Ed5/2: Difference between revisions
m Recategorize; misc. cleanup |
m →Individual pages for ed5/2's: Expand table to match similar ETs with similar numbers of pages |
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== Individual pages for ed5/2's == | == Individual pages for ed5/2's == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ style=white-space:nowrap | | |+ style=white-space:nowrap | 0…99 | ||
| [[0ed5/2|0]] | | [[0ed5/2|0]] | ||
| [[1ed5/2|1]] | | [[1ed5/2|1]] | ||
| Line 41: | Line 42: | ||
| [[26ed5/2|26]] | | [[26ed5/2|26]] | ||
| [[27ed5/2|27]] | | [[27ed5/2|27]] | ||
| [[28ed5/|28]] | | [[28ed5/2|28]] | ||
| [[29ed5/2|29]] | | [[29ed5/2|29]] | ||
|- | |- | ||
| Line 65: | Line 66: | ||
| [[48ed5/2|48]] | | [[48ed5/2|48]] | ||
| [[49ed5/2|49]] | | [[49ed5/2|49]] | ||
|- | |||
| [[50ed5/2|50]] | |||
| [[51ed5/2|51]] | |||
| [[52ed5/2|52]] | |||
| [[53ed5/2|53]] | |||
| [[54ed5/2|54]] | |||
| [[55ed5/2|55]] | |||
| [[56ed5/2|56]] | |||
| [[57ed5/2|57]] | |||
| [[58ed5/2|58]] | |||
| [[59ed5/2|59]] | |||
|- | |||
| [[60ed5/2|60]] | |||
| [[61ed5/2|61]] | |||
| [[62ed5/2|62]] | |||
| [[63ed5/2|63]] | |||
| [[64ed5/2|64]] | |||
| [[65ed5/2|65]] | |||
| [[66ed5/2|66]] | |||
| [[67ed5/2|67]] | |||
| [[68ed5/2|68]] | |||
| [[69ed5/2|69]] | |||
|- | |||
| [[70ed5/2|70]] | |||
| [[71ed5/2|71]] | |||
| [[72ed5/2|72]] | |||
| [[73ed5/2|73]] | |||
| [[74ed5/2|74]] | |||
| [[75ed5/2|75]] | |||
| [[76ed5/2|76]] | |||
| [[77ed5/2|77]] | |||
| [[78ed5/2|78]] | |||
| [[79ed5/2|79]] | |||
|- | |||
| [[80ed5/2|80]] | |||
| [[81ed5/2|81]] | |||
| [[82ed5/2|82]] | |||
| [[83ed5/2|83]] | |||
| [[84ed5/2|84]] | |||
| [[85ed5/2|85]] | |||
| [[86ed5/2|86]] | |||
| [[87ed5/2|87]] | |||
| [[88ed5/2|88]] | |||
| [[89ed5/2|89]] | |||
|- | |||
| [[90ed5/2|90]] | |||
| [[91ed5/2|91]] | |||
| [[92ed5/2|92]] | |||
| [[93ed5/2|93]] | |||
| [[94ed5/2|94]] | |||
| [[95ed5/2|95]] | |||
| [[96ed5/2|96]] | |||
| [[97ed5/2|97]] | |||
| [[98ed5/2|98]] | |||
| [[99ed5/2|99]] | |||
|} | |} | ||
Revision as of 02:16, 1 October 2024
The equal division of 5/2 (ed5/2) is a tuning obtained by dividing the classic major tenth (5/2) in a certain number of equal steps.
Properties
Division of 5/2 into equal parts does not necessarily imply directly using this interval as an equivalence. The question of equivalence has not even been posed yet. The utility of 5/2, (or another tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, 5/2 being the best option for “no-threes” harmony excluding the octave. Many, though not all, of these scales have a perceptually important false octave, with various degrees of accuracy.
Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 3/2 to get to 6/5 (tempering out the comma 3125/3048). So, doing this yields 5-, 7-, and 12-note mos, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Macrodiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the mos formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.
Another option is to treat ed5/2's as "no-threes" systems (like how edts are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four 4/3 to get to 6/5, here it takes one 10/7 to get to 7/5 (tempering out the comma 50/49 in the no-threes 7-limit), producing a nonoctave version of jubilic temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.
Individual pages for ed5/2's
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| 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 |
| 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |
| 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |
| 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 |
| 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |
| 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |