30th-octave temperaments: Difference between revisions

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Due to [[landscape comma]] being a notable comma that divides the octave in 3, many temperaments whose wheel is a multiple of 3 (such as 12, 15, 24, etc.), end up belonging in the [[landscape microtemperaments]]. This page therefore describes theoretical interest specific to [[30edo]], beyond just belonging in that group.

== Zinc ==

[[Zinc]] is a prominent 30th-octave temperament, see [[Landscape microtemperaments#Zinc]] for technical details. From a fractional-octave perspective, MOS scales of zinc are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach. [[Poe]] is another temperament of interest, and [[triacontoid]] as well, belonging in the [[quintosec family]].

~~: ''For technical data~~, see [[Landscape microtemperaments#Zinc]].''

~~''Zinc'' temperament is named after~~ the ~~30th element and in the 7~~-~~limit it can be described by tempering out the~~ [[~~landscape comma~~]] and ~~the~~ [[~~10th-octave temperaments#Neon|neon comma~~]]~~. Tempering out the landscape comma divides the octave in 3~~, ~~the neon comma~~ in ~~10, and respectively zinc divides~~ the ~~octave into 3 x 10 = 30~~.

~~While the landscape comma~~ is ~~considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos~~.

Considered below is oyster.

~~Within~~ the reach of a standard 128-note ~~MIDI~~ keyboard~~, zinc has mos scales of size 60, 90, and~~ 120~~. These scales are significantly distinct from either landscape rank-3 scales or~~ the ~~10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]~~. ~~The 120-tone mos has~~ [[65/64]] ~~within reach~~.

== Oyster ==

Oyster is a 2.7.11.19 weak restriction of zinc of reasonably low badness and contains all the harmonics within the reach of a standard MIDI 128-note keyboard ― 120 notes is sufficient to cover all the temperament for the subgroup. Furthermore, [[7/4]] is the generator. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament.

~~=== Oyster ===~~

Overall, this temperament is a simple augmentation of 30edo with harmonics 7, 11, and 19 that is unique and of decent badness.

~~Oyster~~ is a 2.7.11.19 restriction of zinc of reasonably low badness and contains all the harmonics within the reach of a standard MIDI 128-note keyboard ― 120 notes is sufficient to cover all the temperament for the subgroup. Furthermore, [[7/4]] is ~~the generator~~ and ~~it is~~ of badness ~~comparable to full-limit zinc variants. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament~~.

Named so because oysters are the biggest source of the element zinc, the namesake of the temperament it is derived of.

@@ Line 4: / Line 4: @@
 Due to [[landscape comma]] being a notable comma that divides the octave in 3, many temperaments whose wheel is a multiple of 3 (such as 12, 15, 24, etc.), end up belonging in the [[landscape microtemperaments]]. This page therefore describes theoretical interest specific to [[30edo]], beyond just belonging in that group.
-== Zinc ==
+[[Zinc]] is a prominent 30th-octave temperament, see [[Landscape microtemperaments#Zinc]] for technical details. From a fractional-octave perspective, MOS scales of zinc are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach. [[Poe]] is another temperament of interest, and [[triacontoid]] as well, belonging in the [[quintosec family]].
-: ''For technical data, see [[Landscape microtemperaments#Zinc]].''
-''Zinc'' temperament is named after the 30th element and in the 7-limit it can be described by tempering out the [[landscape comma]] and the [[10th-octave temperaments#Neon|neon comma]]. Tempering out the landscape comma divides the octave in 3, the neon comma in 10, and respectively zinc divides the octave into 3 x 10 = 30.
-While the landscape comma is considered the "most important" comma of zinc, it can be played in ways that don't involve it. For example, it reaches the 11th harmonic in just 2 generators which can be found using the 90-tone mos.
+Considered below is oyster.
-Within the reach of a standard 128-note MIDI keyboard, zinc has mos scales of size 60, 90, and 120. These scales are significantly distinct from either landscape rank-3 scales or the 10th-octave mos scales that produce neon or its descendant temperaments like [[deca]]. The 120-tone mos has [[65/64]] within reach.
+== Oyster ==
+Oyster is a 2.7.11.19 weak restriction of zinc of reasonably low badness and contains all the harmonics within the reach of a standard MIDI 128-note keyboard ― 120 notes is sufficient to cover all the temperament for the subgroup. Furthermore, [[7/4]] is the generator. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament.
-=== Oyster ===
+Overall, this temperament is a simple augmentation of 30edo with harmonics 7, 11, and 19 that is unique and of decent badness.
-Oyster is a 2.7.11.19 restriction of zinc of reasonably low badness and contains all the harmonics within the reach of a standard MIDI 128-note keyboard ― 120 notes is sufficient to cover all the temperament for the subgroup. Furthermore, [[7/4]] is the generator and it is of badness comparable to full-limit zinc variants. As harmonics 3 and 5 are not used, oyster is neither a landscape nor neon temperament.
 Named so because oysters are the biggest source of the element zinc, the namesake of the temperament it is derived of.