 9d-7, the [[65-comma|65-comma.]]
|-
|-
| 12L 53s
| 12L 53s
|12-65
|1.538
| ''comptograckle''
| ''comptograckle''
| 65i12
| 7d6:d-2
| 7d6:d-2
|-
|-
| .<br>.<br>.
| .<br>.<br>.
| '''53L 94s'''<br>'''53L 147s'''<br>'''53L 200s'''
| '''53L 94s'''<br>'''53L 147s'''<br>'''53L 200s'''
| '''''p-chro acupyth'''''<br>'''''s-enhar acupyth'''''<br>'''''uha acupyth'''''
|53-147
| 147i53<br>200i53<br>253i53
53-200
53-253
|
| '''''p-chro acupyth'''''<br>'''''s-enhar acupyth'''''<br>'''''uha-acupyth'''''
| 13d10:7d-6<br>21d15:7d-6<br>28d20:7d-6
| 13d10:7d-6<br>21d15:7d-6<br>28d20:7d-6
| rowspan="2" | Large steps are semiconvergent commas.
|-
|-
| 10th-descendant
| 10th-descendant
| '''53L 253s'''
| '''53L 253s'''
|53-306
|
| '''''qiantonic'''''
| '''''qiantonic'''''
| 306i53
| 36d25:7d-6
| 36d25:7d-6
|-
|-
| 11th-descendant
| 11th-descendant
| '''306L 53s'''
| '''306L 53s'''
|306-359
|
| '''''m-chro qiantonic'''''
| '''''m-chro qiantonic'''''
| 359i306
| 7d-6:43d30
| 7d-6:43d30
| rowspan="2" | 51d-35 and 43d30 are the [[359-comma|large]]<br>and [[306-comma|small]] Qian commas respectively.<br>The chroma is the [[satanic comma]].
|-
|-
| 12th-descendant
| 12th-descendant
| '''306L 359s'''
| '''306L 359s'''
|306-665
|
| '''''<u>picopyth</u>'''''
| '''''<u>picopyth</u>'''''
| 306i665
| 51d-35:43d30
| 51d-35:43d30
|}
|}


Bolded MOS support a pythagorean generator. Bolded and underlined names are also of a record lowest hardness when that generator is used. Italic names only appear in this article.
Some notable MOS scales that diverge from the pythagorean line are:


The names of the MOSes are coined as follows:
{| class="wikitable"
!Diatonic<br>relationship
!Scale<br>Signature
!Fifth ranges
in edos
!Fifth ranges
in cents
!TAMNAMS<br>based name
!L:s describes
|-
| rowspan="2" |3rd-descendant
(m-enharmonic)
|19L 12s
|19-31
|
|''aurotonic''
|d2:dd-2
|-
|12L 19s
|12-31
|
|''meancomptonic''
|dd-2:d2
|-
| rowspan="2" |3rd-descendant
(s-enharmonic)
|5L 17s
|5-22
|
|reinhardic
|dd-3:d-2
|-
|17L 5s
|17-22
|
|protofractalic
|d-2:dd-3
|-
|4th-descendant
(''aurotonic'')
|31L 19s
|31-50
|
|''ultimeantonic''
|dd-2:4d3
|-
|
|}


* countermystonic comes from ''[[countercomp]]'' and ''[[mystery]]'', the two temperaments that converge in this MOS.
Bolded MOS support a pythagorean generator. Bolded and underlined names are also of a record lowest hardness when that generator is used. Italic names only appear in this article. See [[User:Eufalesio/TAMNAMS Extensions]] for more info.
* comptomerc comes from ''[[compton]],'' as 12edo can also generate this MOS, albeit trivially.
* garytonic comes from [[gary]], the temperament that tempers the [[garischisma]].
* acupyth comes from ''acus'' (needle), judging by the accuracy of the fifths in this range.
* pontiacitonic comes from [[pontiac]], which generates this MOS.
* comptograckle comes from compton and [[grackle]], which can both generate this MOS.
* qiantonic comes from Qián Lèzhī, the ancient Chinese astronomer and instrument maker who discovered the 306- and 359- comma.
* picopyth comes from pico-, a SI prefix denoting 10^-12, a minute order of magnitude.
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