Whitewood: Difference between revisions

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'''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> The [[2.3.7 subgroup|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.

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| 32/27, 81/64, 128/105

| 392.7

| '''5/4'''

| '''5/4''', 9/7

|-

| 3

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| [[7/4]]

| 402.603

|

| 2.3.7-subgroup CTE

|-

|

@@ Line 20: / 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.
-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> The [[2.3.7 subgroup|2.3.7-subgroup]] [[restriction]] of whitewood is sometimes known as '''purpleheart'''.
@@ Line 64: / Line 64: @@
 | 32/27, 81/64, 128/105
 | 392.7
-| '''5/4'''
+| '''5/4''', 9/7
 |-
 | 3
@@ Line 259: / Line 259: @@
 | [[7/4]]
 | 402.603
-|
+| 2.3.7-subgroup CTE
 |-
 |