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{{Editable user page}}
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{{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 EiC ('''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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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 ===
=== MOS-based adjectives ===
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 names like ''diatonoid'' ''3/2'', ''sephirothish 5/4'' or ''p-chro machinish 7/4'' may be used, as they are also explicit in their ranges. If the MOS name ends in -ic, substitute by -oid (pentic -> pentoid). If the MOS name doesn't end in -ic or -oid, add -oid (lime -> limoid). If the MOS ends in -oid, recover original ending and add -ish, unless it ends in -us, in which case substitute. (sephiroid -> sephiroth -> sephirothish, dicoid -> dicot -> dicotish, helenoid -> helenus -> helenish).


=== MOS-based adjectives ===
MOS-based names like ''diatonoid'' ''3/2'', ''sephirothish 5/4'' or ''p-chro machinish 7/4'' may be used, as they are also explicit in their ranges. If the MOS name ends in -ic, substitute by -oid (pentic -> pentoid). If the MOS name doesn't end in -ic or -oid, add -oid (lime -> limoid). If the MOS ends in -oid, recover original ending and add -ish, unless it ends in -us, in which case substitute. (sephiroid -> sephiroth -> sephirothish, dicoid -> dicot -> dicotish, helenoid -> helenus -> helenish)
{| class="wikitable"
{| class="wikitable"
|+
|+
!Diatonic
! Diatonic<br>relationship
relationship
! Scale<br>Signature
!Scale
!Fifth ranges
Signature
in edos
!TAMNAMS
!Fifth ranges
based name
in cents
!EiE (3/2)
! TAMNAMS<br>based name
!L:s describes
! L:s describes
!Notes on mappings
|-
| self
| '''[[5L 2s]]'''
|5-7
|34.285
| '''diatonic'''
| M2:m2
|-
| rowspan="2" | daughter
| '''[[5L 7s]]'''
|5-12
|20.000
| '''<u>p-chromatic</u>'''
| A1:m2
|-
| [[7L 5s]]
|7-12
|14.285
| m-chromatic
| m2:A1
|-
| rowspan="4" | granddaughter
| [[5L 12s]]
|5-17
|14.117
| s-enharmonic
| d-2:m2
|-
| '''[[12L 5s]]'''
|12-17
|5.882
| '''p-enharmonic'''
| m2:d-2
|-
| 12L 7s
|12-19
|5.263
| m-enharmonic
| m2:d2
|-
|-
|self
| 7L 12s
|'''5L 2s'''
|7-19
|'''diatonic'''
|9.022
|5i7
| f-enharmonic
|M2:m2
| d2:m2
|M2 and m2 are the major and minor seconds,
A1 is the chroma, the apotome.
|-
|-
| rowspan="2" |daughter
| rowspan="2" | 3rd-descendant
|'''5L 7s'''
| '''12L 17s'''
|'''<u>p-chromatic</u>'''
|12-29
|5i12
|3.448
|A1:m2
| '''pythagotonic'''
| rowspan="2" |d-2 is the chroma, the pythagorean comma.
| dd3:d-2
|-
|-
|7L 5s
| 17L 12s
|m-chromatic
|17-29
|12i7
|2.434
|m2:A1
| gothitonic
| d-2:dd3
|-
|-
| rowspan="4" |granddaughter
| rowspan="2" | 4th-descendant
|5L 12s
| 12L 29s
|s-enharmonic
|12-41
|5i17
|2.439
|d-2:m2
| '''pythamystonic'''
| rowspan="2" |dd3 is the chroma, the ''gothic'' [[17-comma]].
| 4d4:d-2
|-
|-
|'''12L 5s'''
| 29L 12s
|'''p-enharmonic'''
|29-41
|17i12
|1.009
|m2:d-2
| ''countermystonic''
| d-2:4d4
|-
|-
|12L 7s
| rowspan="2" | 5th-descendant
|m-enharmonic
| '''41L 12s'''
|12i19
|41-53
|m2:d2
|0.552
| rowspan="2" |d2 is the meantone diesis; dd-2 is the chroma,
| '''<u>pythomerc</u>'''
the meantone kleisma.
| d-2:6d5
|-
|-
|7L 12s
| 12L 41s
|f-enharmonic
|12-53
|19i7
|1.886
|d2:m2
| ''comptomerc''
| 6d5:d-2
|-
|-
| rowspan="2" |3rd-descendant
| rowspan="4" | 6th-descendant
|'''12L 17s'''
| 41L 53s
|'''pythagotonic'''
|41-94
|29i12
|0.311
|dd3:d-2
| ''garytonic''
| rowspan="2" |4d4 is the chroma, the ''mystery'' [[29-comma]].
| 7d-6:6d5
|-
|-
|17L 12s
| '''53L 41s'''
|gothitonic
|53-94
|29i17
|0.240
|d-2:dd3
| '''''acupyth'''''
| 6d5:7d-6
|-
|-
| rowspan="2" |4th-descendant
| 53L 12s
|12L 29s
|53-65
|'''pythamystonic'''
|0.348
|41i12
| ''pontiacitonic''
|4d4:d-2
| d-2:7d6
| rowspan="2" |6d5 is the chroma,
the ''countercomp'' [[41-comma]].
|-
|-
|29L 12s
| 12L 53s
|''countermystonic''
|12-65
|41i29
|1.538
|d-2:4d4
| ''comptograckle''
| 7d6:d-2
|-
|-
| rowspan="2" |5th-descendant
| .<br>.<br>.
|'''41L 12s'''
| '''53L 94s'''<br>'''53L 147s'''<br>'''53L 200s'''
|'''<u>pythomerc</u>'''
|53-147
|41i53
53-200
|d-2:6d5
53-253
| rowspan="2" |7d-6 is the chroma, the ''mercator'' [[53-comma]].
|
| '''''p-chro acupyth'''''<br>'''''s-enhar acupyth'''''<br>'''''uha-acupyth'''''
| 13d10:7d-6<br>21d15:7d-6<br>28d20:7d-6
|-
|-
|12L 41s
| 10th-descendant
|''comptomerc''
| '''53L 253s'''
|53i12
|53-306
|6d5:d-2
|
| '''''qiantonic'''''
| 36d25:7d-6
|-
|-
| rowspan="4" |6th-descendant
| 11th-descendant
|41L 53s
| '''306L 53s'''
|''garytonic''
|306-359
|41i94
|
|7d-6:6d5
| '''''m-chro qiantonic'''''
| rowspan="2" |13d10 is the chroma, the [[94-comma]].
| 7d-6:43d30
|-
|-
|'''53L 41s'''
| 12th-descendant
|'''''acupyth'''''
| '''306L 359s'''
|94i53
|306-665
|6d5:7d-6
|
| '''''<u>picopyth</u>'''''
| 51d-35:43d30
|}
 
