User:Unque/Buzzard: Difference between revisions
Created page with "'''Buzzard''' is the 2.3.7-subgroup 53 & 58 temperament and its extensions. It splits the third harmonic into four equal parts, each part representing 21/16; thus, it tempers out the comma 65536/64827. This temperament provides a useful interpretation of radically near-equal pentatonic scales using the 2.3.7 subgroup, and it can be used to generate scales that further extend this structure via small inflections. The name Buzzard was giv..." |
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While it makes little sense from the perspective of a target tuning, Meantone occurs quite often in low EDO tunings of 2.3.7 Buzzard, such as 38edo and 43edo, making it a reasonable extension to the Buzzard structure. This extension finds 5-limit consonances by equating them with 3-limit consonances, or equivalently by equating the aberrisma with [[36/35]] (thus tempering out [[81/80]]). 5/4, for instance, can be reached at one inflection below 9/7, and 5/3 at one inflection below 12/7. | While it makes little sense from the perspective of a target tuning, Meantone occurs quite often in low EDO tunings of 2.3.7 Buzzard, such as 38edo and 43edo, making it a reasonable extension to the Buzzard structure. This extension finds 5-limit consonances by equating them with 3-limit consonances, or equivalently by equating the aberrisma with [[36/35]] (thus tempering out [[81/80]]). 5/4, for instance, can be reached at one inflection below 9/7, and 5/3 at one inflection below 12/7. | ||
Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out 413343/409600). 5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7. While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo. | Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out [[413343/409600]]). 5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7. While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo. | ||
== Interval Chain == | == Interval Chain == | ||
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=== Buzzard[5] === | === Buzzard[5] === | ||
<pre>! buzzard5.scl | Buzzard gives us a roughly-equal pentatonic scale of [[3L 2s]]; the large step and small step differ by a tiny step that represents [[64/63]].<pre>! buzzard5.scl | ||
! | ! | ||
Buzzard[5] 2|2 mode (LsLsL) in 19\48 tuning | Buzzard[5] 2|2 mode (LsLsL) in 19\48 tuning | ||
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=== Buzzard[8] === | === Buzzard[8] === | ||
<pre> | The 8-note [[MOS scale|MOS]] introduces three small steps of 64/63, and thus it has the pattern [[5L 3s]]. These small steps act as inflections and allow more complex consonances to be reached, while the disparity between the step sizes allows the structure to largely adhere to the pentatonic form despite the greater number of notes.<pre> | ||
! buzzard8.scl | ! buzzard8.scl | ||
! | ! | ||
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=== Buzzard[13] === | === Buzzard[13] === | ||
<pre> | The 13-note MOS functions much the same as the 8-note one, using small inflections to reach nearby consonances in the largely pentatonic structure; however, unlike the 8-note MOS, it includes certain chains of two consecutive inflections in a row, which allows for more complex inflections. This scale has the pattern [[5L 8s]].<pre> | ||
! buzzard13.scl | ! buzzard13.scl | ||
! | ! | ||
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|0-comma | |0-comma | ||
|470.781 | |470.781 | ||
|21 | |21 | ||
|Degenerate case; lower boundary of Buzzard targets. | |Degenerate case; lower boundary of Buzzard targets. | ||
|- | |- | ||
|1/4-comma | |1/4-comma | ||
|475.489 | |475.489 | ||
|3 | |3 | ||
| | | | ||
|- | |- | ||
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|1/3-comma | |1/3-comma | ||
|477.058 | |477.058 | ||
|7 | |7 | ||
| | | | ||
|- | |- | ||
|1/2-comma | |1/2-comma | ||
|480.192 | |480.192 | ||
|147 | |147 | ||
|5-limit MOS is almost completely equalized. | |5-limit MOS is almost completely equalized. | ||
|- | |- | ||
|1-comma | |1-comma | ||
|489.612 | |489.612 | ||
|3087 | |3087 | ||
|Degenerate case; upper boundary of Buzzard targets. | |Degenerate case; upper boundary of Buzzard targets. | ||
|} | |} | ||
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|[[28edo|11\28]] | |[[28edo|11\28]] | ||
|471.429 | |471.429 | ||
| | |Semi-Aberrismic | ||
|Near-just 5/4 | |Near-just 5/4 | ||
|- | |- | ||
|[[33edo|13\33]] | |[[33edo|13\33]] | ||
|472.727 | |472.727 | ||
| | |Semi-Aberrismic | ||
| | | | ||
|- | |- | ||