Meantone: Difference between revisions

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== Tunings ==

Common meantone tunings can be classified into [[eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, norm-based tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. ~~Prime~~-~~optimized~~ tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.

Common meantone tunings can be classified into [[eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, norm-based tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Norm-based tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.

; Notable eigenmonzo (unchanged-interval) tunings

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* 5-limit [[DKW theory|DKW]]: ~2 = 1200.000{{c}}, ~3/2 = 696.353{{c}}

=== ~~Prime~~-~~optimized~~ tunings ===

=== Norm-based tunings ===

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

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

@@ Line 196: / Line 196: @@
 == Tunings ==
-Common meantone tunings can be classified into [[eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, norm-based tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Prime-optimized tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.
+Common meantone tunings can be classified into [[eigenmonzo|eigenmonzo (unchanged-interval)]] tunings, edo tunings, norm-based tunings and others. In eigenmonzo tunings such as the [[quarter-comma meantone]], a certain interval is tuned pure and certain others are equally off. Edo tunings like [[31edo]] have rational size relationship between steps, and happen to send an additional comma to unison. Norm-based tunings are optimized for all intervals. For a more complete list, see the table below. These different tunings are referred to as "temperaments" in traditional terms.
 ; Notable eigenmonzo (unchanged-interval) tunings
@@ Line 215: / Line 215: @@
 * 5-limit [[DKW theory|DKW]]: ~2 = 1200.000{{c}}, ~3/2 = 696.353{{c}}
-=== Prime-optimized tunings ===
+=== Norm-based tunings ===
 {| class="wikitable mw-collapsible mw-collapsed"
 |+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings