Whitewood: Difference between revisions

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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 major seconds and minor thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning 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.

=== ~~Target~~ tunings ===

=== Norm-based tunings ===

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings

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 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 major seconds and minor thirds are equated, and every interval is either a 7edo interval or halfway between two 7edo intervals. While the 14edo tuning 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.
-=== Target tunings ===
+=== Norm-based tunings ===
 {| class="wikitable mw-collapsible mw-collapsed"
 |+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings