Xenharmonic Wiki

Whitewood: Difference between revisions

← Older edit
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,767 edits
→Tunings: melodic consideration
Wording & misc. additions
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{interwiki
{{Interwiki
| en = Whitewood
| de = Whitewood
| de = Whitewood
| en = Whitewood
}}
}}{{Infobox regtemp
{{Infobox regtemp
| Title = Whitewood
| Title = Whitewood
| Subgroups = 2.3.5, 2.3.5.7
| Subgroups = 2.3.5, 2.3.5.7
Line 19: Line 20:
'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], and every interval on the chain of fifths is [[neutral (interval quality)|neutral]] in quality. The whitewood temperament adds prime [[5/1|5]] as an independent [[generator]], adding subchromatically inflected intervals (notated with ups and downs below) on either side of the neutral ones.
'''Whitewood''' is the [[rank-2 temperament]] tempering out [[2187/2048]], the Pythagorean chromatic semitone. As a result, the [[circle of fifths]] is the same as that of [[7edo]], and every interval on the chain of fifths is [[neutral (interval quality)|neutral]] in quality. The whitewood temperament adds prime [[5/1|5]] as an independent [[generator]], adding subchromatically inflected intervals (notated with ups and downs below) on either side of the neutral ones.


The canonical [[extension]] to prime [[7/1|7]] adds [[36/35]] to the commas, thus equating [[5-limit]] major and minor intervals with [[7-limit]] subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.
The canonical [[extension]] to the [[7-limit]] adds [[36/35]] to the commas, thus equating classical major and minor intervals with septimal subminor and supermajor ones. It finds [[7/4]] at the down seventh, [[7/6]] at the down third, and [[9/7]] at the up third.


Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group | ''7&14 temperament - 14 out of 35'']</ref>  
Whitewood was named by [[Mike Battaglia]] in 2010 to serve in contrast with the [[blackwood]] temperament, which tempers out 256/243, the [[Pythagorean limma]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95296.html Yahoo! Tuning Group | ''7&14 temperament - 14 out of 35'']</ref> The [[2.3.7 subgroup|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.


For technical data, see [[Whitewood family #Whitewood]].
For technical data, see [[Whitewood family #Whitewood]] and [[No-fives subgroup temperaments #Purpleheart]].  


== Intervals ==
== Intervals ==
Line 63: Line 64:
| 32/27, 81/64, 128/105
| 32/27, 81/64, 128/105
| 392.7
| 392.7
| '''5/4'''
| '''5/4''', 9/7
|-
|-
| 3
| 3
Line 185: Line 186:
! Comments
! Comments
|-
|-
| '''2\7'''
| '''[[7edo|2\7]]'''
|  
|  
| '''342.857'''
| '''342.857'''
| '''Lower bound of 5-odd-limit diamond monotone'''
| '''Lower bound of 5-odd-limit [[diamond monotone]]'''
|-
|-
|  
|  
| 9/5
| [[9/5]]
| 353.832
| 353.832
|  
|  
|-
|-
|  
|  
| 6/5
| [[6/5]]
| 370.073
| 370.073
|  
|  
|-
|-
| 11\35
| [[35edo|11\35]]
|  
|  
| 377.143
| 377.143
| 35d val
| 35d [[val]]
|-
|-
|  
|  
| 25/24
| [[25/24]]
| 378.193
| 378.193
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
| '''9\28'''
| '''[[28edo|9\28]]'''
|  
|  
| '''385.714'''
| '''385.714'''
Line 216: Line 217:
|-
|-
|  
|  
| 5/4
| [[5/4]]
| 386.314
| 386.314
| 5-limit CTE
| 5-limit CTE
|-
|-
|  
|  
| 21/20
| [[21/20]]
| 386.338
| 386.338
|  
|  
|-
|-
|  
|  
| 21/16
| [[21/16]]
| 386.362
| 386.362
|  
|  
|-
|-
| [[49edo|16\49]]
|  
|  
| 7/5
| 391.837
| 49b val
|-
|
| [[7/5]]
| 394.458
| 394.458
| 7- and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| 7\21
| [[21edo|7\21]]
|  
|  
| 400.000
| 400.000
Line 241: Line 247:
|-
|-
|  
|  
| 15/8
| [[15/8]]
| 402.554
| 402.554
|  
|  
|-
|-
|  
|  
| 15/14
| [[15/14]]
| 402.579
| 402.579
|  
|  
|-
|-
|  
|  
| 7/4
| [[7/4]]
| 402.603
| 402.603
|  
| 2.3.7-subgroup CTE
|-
|-
|  
|  
| 49/48
| [[49/48]]
| 410.723
| 410.723
|  
|  
|-
| [[35edo|12\35]]
|
| 411.429
| 35c val
|-
|-
|  
|  
| 7/6
| [[7/6]]
| 418.843
| 418.843
|  
|  
|-
|-
| '''5\14'''
| '''[[14edo|5\14]]'''
|  
|  
| '''428.571'''
| '''428.571'''
Line 271: Line 282:
|-
|-
|  
|  
| 9/7
| [[9/7]]
| 435.084
| 435.084
|  
|  
|-
|-
| '''3\7'''
| '''[[7edo|3\7]]'''
|  
|  
| '''514.286'''
| '''514.286'''
Retrieved from "https://en.xen.wiki/w/Whitewood"