Xenharmonic Wiki

Ploidacot/Alpha-dicot: Difference between revisions

← Older edit
VisualWikitext
Jerdle (talk | contribs)
autopatrolled, emailconfirmed
253 edits
No edit summary
Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit
Fredg999 category edits (talk | contribs)
autopatrolled, Bots, emailconfirmed
4,457 edits
m Removing from Category:Ploidacots using Cat-a-lot
 
(9 intermediate revisions by 6 users not shown)
Line 1: Line 1:
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14|Title=Alpha-dicot; omega-dicot}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.
{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=1|Cots=2|Pergen=[P8, P4/2]|Forms=5, 9, 14, 19|Title=Alpha-dicot|Wedgie=2}}'''Alpha-dicot''' is a temperament archetype where the generator is a [[Interseptimal interval|semitwelfth]], two of which make a perfect twelfth of [[3/1]], and the period is a [[2/1]] octave. Equivalently, the generator could be a semifourth, two of which make a [[4/3]], so '''omega-dicot''' would mean the same thing. However, the preferred term is alpha-dicot.


Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.
Alpha-dicot temperaments usually generate the [[5L 4s]] MOS structure, named "semiquartal" after the semifourth generator, as well as the child scale [[5L 9s]]. Alpha-dicot temperaments tend to involve interseptimal intervals, which are in between conventional diatonic intervals.


== Intervals and notation ==
== Intervals and notation ==
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[Chain-of-fifths notation]]).
Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "[[hemipythagorean]]" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).
 
{| class="wikitable"
{| class="wikitable"
|+Alpha-dicot intervals (assuming pure octave and fifth)
|+ style="font-size: 105%;" | Alpha-dicot intervals (assuming pure octave and fifth)
!#
!Cents
!Notation
!Name
|-
|-
| -9
! #
|1041.20
! Cents
|
! Notation
|
! Name
|-
|-
| -8
| −9
|792.18
| 1041.20
|Ab
|  
|minor sixth
|  
|-
|-
| -7
| −8
|543.16
| 792.18
|
| Ab
|
| minor sixth
|-
|-
| -6
| −7
|294.14
| 543.16
|Eb
|  
|minor third
|  
|-
|-
| -5
| −6
|45.11
| 294.13
|
| Eb
|
| minor third
|-
|-
| -4
| −5
|996.09
| 45.11
|Bb
|  
|minor seventh
|  
|-
|-
| -3
| −4
|747.07
| 996.09
|
| Bb
|
| minor seventh
|-
|-
| -2
| −3
|498.05
| 747.07
|F
|  
|perfect fourth
|  
|-
|-
| -1
| −2
|249.02
| 498.04
|
| F
|
| perfect fourth
|-
|-
|0
| −1
|0
| 249.02
|C
|  
|perfect unison
|  
|-
|-
|1
| 0
|950.98
| 0
|
| C
|
| perfect unison
|-
|-
|2
| 1
|701.96
| 950.98
|G
|  
|perfect fifth
|  
|-
|-
|3
| 2
|452.93
| 701.96
|
| G
|
| perfect fifth
|-
|-
|4
| 3
|203.91
| 452.93
|D
|  
|major second
|  
|-
|-
|5
| 4
|1154.89
| 203.91
|
| D
|
| major second
|-
|-
|6
| 5
|905.87
| 1154.89
|A
|  
|major sixth
|  
|-
|-
|7
| 6
|656.84
| 905.87
|
| A
|
| major sixth
|-
|-
|8
| 7
|407.82
| 656.84
|E
|  
|major third
|  
|-
|-
|9
| 8
|158.8
| 407.82
|
| E
|
| major third
|-
| 9
| 158.80
|  
|  
|}
|}


Line 114: Line 116:


=== Bug ===
=== Bug ===
[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the best 5-limit interpretation of this ploidacot.
[[Bug]] is an exotemperament, equating the semitwelfth generator to 5/3. This means that 9/5 is the same interval (tempering out [[27/25]]), and the semifourth represents both 6/5 and 10/9. This is clearly badly inaccurate, but is probably the simplest (arguably) reasonable 5-limit interpretation of this ploidacot.


The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].
The best tunings tend to be around 940{{c}} for the semitwelfth, with a somewhat flat twelfth. This sets the semifourth to 260{{c}}, which is close to [[7/6]].
Line 124: Line 126:


=== Barbados ===
=== Barbados ===
Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is [[15/13]][[~]][[52/45]].
Here, the generator actually is 26/15, equated with [[45/26]]. This is an accurate temperament, tempering out the unnoticeable comma of [[676/675]], but it is defined in the awkward 2.3.13/5 subgroup. The semifourth here is {{nowrap|[[15/13]][[~]][[52/45]]}}.


As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.
As the comma is so small, the best tunings are close to just. The semitwelfth is around 951{{c}}, leading to a near-just twelfth.
{{Todo| unify precision }}
Retrieved from "https://en.xen.wiki/w/Ploidacot/Alpha-dicot"