Unque
Joined 18 May 2024
43edo |
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While 15edo does not provide accurate representations of the harmonic series, it does provide extremely useful melodic frameworks. The [[5L 5s|Blackwood Decatonic scale]], for instance, contains several copies of [[Nicetone]] over each degree, allowing for diatonic-like chord progressions to move smoothly between keys that may seem unrelated in systems with a more accurate chain of fifths. | While 15edo does not provide accurate representations of the harmonic series, it does provide extremely useful melodic frameworks. The [[5L 5s|Blackwood Decatonic scale]], for instance, contains several copies of [[Nicetone]] over each degree, allowing for diatonic-like chord progressions to move smoothly between keys that may seem unrelated in systems with a more accurate chain of fifths. | ||
Additionally, it can be noted that if one makes an [[Delta-rational chord| | Additionally, it can be noted that if one makes an [[Delta-rational chord|isodifferential]] triad with an interval of 400c (the familiar major third from 12edo) between the bottom two pitches, this chord will have a "fifth" which very closely resembles the "fifth" of 5edo. Thus, we can assume that a tuning which contains 3edo and 5edo as subsets has a close approximation of this chord. This can be seen as an alternative way to "fix" the lack of harmonic effect in the 12edo major triad, which detunes the fifth rather than the third. | ||
=== [[30edt]] === | === [[30edt]] === | ||
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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, 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 | 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 I find this important. | ||
Finally, for those who like microtemperaments, simple harmonics such as 5 and 7 are very easy to find in supersets such as | Finally, for those who like microtemperaments, simple harmonics such as 5 and 7 are very easy to find in supersets such as [[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; additionally, 87edo supports [[Rodan]] temperament, an extremely efficient system which extends the harmonies of the chain of fifths by adding a formal chroma [[81/80|S9]]~[[64/63|S8]]~[[49/48|S7]] at (8/7) ^ 5. Rodan also contains [[Slendric]] and [[Hemifamity]] as subset parts of its structure | ||
=== [[36edo]] === | === [[36edo]] === | ||
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=== [[43edo]] === | === [[43edo]] === | ||
By the size of 43edo, even rank-2 thinking is rather difficult for conceptualizing how the system fits together. However, 43edo can very intuitively be taken as a Septimal Meantone system with 45/44~56/55~100/99 as a secondary chroma to provide access to 11-limit intervals. Because the chromatic semitone of the diatonic scale is three of these undecimal chromata, any interval in the system can be notated with no more than one accidental of each kind. | By the size of 43edo, even rank-2 thinking is rather difficult for conceptualizing how the system fits together. However, 43edo can very intuitively be taken as a Septimal Meantone system with 45/44~56/55~100/99 as a secondary chroma to provide access to 11-limit intervals. Because the chromatic semitone of the diatonic scale is three of these undecimal chromata, any interval size in the system can be notated with no more than one accidental of each kind. | ||
This threefold division of the chroma additionally allows the wholetone to be altered into a down-wholetone such that three of them make a perfect fourth instead of an augmented one; the structure | This threefold division of the chroma additionally allows the wholetone to be altered into a down-wholetone such that three of them make a perfect fourth instead of an augmented one; the structure begotten by these down-wholetones resembles [[Porcupine]] in its form, but does not contain the classical minor third. | ||
Finally, 43edo offers a rather accurate tuning of [[Bleu]], the temperament which cleaves the perfect fifth into five parts; two of these parts reaches 7/6, three reach 14/11, and four reach 11/8. | Finally, 43edo offers a rather accurate tuning of [[Bleu]], the temperament which cleaves the perfect fifth into five parts; two of these parts reaches 7/6, three reach 14/11, and four reach 11/8. | ||
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Here are some other contributions I've made to theory on my personal user space: | Here are some other contributions I've made to theory on my personal user space: | ||
* A | * A system for describing [[User:Unque/15edo-Chords|15-EDO Chords]] | ||
*[[User:Unque/Dhembrwood|Dhembrwood Temperament]] | *[[User:Unque/Dhembrwood|Dhembrwood Temperament]] | ||
*[[User:Unque/Redeye scale|Redeye Scale]] | *[[User:Unque/Redeye scale|Redeye Scale]] | ||
*[[User:Unque/On Imaginary Harmonics|A study on Imaginary Harmonics]] | *[[User:Unque/On Imaginary Harmonics|A study on Imaginary Harmonics]] | ||
*[[User:Unque/Chord interlacing (scale building method)|Chord Interlace Scales]] | *[[User:Unque/Chord interlacing (scale building method)|Chord Interlace Scales]] | ||
* A [[User:Unque/TERNAMS|naming convention]] for MV3 ternary scales (which | * A [[User:Unque/TERNAMS|naming convention]] for MV3 ternary scales (a largely forgotten project which probably remain perpetually unfinished) | ||
* A [[User:Unque/Barbershop Tuning Theory|study on tuning theory as applied to Barbershop music]] | * A [[User:Unque/Barbershop Tuning Theory|study on tuning theory as applied to Barbershop music]] | ||
* The [[User:Unque/Dietic Minor|Dietic Minor]] scale | * The [[User:Unque/Dietic Minor|Dietic Minor]] scale | ||