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The '''equal division of 9/5''' ('''ed9/5''') is a [[tuning]] obtained by dividing the [[9/5|classic minor seventh (9/5)]] in a certain number of [[equal]] steps. | |||
== Properties == | == Properties == | ||
Division of | Division of 9/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed9/5 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | ||
The structural importance of 9/5 is suggested by its being the most common width for a [[tetrad]] in Western harmony, though it could be argued that this distinction belongs instead to [[7/4]] or [[16/9]] depending how one converts [[12edo|10\12]] into [[JI]]. | |||
One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 ([[tempering out]] the comma [[2430/2401]]). So, doing this yields 5-, 7-, and 12-note [[mos scale]]s, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. [[Joseph Ruhf]] proposed the term "microdiatonic"{{idiosyncratic}} for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed. | |||
However, a just or very slightly flat 9/5 leads to the just 7/5 [[generator]] converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the [[harmonic entropy]] of a [[pelogic]] temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 [[cents]] of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously. | |||
[[Category: | == Individual pages for ed9/5's == | ||
{| class="wikitable center-all" | |||
|+ style=white-space:nowrap | 0…99 | |||
| [[0ed9/5|0]] | |||
| [[1ed9/5|1]] | |||
| [[2ed9/5|2]] | |||
| [[3ed9/5|3]] | |||
| [[4ed9/5|4]] | |||
| [[5ed9/5|5]] | |||
| [[6ed9/5|6]] | |||
| [[7ed9/5|7]] | |||
| [[8ed9/5|8]] | |||
| [[9ed9/5|9]] | |||
|- | |||
| [[10ed9/5|10]] | |||
| [[11ed9/5|11]] | |||
| [[12ed9/5|12]] | |||
| [[13ed9/5|13]] | |||
| [[14ed9/5|14]] | |||
| [[15ed9/5|15]] | |||
| [[16ed9/5|16]] | |||
| [[17ed9/5|17]] | |||
| [[18ed9/5|18]] | |||
| [[19ed9/5|19]] | |||
|- | |||
| [[20ed9/5|20]] | |||
| [[21ed9/5|21]] | |||
| [[22ed9/5|22]] | |||
| [[23ed9/5|23]] | |||
| [[24ed9/5|24]] | |||
| [[25ed9/5|25]] | |||
| [[26ed9/5|26]] | |||
| [[27ed9/5|27]] | |||
| [[28ed9/5|28]] | |||
| [[29ed9/5|29]] | |||
|- | |||
| [[30ed9/5|30]] | |||
| [[31ed9/5|31]] | |||
| [[32ed9/5|32]] | |||
| [[33ed9/5|33]] | |||
| [[34ed9/5|34]] | |||
| [[35ed9/5|35]] | |||
| [[36ed9/5|36]] | |||
| [[37ed9/5|37]] | |||
| [[38ed9/5|38]] | |||
| [[39ed9/5|39]] | |||
|- | |||
| [[40ed9/5|40]] | |||
| [[41ed9/5|41]] | |||
| [[42ed9/5|42]] | |||
| [[43ed9/5|43]] | |||
| [[44ed9/5|44]] | |||
| [[45ed9/5|45]] | |||
| [[46ed9/5|46]] | |||
| [[47ed9/5|47]] | |||
| [[48ed9/5|48]] | |||
| [[49ed9/5|49]] | |||
|} | |||
[[Category:Ed9/5's| ]] <!-- main article --> | |||
[[Category:Lists of scales]] | |||
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The equal division of 9/5 (ed9/5) is a tuning obtained by dividing the classic minor seventh (9/5) in a certain number of equal steps.
Properties
Division of 9/5 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed9/5 scales have a perceptually important false octave, with various degrees of accuracy.
The structural importance of 9/5 is suggested by its being the most common width for a tetrad in Western harmony, though it could be argued that this distinction belongs instead to 7/4 or 16/9 depending how one converts 10\12 into JI.
One approach to some ed9/5 tunings is the use of the 5:6:7:(9) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 7/5 to get to 6/5 (tempering out the comma 2430/2401). So, doing this yields 5-, 7-, and 12-note mos scales, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. Joseph Ruhf proposed the term "microdiatonic"[idiosyncratic term] for this because it uses a scheme that turns out exactly identical to meantone, though severely compressed.
However, a just or very slightly flat 9/5 leads to the just 7/5 generator converging to a scale where the '6/5' and '7/6' are only ~3.6 cents off of half a generator in opposite directions, which is acceptable with the harmonic entropy of a pelogic temperament, but this temperament is not intended to be understood as pelogic. It is rather intended to be understood as meantone, albeit severely compressed, but in theory still has plus or minus ~36.85 cents of harmonic entropy for '7/6' and '6/5', though in potential practice no more than ~36% of this should ever be used very seriously.
Individual pages for ed9/5's
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
| 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
| 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |