Ed5/2: Difference between revisions
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''' | The '''equal division of 5/2''' ('''ed5/2''') is a [[tuning]] obtained by dividing the [[5/2|classic major tenth (5/2)]] in a certain number of [[equal]] steps. | ||
== Properties == | == Properties == | ||
Division of 5/2 into equal parts | 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 | 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 and microdiatonic scales|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 ED5/2s as "no-threes" systems (like how [[EDT]]s 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 | Another option is to treat ED5/2s as "no-threes" systems (like how [[EDT]]s 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 | == Individual pages for ed5/2's == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ style=white-space:nowrap | 0…49 | |+ style=white-space:nowrap | 0…49 | ||
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| [[49ed5/2|49]] | | [[49ed5/2|49]] | ||
|} | |} | ||
[[Category:Ed5/2| ]] <!-- main article --> | [[Category:Ed5/2| ]] <!-- main article --> | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
Revision as of 16:15, 18 May 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 ED5/2s 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 |