99edo: Difference between revisions

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Being a [[zeta peak edo]], 99edo is also a very strong no-11 no-13 system, where it is consistent to the [[29-odd-limit]] with a sharp tendency. This favors the sharp mapping of 11 and 13, and allows these relatively weak approximations to somewhat blend with the rest for a full [[29-limit]] (or [[31-limit]], using the sharp-tending 99efk val) temperament. In fact, the 99efk val is the first to achieve [[diamond monotone]] in the [[31-odd-limit]], though it fails in the [[33-odd-limit]] due to mapping [[33/32]] to 5 steps, while [[32/31]] is mapped to 4 steps.

One step of 99edo is close to [[144/143]], the grossma. Unfortunately, neither 99ef nor the patent val map it consistently, though [[198edo]] does.

=== Prime harmonics ===

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== Notation ==

=== ~~Ups~~ and downs notation ===

[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:

99edo can be notated with [[Kite's ups and downs notation]]. Note that quip (quintuple-up) is the same as quudsharp (quadruple-down sharp) and that quid (quintuple-down) is the same as quupflat (quadruple-up flat):

=== Kite's ups and downs notation ===

99edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]]. Note that quip (quintuple-up) is the same as quudsharp (quadruple-down sharp) and that quid (quintuple-down) is the same as quupflat (quadruple-up flat):

Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:

~~{{Sharpness-sharp10-qt1}}~~

== Approximation to JI ==

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| 339.394

| 128/105

| [[Amity]] (99ef) / hitchcock (99)

| [[Amity]] (99ef) / stalagmite (99ef) / hitchcock (99)

|-

| 1

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| 48.485

| 36/35

| [[Ennealimmal]] (~~99e~~) / ~~ennealimmia~~ (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)

| [[Ennealimmal]] / enneabiotic (99ef) / ennealympic (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)

|-

| 11

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* [[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone, and grosstone

[[Category:~~Hemifamity~~]]

[[Category:Aberschismic]]

[[Category:Hemififths]]

[[Category:Hendecatonic]]

@@ Line 8: / Line 8: @@
 Being a [[zeta peak edo]], 99edo is also a very strong no-11 no-13 system, where it is consistent to the [[29-odd-limit]] with a sharp tendency. This favors the sharp mapping of 11 and 13, and allows these relatively weak approximations to somewhat blend with the rest for a full [[29-limit]] (or [[31-limit]], using the sharp-tending 99efk val) temperament. In fact, the 99efk val is the first to achieve [[diamond monotone]] in the [[31-odd-limit]], though it fails in the [[33-odd-limit]] due to mapping [[33/32]] to 5 steps, while [[32/31]] is mapped to 4 steps.
+One step of 99edo is close to [[144/143]], the grossma. Unfortunately, neither 99ef nor the patent val map it consistently, though [[198edo]] does.
 === Prime harmonics ===
@@ Line 19: / Line 21: @@
 == Notation ==
-=== Ups and downs notation ===
+[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
-edo can be notated with [[Kite's ups and downs notation]]. Note that quip (quintuple-up) is the same as quudsharp (quadruple-down sharp) and that quid (quintuple-down) is the same as quupflat (quadruple-up flat):
+{{Sharpness-sharp10-qt1-szg}}
+=== Kite's ups and downs notation ===
+edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]]. Note that quip (quintuple-up) is the same as quudsharp (quadruple-down sharp) and that quid (quintuple-down) is the same as quupflat (quadruple-up flat):
 {{Ups and downs sharpness|99|true}}
-Another notation uses [[Alternative symbols for ups and downs notation#Sharp-5|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
-{{Sharpness-sharp10-qt1}}
 == Approximation to JI ==
@@ Line 343: / Line 345: @@
 | 339.394
 | 128/105
-| [[Amity]] (99ef) / hitchcock (99)
+| [[Amity]] (99ef) / stalagmite (99ef) / hitchcock (99)
 |-
 | 1
@@ Line 391: / Line 393: @@
 | 48.485
 | 36/35
-| [[Ennealimmal]] (99e) / ennealimmia (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)
+| [[Ennealimmal]] / enneabiotic (99ef) / ennealympic (99) / <br>ennealimnic (99ef) / ennealim (99e) / ennealiminal (99)
 |-
 | 11
@@ Line 457: / Line 459: @@
 * [[105edo]], a similarly sized edo that supports meantone, septimal meantone, undecimal meantone, and grosstone
-[[Category:Hemifamity]]
+[[Category:Aberschismic]]
 [[Category:Hemififths]]
 [[Category:Hendecatonic]]