Some notable MOS scales that diverge from the pythagorean line are:
 
{| class="wikitable"
!Diatonic<br>relationship
!Scale<br>Signature
!Fifth ranges
in edos
!Fifth ranges
in cents
!TAMNAMS<br>based name
!L:s describes
|-
|-
|53L 12s
| rowspan="2" |3rd-descendant
|''pontiacitonic''
(m-enharmonic)
|53i65
|19L 12s
|d-2:7d6
|19-31
| rowspan="2" |7d6 is the inverse mercator comma.
|
The chroma is 9d-7, the [[65-comma|65-comma.]]
|''aurotonic''
|d2:dd-2
|-
|-
|12L 53s
|12L 19s
|''comptograc''
|12-31
|65i12
|
|7d6:d-2
|''meancomptonic''
|dd-2:d2
|-
|-
|.
| rowspan="2" |3rd-descendant
.
(s-enharmonic)
.
|5L 17s
|'''53L 94s'''
|5-22
'''53L 147s'''
|
'''53L 200s'''
|reinhardic
|'''''p-chro acupyth'''''
|dd-3:d-2
'''''s-enhar acupyth'''''
'''''uha acupyth'''''
|147i53
200i53
253i53
|13d10:7d-6
21d15:7d-6
28d20:7d-6
| rowspan="2" |Large steps are semiconvergent commas.
|-
|-
|10th-descendant
|17L 5s
|'''53L 253s'''
|17-22
|'''''qiantonic'''''
|
|306i53
|protofractalic
|36d25:7d-6
|d-2:dd-3
|-
|-
|11th-descendant
|4th-descendant
|'''306L 53s'''
(''aurotonic'')
|'''''m-chro qiantonic'''''
|31L 19s
|359i306
|31-50
|7d-6:43d30
|
| rowspan="2" |51d-35 and 43d30 are the [[359-comma|large]] and [[306-comma|small]]
|''ultimeantonic''
Qian commas respectively.
|dd-2:4d3
The chroma is the [[satanic comma]].
|-
|-
|12th-descendant
|
|'''306L 359s'''
|'''picopyth'''
|306i665
|51d-35:43d30
|}
|}
The names of the MOSes are coined as follows:


* 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 Qian, the man 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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