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User:Eufalesio/Fifth scale tree: Difference between revisions

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autopatrolled
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Divergent MOSes and other things
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|-
|-
| self
| self
| '''5L 2s'''
| '''[[5L 2s]]'''
| '''diatonic'''
| '''diatonic'''
| 5i7
| 5i7
| M2:m2
| M2:m2
| M2 and m2 are the major and minor seconds;<br>A1 is the chroma, the apotome.
| 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]]'''
| '''<u>p-chromatic</u>'''
| '''<u>p-chromatic</u>'''
| 5i12
| 5i12
| A1:m2
| A1:m2
| rowspan="2" | d-2 is the chroma, the pythagorean comma.
| rowspan="2" | d-2 is the chroma, the [[pythagorean comma]]. Inverted in m-chromatic (d2) where it is called ''meantone diesis''.
|-
|-
| 7L 5s
| [[7L 5s]]
| m-chromatic
| m-chromatic
| 12i7
| 12i7
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|-
|-
| rowspan="4" | granddaughter
| rowspan="4" | granddaughter
| 5L 12s
| [[5L 12s]]
| s-enharmonic
| s-enharmonic
| 5i17
| 5i17
| d-2:m2
| d-2:m2
| rowspan="2" | dd3 is the chroma, the ''gothic'' [[17-comma]].
| rowspan="2" | dd3 is the chroma, the ''gothic'' [[17-comma]].
Inverted in s-enharmonic (dd-3).
|-
|-
| '''12L 5s'''
| '''[[12L 5s]]'''
| '''p-enharmonic'''
| '''p-enharmonic'''
| 17i12
| 17i12
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| 12i19
| 12i19
| m2:d2
| m2:d2
| rowspan="2" | d2 is the meantone diesis; dd-2 is the chroma, <br>the meantone kleisma.
| rowspan="2" | dd-2 is the chroma, the meantone kleisma.
Inverted in f-enharmonic (dd2).
|-
|-
| 7L 12s
| 7L 12s
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| 29i12
| 29i12
| dd3:d-2
| dd3:d-2
| rowspan="2" | 4d4 is the chroma, the ''mystery'' [[29-comma]].
| rowspan="2" | 4d4 is the chroma, the ''mystery'' [[29-comma]].
Inverted in gothitonic (4d-4).
|-
|-
| 17L 12s
| 17L 12s
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| 41i12
| 41i12
| 4d4:d-2
| 4d4:d-2
| rowspan="2" | 6d5 is the chroma, <br>the ''countercomp'' [[41-comma]].
| rowspan="2" | 6d5 is the chroma, the ''countercomp'' [[41-comma]].
Inverted in countermystonic (6d-5).
|-
|-
| 29L 12s
| 29L 12s
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| d-2:6d5
| d-2:6d5
| rowspan="2" | 7d-6 is the chroma, the ''mercator'' [[53-comma]].
| rowspan="2" | 7d-6 is the chroma, the ''mercator'' [[53-comma]].
Inverted in comptomerc (7d6).
|-
|-
| 12L 41s
| 12L 41s
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| 7d-6:6d5
| 7d-6:6d5
| rowspan="2" | 13d10 is the chroma, the [[94-comma]].
| rowspan="2" | 13d10 is the chroma, the [[94-comma]].
Inverted in garytonic (13d-10).
|-
|-
| '''53L 41s'''
| '''53L 41s'''
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| 53i65
| 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.]]
| rowspan="2" | The chroma is 9d-7, the [[65-comma|65-comma.]]
Inverted in comptograckle (9d7).
|-
|-
| 12L 53s
| 12L 53s
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| 7d6:d-2
| 7d6:d-2
|-
|-
| .<br>.<br>.
| <small>.<br>.<br>.</small>
| '''53L 94s'''<br>'''53L 147s'''<br>'''53L 200s'''
| <small>'''53L 94s'''<br>'''53L 147s'''<br>'''53L 200s'''</small>
| '''''p-chro acupyth'''''<br>'''''s-enhar acupyth'''''<br>'''''uha acupyth'''''
| <small>'''''p-chro acupyth'''''<br>'''''s-enhar acupyth'''''<br>'''''uha acupyth'''''</small>
| 147i53<br>200i53<br>253i53
| 147i53<br>200i53<br>253i53
| 13d10:7d-6<br>21d15:7d-6<br>28d20:7d-6
| 13d10:7d-6<br>21d15:7d-6<br>28d20:7d-6
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| 11th-descendant
| 11th-descendant
| '''306L 53s'''
| '''306L 53s'''
| '''''m-chro qiantonic'''''
| '''''<small>m-chro qiantonic</small>'''''
| 359i306
| 359i306
| 7d-6:43d30
| 7d-6:43d30
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| 51d-35:43d30
| 51d-35:43d30
|}
|}
Some notable MOS scales that diverge from the pythagorean line are:
{| class="wikitable"
!Diatonic<br>relationship
!Scale<br>Signature
!TAMNAMS<br>based name
!EiE (3/2)
!L:s describes
!Notes on mappings
|-
| rowspan="4" |3rd-descendant
|19L 12s
|''aurotonic''
|31i19
|d2:dd-2
| rowspan="2" |4d3 is the chroma, the 31-comma. Reversed in comptomean (4d-3).
|-
|12L 19s
|''meancomptonic''
|12i31
|dd-2:d2
|-
|5L 17s
|reinhardic
|5i22
|dd-3:d-2
| rowspan="2" |3d-4 is the chroma, the 22-comma. Reversed in protofractalic (3d4).
|-
|17L 5s
|protofractalic
|22i17
|d-2:dd-3
|-
|4th-descendant
|31L 19s
|''ultimeantonic''
|50i31
|dd-2:4d3
|7d-4 is the comma, the 50-comma.
|-
|}


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.
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.
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* qiantonic comes from Qián Lèzhī, the ancient Chinese astronomer and instrument maker who discovered the 306- and 359- comma.
* 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.
* picopyth comes from pico-, a SI prefix denoting 10^-12, a minute order of magnitude.
* aurotonic comes from the [[golden meantone]], as it supports a generator of 696.214 cents.
* meancomptonic comes from compton and [[meantone]], as the ranges are between sharper meantone and compton.
* ultimeantonic comes from the fact that the basic tuning 47\81 is the last patent val fifth that supports golden meantone.
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