120edo: Difference between revisions

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120edo means division of the octave into equal parts of 10 cents each. Its [[patent val]] is [[contorted]] only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it). Being the simplest division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the fine relative cent of [[1edo|1edo]].

120edo ~~also has a concoctic generator that resembles~~ the ~~leap day excess of earth~~, 29~~\120 corresponding to~~ 5 ~~hours and 48 minutes~~.

== Theory ==

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.

~~120edo~~ is ~~the 5th factorial EDO, and the 10th highly melodic EDO~~.

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.

[[~~Category:Highly melodic~~]]

=== Prime harmonics ===

=== Subsets and supersets ===

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 ===

120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

== JI approximation ==

== 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 means division of the octave into equal parts of 10 cents each. Its [[patent val]] is [[contorted]] only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it). Being the simplest division of the octave by the Germanic [https://en.wikipedia.org/wiki/Long_hundred long hundred], it has a unit step which is the fine relative cent of [[1edo|1edo]].
+{{Infobox ET}}
+{{ED intro}}
-edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.
+== Theory ==
+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.
-edo is the 5th factorial EDO, and the 10th highly melodic EDO.
+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.
-[[Category:Highly melodic]]
+=== Prime harmonics ===
+{{Harmonics in equal|120}}
+=== Subsets and supersets ===
+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 ===
+edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.
+== JI approximation ==
+{{Q-odd-limit intervals|120}}
+== 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-qt1|120}}