Ed5/3: Difference between revisions
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== Properties == | == Properties == | ||
Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]] | Division of 5/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy. | ||
5/3 is the most consonant interval in between 1/1 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature. | |||
[[Joseph Ruhf]] suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note [[mos]] either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for [[edf]]s as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-[[7L 2s|armotonic]]. | |||
If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach. | If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in [[Blackcomb]] temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach. | ||
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[[Category:Ed5/3| ]] <!-- main article --> | [[Category:Ed5/3's| ]] | ||
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[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 5/3 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.}} | |||
Latest revision as of 18:40, 1 August 2025
The equal division of 5/3 (ed5/3) is a tuning obtained by dividing the just major sixth (5/3) into a number of equal steps.
Properties
Division of 5/3 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed5/3 scales have a perceptually important false octave, with various degrees of accuracy.
5/3 is the most consonant interval in between 1/1 and 2/1, so this suggests it could be useful either as an equivalence, or as just an important structural feature.
Joseph Ruhf suggested the use of the 6:7:8:(10) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone as a way to evoke 5/3-equivalence. Though it could also be used just as a useful sonority, even without equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224). So, doing this yields 7-, 9-, and 16-note mos either way, the 16-note mos being 7L 9s. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic mos) though it is, technically speaking, micro-armotonic.
If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, resulting in Blackcomb temperament that tempers out the comma 250/243. This yields mos scales of 4, 5, 6, 11, 16, and 21 notes. Although, it should be noted that doing this will often create a pseudo-octave unlike the 6:7:8 approach.
ED5/3 tuning systems that accurately represent the intervals 5/4 and 4/3 include: 7ed5/3 (7.30 cent error), 9ed5/3 (6.73 cent error), and 16ed5/3 (0.59 cent error).
7ed5/3, 9ed5/3, and 16ed5/3 are to the division of 5/3 what 5edo, 7edo, and 12edo are to the division of 2/1.
Individual pages for ed5/3'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 |
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Todo: cleanup , explain edonoi Most people do not think 5/3 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. |