99edo: Difference between revisions

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Since 99 factors into primes as {{nowrap| 3<sup>2</sup> × 11 }}, 99edo has subset edos {{EDOs| 3, 9, 11, and 33 }}. Splitting 99edo's step in half yields [[198edo]], correcting prime 11, slightly improving prime 13, and aligning both 11 and 13 with the sharp tunings of the lower odd primes. Because of this, 198edo can be seen as a complex yet notable true full 13-limit tuning.

== Intervals ==

== Notation ==

=== Ups and downs notation ===

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):

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]]:

== Approximation to JI ==

=== 7-prime-limited odd-limit analysis ===

Unlike all previous edos, 99edo is ''distinctly'' [[consistent]] and monotone (i.e. when tempered using the patent val, the relative sizes of any two intervals are never conflated ''or'' reversed) up to the 7-prime-limited 45-odd-limit:

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</pre>

}}

~~== Intervals ==~~

~~{{Main| Table of 99edo intervals }}~~

~~== Notation ==~~

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

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):

~~{{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}}~~

== Regular temperament properties ==

@@ Line 15: / Line 15: @@
 Since 99 factors into primes as {{nowrap| 3<sup>2</sup> × 11 }}, 99edo has subset edos {{EDOs| 3, 9, 11, and 33 }}. Splitting 99edo's step in half yields [[198edo]], correcting prime 11, slightly improving prime 13, and aligning both 11 and 13 with the sharp tunings of the lower odd primes. Because of this, 198edo can be seen as a complex yet notable true full 13-limit tuning.
+== Intervals ==
+{{Main| Table of 99edo intervals }}
+== Notation ==
+=== Ups and downs notation ===
+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):
+{{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 ==
 === 7-prime-limited odd-limit analysis ===
 Unlike all previous edos, 99edo is ''distinctly'' [[consistent]] and monotone (i.e. when tempered using the patent val, the relative sizes of any two intervals are never conflated ''or'' reversed) up to the 7-prime-limited 45-odd-limit:
@@ Line 196: / Line 208: @@
 </pre>
 }}
-== Intervals ==
-{{Main| Table of 99edo intervals }}
-== Notation ==
-=== Ups and downs notation ===
-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):
-{{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}}
 == Regular temperament properties ==