User:Unque: Difference between revisions

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I strongly believe that 29edo should be alongside systems such as 19edo and 31edo as introductions to xenharmonic tunings for beginners. Not only does it represent the third harmonic within less than two cents of error (making the diatonic scale roughly equivalent to its familiar representations in western music), but it additionally contains distinct, unambiguous representations for [[interordinal]] intervals. The ability to place these unfamiliar intervals onto the familiar circle of fifths is extremely beneficial, as it allows beginners to more clearly get a feel for how these intervals can be used to create sounds unavailable in 12edo. This provides a benefit over systems such as Meantone, in that the circle of fifths requires less relearning to account for the difference in intonation compared to 12edo, and in that the interordinals represented are distinct and unambiguous (compare to 31edo, where there is no clear representation for, say, the semifourth or the semisixth).

Additionally, 29edo finds the perfect fourth at 12 steps, a highly divisible size, supporting [[Porcupine]], [[28812/28561#Tesseract|Tesseract]], ~~and~~ [[~~Unicorn~~]]. This helps provide an introduction into systems that divide simple intervals into a certain number of steps, and how those divisions can apply to writing melodies and chord progressions.

Additionally, 29edo finds the perfect fourth at 12 steps, a highly divisible size, supporting [[Porcupine]], [[28812/28561#Tesseract|Tesseract]], [[Negri]], [[Semaphore and godzilla|Semaphore]], and other similar structures. This helps provide an introduction into systems that divide simple intervals into a certain number of steps, and how those divisions can apply to writing melodies and chord progressions; see my treatise [[User:Unque/On Voice Leading|on voice leading]] for a more detailed explanation of why this is important.

Finally, for those who like microtemperaments, simple harmonics such as 5 and 7 are very easy to find in supersets such as [[58edo]] and [[87edo]], since these harmonics have a relative error very close to simple fractions. The perfect fifth of 29edo is optimal for [[parapyth]] tuning, which makes supersets of 29edo extremely desirable if one seeks an extremely high accuracy equal temperament sequence.

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 I strongly believe that 29edo should be alongside systems such as 19edo and 31edo as introductions to xenharmonic tunings for beginners.  Not only does it represent the third harmonic within less than two cents of error (making the diatonic scale roughly equivalent to its familiar representations in western music), but it additionally contains distinct, unambiguous representations for [[interordinal]] intervals.  The ability to place these unfamiliar intervals onto the familiar circle of fifths is extremely beneficial, as it allows beginners to more clearly get a feel for how these intervals can be used to create sounds unavailable in 12edo.  This provides a benefit over systems such as Meantone, in that the circle of fifths requires less relearning to account for the difference in intonation compared to 12edo, and in that the interordinals represented are distinct and unambiguous (compare to 31edo, where there is no clear representation for, say, the semifourth or the semisixth).
-Additionally, 29edo finds the perfect fourth at 12 steps, a highly divisible size, supporting [[Porcupine]], [[28812/28561#Tesseract|Tesseract]], and [[Unicorn]].  This helps provide an introduction into systems that divide simple intervals into a certain number of steps, and how those divisions can apply to writing melodies and chord progressions.
+Additionally, 29edo finds the perfect fourth at 12 steps, a highly divisible size, supporting [[Porcupine]], [[28812/28561#Tesseract|Tesseract]], [[Negri]], [[Semaphore and godzilla|Semaphore]], and other similar structures.  This helps provide an introduction into systems that divide simple intervals into a certain number of steps, and how those divisions can apply to writing melodies and chord progressions; see my treatise [[User:Unque/On Voice Leading|on voice leading]] for a more detailed explanation of why this is important.
 Finally, for those who like microtemperaments, simple harmonics such as 5 and 7 are very easy to find in supersets such as [[58edo]] and [[87edo]], since these harmonics have a relative error very close to simple fractions.  The perfect fifth of 29edo is optimal for [[parapyth]] tuning, which makes supersets of 29edo extremely desirable if one seeks an extremely high accuracy equal temperament sequence.