Ed8/3: Difference between revisions
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The '''equal division of 8/3''' ('''ed8/3''') is a [[tuning]] obtained by dividing the [[8/3|Pythagorean perfect eleventh (8/3)]] in a certain number of [[equal]] steps. | The '''equal division of 8/3''' ('''ed8/3''') is a [[tuning]] obtained by dividing the [[8/3|Pythagorean perfect eleventh (8/3)]] in a certain number of [[equal]] steps. | ||
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Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | ||
The eleventh is the highest [[period]] where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the | The eleventh is the highest [[period]] where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the {{w|avoid note}} in a major modality. This matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway. | ||
One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. | One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. | ||
== Joseph Ruhf's approach == | == Joseph Ruhf's approach == | ||
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* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal | * Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal | ||
[[Category:Ed8/3| ]] <!-- main article --> | == Individual pages for ed8/3's == | ||
{| class="wikitable center-all" | |||
|+ style=white-space:nowrap | 0…49 | |||
| [[0ed8/3|0]] | |||
| [[1ed8/3|1]] | |||
| [[2ed8/3|2]] | |||
| [[3ed8/3|3]] | |||
| [[4ed8/3|4]] | |||
| [[5ed8/3|5]] | |||
| [[6ed8/3|6]] | |||
| [[7ed8/3|7]] | |||
| [[8ed8/3|8]] | |||
| [[9ed8/3|9]] | |||
|- | |||
| [[10ed8/3|10]] | |||
| [[11ed8/3|11]] | |||
| [[12ed8/3|12]] | |||
| [[13ed8/3|13]] | |||
| [[14ed8/3|14]] | |||
| [[15ed8/3|15]] | |||
| [[16ed8/3|16]] | |||
| [[17ed8/3|17]] | |||
| [[18ed8/3|18]] | |||
| [[19ed8/3|19]] | |||
|- | |||
| [[20ed8/3|20]] | |||
| [[21ed8/3|21]] | |||
| [[22ed8/3|22]] | |||
| [[23ed8/3|23]] | |||
| [[24ed8/3|24]] | |||
| [[25ed8/3|25]] | |||
| [[26ed8/3|26]] | |||
| [[27ed8/3|27]] | |||
| [[28ed8/3|28]] | |||
| [[29ed8/3|29]] | |||
|- | |||
| [[30ed8/3|30]] | |||
| [[31ed8/3|31]] | |||
| [[32ed8/3|32]] | |||
| [[33ed8/3|33]] | |||
| [[34ed8/3|34]] | |||
| [[35ed8/3|35]] | |||
| [[36ed8/3|36]] | |||
| [[37ed8/3|37]] | |||
| [[38ed8/3|38]] | |||
| [[39ed8/3|39]] | |||
|- | |||
| [[40ed8/3|40]] | |||
| [[41ed8/3|41]] | |||
| [[42ed8/3|42]] | |||
| [[43ed8/3|43]] | |||
| [[44ed8/3|44]] | |||
| [[45ed8/3|45]] | |||
| [[46ed8/3|46]] | |||
| [[47ed8/3|47]] | |||
| [[48ed8/3|48]] | |||
| [[49ed8/3|49]] | |||
|} | |||
[[Category:Ed8/3's| ]] | |||
<!-- main article --> | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
{{todo|inline=1| | {{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 8/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}} | ||