100edo: Difference between revisions

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=Scales=

[[~~greeley8|greeley8~~]]

*[[Greeley8]]

*[[Greeley15]]

[[~~greeley15|greeley15~~]]

=100bddd and the 22-note scales=

The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo|~~22edo~~]] for [[~~pajara~~|pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.

The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo|22EDO]] for [[Diaschismic family|pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.

The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of the "wolves" are still usable (albeit xenharmonic), it might be better to use the term ''dog'' rather than wolf for these intervals. Dog intervals frequently provide ''closer'' matches to intervals involving the 7th and 11th harmonics. Even ''if'' the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.

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Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [https://en.wikipedia.org/wiki/Augmented-fourths_tuning are tuned in tritones]. This makes guitar construction much easier compared to other non-equally-tempered scales. The MODMOS would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2MOS is simpler, the MODMOS very closely approximates the [[~~Indian|~~Indian]] sruti system.

Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [https://en.wikipedia.org/wiki/Augmented-fourths_tuning are tuned in tritones]. This makes guitar construction much easier compared to other non-equally-tempered scales. The MODMOS would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2MOS is simpler, the MODMOS very closely approximates the [[Indian]] sruti system.

Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively.

[[Category:100edo]]

[[Category:edo]]

~~[[Category:todo:add_definition]]~~

@@ Line 6: / Line 6: @@
 =Scales=
-[[greeley8|greeley8]]
+*[[Greeley8]]
+*[[Greeley15]]
-[[greeley15|greeley15]]
 =100bddd and the 22-note scales=
-The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo|22edo]] for [[pajara|pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.
+The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo|22EDO]] for [[Diaschismic family|pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.
 The 22-note MODMOS 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of the "wolves" are still usable (albeit xenharmonic), it might be better to use the term ''dog'' rather than wolf for these intervals. Dog intervals frequently provide ''closer'' matches to intervals involving the 7th and 11th harmonics. Even ''if'' the dog intervals are completely avoided, this MODMOS still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to 12edo.
@@ Line 171: / Line 170: @@
 |}
-Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [https://en.wikipedia.org/wiki/Augmented-fourths_tuning are tuned in tritones]. This makes guitar construction much easier compared to other non-equally-tempered scales. The MODMOS would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2MOS is simpler, the MODMOS very closely approximates the [[Indian|Indian]] sruti system.
+Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [https://en.wikipedia.org/wiki/Augmented-fourths_tuning are tuned in tritones]. This makes guitar construction much easier compared to other non-equally-tempered scales. The MODMOS would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2MOS is simpler, the MODMOS very closely approximates the [[Indian]] sruti system.
 Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively.
 [[Category:100edo]]
 [[Category:edo]]
-[[Category:todo:add_definition]]