Xenharmonic Wiki

User:Eufalesio/Fifth scale tree: Difference between revisions

← Older edit
VisualWikitext
Eufalesio (talk | contribs)
autopatrolled
629 edits
mNo edit summary
Eufalesio (talk | contribs)
autopatrolled
629 edits
Some changes
 
Line 25: Line 25:
! 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
! L:s describes
! L:s describes
! Notes on mappings
|-
|-
| self
| self
| '''[[5L 2s]]'''
| '''[[5L 2s]]'''
|5-7
|34.285
| '''diatonic'''
| '''diatonic'''
| 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>'''
| A1:m2
| A1:m2
| 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]]
|7-12
|14.285
| m-chromatic
| m-chromatic
| m2:A1
| m2:A1
Line 47: Line 54:
| rowspan="4" | granddaughter
| rowspan="4" | granddaughter
| [[5L 12s]]
| [[5L 12s]]
|5-17
|14.117
| s-enharmonic
| s-enharmonic
| d-2:m2
| d-2:m2
| rowspan="2" | dd3 is the chroma, the ''gothic'' [[17-comma]].
Inverted in s-enharmonic (dd-3).
|-
|-
| '''[[12L 5s]]'''
| '''[[12L 5s]]'''
|12-17
|5.882
| '''p-enharmonic'''
| '''p-enharmonic'''
| m2:d-2
| m2:d-2
|-
|-
| 12L 7s
| 12L 7s
|12-19
|5.263
| m-enharmonic
| m-enharmonic
| m2:d2
| m2:d2
| rowspan="2" | dd-2 is the chroma, the meantone kleisma.
Inverted in f-enharmonic (dd2).
|-
|-
| 7L 12s
| 7L 12s
|7-19
|9.022
| f-enharmonic
| f-enharmonic
| d2:m2
| d2:m2
Line 68: Line 79:
| rowspan="2" | 3rd-descendant
| rowspan="2" | 3rd-descendant
| '''12L 17s'''
| '''12L 17s'''
|12-29
|3.448
| '''pythagotonic'''
| '''pythagotonic'''
| dd3:d-2
| dd3:d-2
| rowspan="2" | 4d4 is the chroma, the ''mystery'' [[29-comma]].
Inverted in gothitonic (4d-4).
|-
|-
| 17L 12s
| 17L 12s
|17-29
|2.434
| gothitonic
| gothitonic
| d-2:dd3
| d-2:dd3
Line 79: Line 92:
| rowspan="2" | 4th-descendant
| rowspan="2" | 4th-descendant
| 12L 29s
| 12L 29s
|12-41
|2.439
| '''pythamystonic'''
| '''pythamystonic'''
| 4d4:d-2
| 4d4:d-2
| rowspan="2" | 6d5 is the chroma, the ''countercomp'' [[41-comma]].
Inverted in countermystonic (6d-5).
|-
|-
| 29L 12s
| 29L 12s
|29-41
|1.009
| ''countermystonic''
| ''countermystonic''
| d-2:4d4
| d-2:4d4
Line 90: Line 105:
| rowspan="2" | 5th-descendant
| rowspan="2" | 5th-descendant
| '''41L 12s'''
| '''41L 12s'''
|41-53
|0.552
| '''<u>pythomerc</u>'''
| '''<u>pythomerc</u>'''
| d-2:6d5
| d-2:6d5
| rowspan="2" | 7d-6 is the chroma, the ''mercator'' [[53-comma]].
Inverted in comptomerc (7d6).
|-
|-
| 12L 41s
| 12L 41s
|12-53
|1.886
| ''comptomerc''
| ''comptomerc''
| 6d5:d-2
| 6d5:d-2
Line 101: Line 118:
| rowspan="4" | 6th-descendant
| rowspan="4" | 6th-descendant
| 41L 53s
| 41L 53s
|41-94
|0.311
| ''garytonic''
| ''garytonic''
| 7d-6:6d5
| 7d-6:6d5
| rowspan="2" | 13d10 is the chroma, the [[94-comma]].
Inverted in garytonic (13d-10).
|-
|-
| '''53L 41s'''
| '''53L 41s'''
|53-94
|0.240
| '''''acupyth'''''
| '''''acupyth'''''
| 6d5:7d-6
| 6d5:7d-6
|-
|-
| 53L 12s
| 53L 12s
|53-65
|0.348
| ''pontiacitonic''
| ''pontiacitonic''
| d-2:7d6
| d-2:7d6
| rowspan="2" | The chroma is 9d-7, the [[65-comma|65-comma.]]
Inverted in comptograckle (9d7).
|-
|-
| 12L 53s
| 12L 53s
|12-65
|1.538
| ''comptograckle''
| ''comptograckle''
| 7d6:d-2
| 7d6:d-2
|-
|-
| <small>.<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>
|53-147
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'''''
| 36d25:7d-6
| 36d25:7d-6
Line 133: Line 159:
| 11th-descendant
| 11th-descendant
| '''306L 53s'''
| '''306L 53s'''
| '''''<small>m-chro qiantonic</small>'''''
|306-359
|
| '''''m-chro qiantonic'''''
| 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>'''''
| 51d-35:43d30
| 51d-35:43d30
Line 148: Line 177:
!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
!L:s describes
!L:s describes
!Notes on mappings
|-
|-
| rowspan="2" |3rd-descendant  
| rowspan="2" |3rd-descendant  
(m-enharmonic)
(m-enharmonic)
|19L 12s
|19L 12s
|19-31
|
|''aurotonic''
|''aurotonic''
|d2:dd-2
|d2:dd-2
| rowspan="2" |4d3 is the chroma, the 31-comma. Reversed in comptomean (4d-3).
|-
|-
|12L 19s
|12L 19s
|12-31
|
|''meancomptonic''
|''meancomptonic''
|dd-2:d2
|dd-2:d2
Line 166: Line 201:
(s-enharmonic)
(s-enharmonic)
|5L 17s
|5L 17s
|5-22
|
|reinhardic
|reinhardic
|dd-3:d-2
|dd-3:d-2
| rowspan="2" |3d-4 is the chroma, the 22-comma. Reversed in protofractalic (3d4).
|-
|-
|17L 5s
|17L 5s
|17-22
|
|protofractalic
|protofractalic
|d-2:dd-3
|d-2:dd-3
Line 177: Line 215:
(''aurotonic'')
(''aurotonic'')
|31L 19s
|31L 19s
|31-50
|
|''ultimeantonic''
|''ultimeantonic''
|dd-2:4d3
|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. See [[User:Eufalesio/TAMNAMS Extensions]] for more info.
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.
Retrieved from "https://en.xen.wiki/w/User:Eufalesio/Fifth_scale_tree"