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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|44}}
{{ED intro}}
== Theory ==
== Theory ==
44edo is a double of 22edo, to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the 13th harmonic with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed. In the 13-limit it supplies the optimal patent val for [[vigin]] temperament. The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]].
44edo is a double of [[22edo]], to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the [[13/1|13th harmonic]] with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed.
 
It is on the [[optimal ET sequence]] for 7-, 11- and 13-limit [[nautilus]] temperament, for 11-limit [[spell]] temperament, and for 13-limit [[cantrip]] temperament. In the [[13-limit]] it supplies the optimal [[patent val]] for [[vigin]] temperament.  
 
The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]].


=== Harmonics ===
=== Harmonics ===
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== Intervals ==
== Intervals ==
In 44edo, sharps and flats alter pitch by 6 EDOsteps. This means intervals can be notated with half sharps and half flats equal to 3 EDOsteps, in addition to ups and downs. The table below uses only sharps, flats, and ups and downs. When translating music from 22edo to 44edo, single ups and downs simply become double ups and downs (vEb in 22edo would be vvEb in 44edo).
In 44edo, sharps and flats alter pitch by 6 EDOsteps. This means intervals can be notated with half sharps and half flats equal to 3 EDOsteps, in addition to ups and downs. The table below uses only sharps, flats, and ups and downs. When translating music from 22edo to 44edo, single ups and downs simply become double ups and downs (vEb in 22edo would be vvEb in 44edo). {{todo|complete table|text=add a column of JI approximations}}
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! Degrees
! Degrees
! Cents
! Cents
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
| 0
| 0
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| D
| D
|}
|}
== Notation ==
=== Ups and downs notation ===
44edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
{{Sharpness-sharp6a}}
Half-sharps and half-flats can be used to avoid triple arrows:
{{Sharpness-sharp6b}}
[[Alternative symbols for ups and downs notation#Sharp-6| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp6}}
If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
{{Sharpness-sharp6-qt}}
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[23edo#Second-best fifth notation|23b]], [[30edo#Sagittal notation|30]], and [[37edo#Sagittal notation|37]], and is a superset of the notations for EDOs [[22edo#Sagittal notation|22]] and [[11edo#Sagittal notation|11]].
==== Evo flavor ====
<imagemap>
File:44-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 711 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[513/512]]
rect 140 80 240 106 [[81/80]]
rect 240 80 360 106 [[27/26]]
default [[File:44-EDO_Evo_Sagittal.svg]]
</imagemap>
==== Revo flavor ====
<imagemap>
File:44-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[513/512]]
rect 140 80 240 106 [[81/80]]
rect 240 80 360 106 [[27/26]]
default [[File:44-EDO_Revo_Sagittal.svg]]
</imagemap>
==== Evo-SZ flavor ====
<imagemap>
File:44-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 695 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 140 106 [[513/512]]
rect 140 80 240 106 [[81/80]]
rect 240 80 360 106 [[27/26]]
default [[File:44-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
== Regular temperament properties ==
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 3\44
| 81.82
| 22/21
| [[Nautilus]]
|-
| 1
| 7\44
| 190.91
| 9/8
| [[Spell]]/[[cantrip]]
|-
| 1
| 9\44
| 245.46
| 15/13
| [[Immunity]]
|-
| 1
| 13\44
| 354.55
| 11/9
| [[Ringo]]
|-
| 1
| 15\44
| 409.09
| 5/4
| [[Hocus]]
|-
| 2
| 3\44
| 81.82
| 22/21
| [[Harry]]
|-
| 4
| 4\44
| 109.09
| 16/15
| [[Bidia]]
|-
| 11
| 2\44
| 54.55
| 33/32
| [[Hendecatonic]]
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave
== Scales ==
* Evacuated planet{{idiosyncratic}} (approximated from [[66afdo|66]][[afdo]]): 5 13 8 12 6
* Approximations of [[gamelan]] scales:
** 5-tone pelog: 4 6 15 4 15
** 7-tone pelog: 4 6 9 6 4 10 5
** 5-tone slendro: 9 9 8 9 9


== Instrument layouts ==
== Instrument layouts ==
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[[Skip fretting system 44 2 11]]
[[Skip fretting system 44 2 11]]
== Music ==
* ''[https://m.youtube.com/watch?v=ljaSpsQP2qc Improvisation in 44edo]'' - composed and played by [[Bryan Deister]] (May 2023), transcribed by [[Stephen Weigel]] (Sept 2024)
* ''[https://m.youtube.com/watch?v=U_7nziRy91g Leaning Dream - Pizza Tower]'' - adapted into 44edo by [[Bryan Deister]] (July 2024)
* ''[https://youtu.be/8iS_yIYYS9Q 44edo improvisation]'' - [[Bryan Deister]] (Oct 2024)


[[Category:44edo| ]] <!-- main article -->
[[Category:44edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Todo:add rank 2 temperaments table]]
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