Unque
Joined 18 May 2024
Spread the good word of my favorite tunings. |
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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). | 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. 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]], 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. | ||
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. | 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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=== [[36edo]] === | === [[36edo]] === | ||
I don't have too much to say regarding 36edo. It is a superset of 12edo, which provides a very accurate representation of prime 7. It is roughly the optimal tuning for [[Slendric]] temperament, as well as a good EDO representation for 2.3.7 JI scales such as [[Nicetone|Septimal Zarlino]] and [[Diasem]]. | I don't have too much to say regarding 36edo. It is a superset of 12edo, which provides a very accurate representation of prime 7. It is roughly the optimal tuning for [[Slendric]] temperament, as well as a good EDO representation for 2.3.7 JI scales such as [[Nicetone|Septimal Zarlino]] and [[Diasem]]. | ||
=== [[41edo]] === | |||
While a bit larger than the typical optimal size for practicality, physical instruments such as the [[Kite Guitar]] have made 41edo significantly more accessible than it may seem at first. | |||
In terms of tone organization, 41edo is extremely accurate and efficient. The first fifteen harmonics are practically indistinguishable from JI (potentially excluding 13), and the edostep acts as an all-purpose formal comma, representing [[100/99|S10]]~[[81/80|S9]]~[[78/77]]~[[66/65]]~[[64/63|S8]]~[[49/48|S7]]~[[45/44]]. Additionally, 41edo is the unique intersection of [[Magic]], [[Sensamagic]], and [[Pentacircle]], all extremely intuitive relationships that make it a perfect choice for composers who want to access strong low-complexity JI-like sound while retaining all the benefits of an equal temperament sequence. | |||
Additionally, and perhaps more convincingly for practical composers, 41edo maps the perfect fifth to 24 steps. Just like with the perfect fourth of 29edo, this highly divisible interval allows for many useful melodic structures, including (but not limited to) [[Rastmic clan|Neutral]], [[Slendric]], [[Tetracot]], and [[Miracle]]. | |||
== Music == | == Music == | ||
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* Methane Lamentation (31-EDO): https://youtu.be/CBmYRoej2yQ | * Methane Lamentation (31-EDO): https://youtu.be/CBmYRoej2yQ | ||
* Autumn (27-EDO): https://youtu.be/dcQe6ebpGFU | * Autumn (27-EDO): https://youtu.be/dcQe6ebpGFU | ||
* Winter (37-EDO): https:// | * Winter (37-EDO): [https://youtu.be/rE9L56yZ1Kw?si=K9LGwj_VsbbAJn3H https://youtu.be/rE9L56yZ1Kw] | ||
== Main Space Contributions == | == Main Space Contributions == | ||