Meantone: Difference between revisions
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== Tunings == | == Tunings == | ||
Common meantone tunings can be classified into [[ | Common meantone tunings can be classified into [[target tuning]]s, edo tunings, prime-optimized tunings and others. In target 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. | ||
; Notable | ; Notable target tunings | ||
* [[1/2-comma meantone]] – with eigenmonzo [[10/9]] | * [[1/2-comma meantone]] – with eigenmonzo [[10/9]] | ||
* [[1/3-comma meantone]] – with eigenmonzo [[5/3]] | * [[1/3-comma meantone]] – with eigenmonzo [[5/3]] | ||
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* [[Lucy tuning]] | * [[Lucy tuning]] | ||
* Equal beating tunings | * Equal beating tunings | ||
* 5-limit [[DKW theory|DKW]]: ~2 = 1200.000{{c}}, ~3/2 = 696.353{{c}} | |||
=== Prime-optimized tunings === | === Prime-optimized tunings === | ||
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| [[9/5]] | | [[9/5]] | ||
| 691.202 | | 691.202 | ||
| '''Lower bound of 9-odd-limit diamond tradeoff'''<br | | '''Lower bound of 9-odd-limit diamond tradeoff'''<br>[[1/2-comma meantone|1/2 comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9 | ||
|- | |- | ||
| [[59edo|34\59]] | | [[59edo|34\59]] | ||
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$$ n = (g_J - g)/g_c $$ | $$ n = (g_J - g)/g_c $$ | ||
== Music == | == Music == | ||