120edo: Difference between revisions

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120edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710 ~~cents~~. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome|newcome]] temperament.

The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710{{c}}. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome|newcome]] temperament.

=== Prime harmonics ===

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=== Subsets and supersets ===

120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5). It has many subsets: {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.

120edo is the 10th highly composite edo and the 5th factorial edo (since {{nowrap|120 {{=}} 5!}} {{nowrap|{{=}} 1 × 2 × 3 × 4 × 5}}). It has many subsets: {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.

=== Miscellaneous properties ===

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== Intervals ==

== Notation ==

=== Ups and downs notation ===

120edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals:

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 edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.
-The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710 cents. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome|newcome]] temperament.
+The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710{{c}}. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome|newcome]] temperament.
 === Prime harmonics ===
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5). It has many subsets: {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.
+edo is the 10th highly composite edo and the 5th factorial edo (since {{nowrap|120 {{=}} 5!}} {{nowrap|{{=}} 1 × 2 × 3 × 4 × 5}}). It has many subsets: {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.
 === Miscellaneous properties ===
@@ Line 23: / Line 23: @@
 == Intervals ==
 {{Interval table}}
+== Notation ==
+=== Ups and downs notation ===
+edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation|quarter-tone]] accidentals:
+{{Sharpness-sharp10|120}}