Semifourth-generated scales: Difference between revisions
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[[File:Semaphore5.png|thumb|Semaphore pentatonic]] | |||
'''Semifourth-generated scales''' are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called '''alpha-dicot''' or '''omega-dicot'''{{Adv|, and notated [P8, P4/2] in pergen notation.}} | |||
The semifourth-generated scales are characteristically 4L 1s, [[semiquartal]] (5L 4s), and 5L 9s. 4L 1s is structurally significant because it is the [[Equipentatonic|equal trichordal pentatonic]]. | |||
== Intervals and notation == | |||
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "hemi-Pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. An intuitive option, if one that takes getting used to, is to use [https://en.xen.wiki/w/KISS_notation KISS] notation or [https://en.xen.wiki/w/Diamond-mos_notation diamond-mos] notation for 5L 4s. | |||
== Temperaments == | |||
Semifourth-generated temperaments have the edo join 5 & 9 (ignoring [[val#Wart notation|warts]]). | |||
* '''Interseptimal''' or '''Semaphore''' is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate. | |||
* '''Island''' temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13. | |||
* '''Intergan''' (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13 or 13/5).17.19 temperament by [[User:Ground]] that seeks to cover all of the notable concordances generated by a meantone-range semifourth. | |||
== | == See also == | ||
* [[Chthonic harmony]] | |||
* [[Semiquartal]] | |||
Latest revision as of 01:56, 2 June 2026
This page or section is a work in progress. It may lack sufficient justification, content, or organization, and is subject to future overhaul.
Semifourth-generated scales are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called alpha-dicot or omega-dicot, and notated [P8, P4/2] in pergen notation.
The semifourth-generated scales are characteristically 4L 1s, semiquartal (5L 4s), and 5L 9s. 4L 1s is structurally significant because it is the equal trichordal pentatonic.
Intervals and notation
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "hemi-Pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. An intuitive option, if one that takes getting used to, is to use KISS notation or diamond-mos notation for 5L 4s.
Temperaments
Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).
- Interseptimal or Semaphore is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
- Island temperament is a 2.3.13/5 temperament that tempers out 676/675, equating the semifourth to 15/13.
- Intergan (short for Interganassismic, a superset of 12edo's 2.3.17.19 Ganassismic) is a proposed 19&24 2.3.(5).11.(13 or 13/5).17.19 temperament by User:Ground that seeks to cover all of the notable concordances generated by a meantone-range semifourth.
