Whitewood: Difference between revisions

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== Tunings ==

While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – as individually a [[5-limit|2.3.5-]] or [[2.3.7 subgroup|2.3.7-subgroup]] ~~temperament~~. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.

While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – targeting individually the [[5-limit|2.3.5-]] or [[2.3.7 subgroup|2.3.7-subgroup]]. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.

Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.

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| 5/4

| 386.314

|

| 5-limit CTE

|-

|

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|

| '''514.286'''

| 7cd val, '''~~Upper~~ bound of 5-odd-limit diamond monotone'''

| 7cd val, '''upper bound of 5-odd-limit diamond monotone'''

|}

<nowiki/>* Besides the octave

@@ Line 111: / Line 111: @@
 == Tunings ==
-While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – as individually a [[5-limit|2.3.5-]] or [[2.3.7 subgroup|2.3.7-subgroup]] temperament. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.
+While blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning – targeting individually the [[5-limit|2.3.5-]] or [[2.3.7 subgroup|2.3.7-subgroup]]. Septimal whitewood entails a rather different tuning profile, as the vanishing of 36/35 means 5 and 7 should be tuned somewhat sharp.
 Any multiple of [[7edo]], up until [[35edo]], contains 7edo's [[perfect fifth]], and thus supports whitewood, with all but 35edo supporting the canonical 7-limit extension by [[patent val]]. The most extreme tuning is [[14edo]], where up seconds and down thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning poorly approximates 5-limit intervals, it does approximate the [[6:7:9]] subminor and [[14:18:21|1/(9:7:6)]] supermajor triads fairly well. A less extreme tuning is [[21edo]], tuning [[7/4]] close to just and tuning [[5/4]] to the same 400{{c}} major third as in [[12edo]], though [[6/5]] is still about 30 cents flat. The [[28edo]] tuning has a near-just 5/4, and tunes whitewood about as best as it can be tuned.
@@ Line 211: / Line 211: @@
 | 5/4
 | 386.314
-|
+| 5-limit CTE
 |-
 |
@@ Line 271: / Line 271: @@
 |
 | '''514.286'''
-| 7cd val, '''Upper bound of 5-odd-limit diamond monotone'''
+| 7cd val, '''upper bound of 5-odd-limit diamond monotone'''
 |}
 <nowiki/>* Besides the octave