Xenharmonic Wiki

22edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,322 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,322 edits
Line 221: Line 221:


== Notations ==
== Notations ==
=== Superpyth/Porcupine Notation, Porcupine Notation and Pentatonic Notation ===
=== Superpyth/Porcupine Notation ===
Superpyth/Porcupine Notation is a system arising from both superpyth and porcupine temperament. It categorizes each 22edo interval as major and minor of one or both of those temperaments. s indicates superpyth and p indicates porcupine. Because p now represents porcupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or "Natural". Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.
Superpyth/Porcupine Notation is a system arising from both superpyth and porcupine temperament. It categorizes each 22edo interval as major and minor of one or both of those temperaments. s indicates superpyth and p indicates porcupine. Because p now represents porcupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or "Natural". Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.


=== Porcupine Notation ===
Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.
Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.


=== Pentatonic Notation ===
Yet another notation is pentatonic. The degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. This is the only way to use a chain-of-fifths notation without additional accidentals. The keyboard runs D * * * * F * * * G * * * A * * * * C * * * D. The natural notes represent a chain of 5ths FCGDA.
Yet another notation is pentatonic. The degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. This is the only way to use a chain-of-fifths notation without additional accidentals. The keyboard runs D * * * * F * * * G * * * A * * * * C * * * D. The natural notes represent a chain of 5ths FCGDA.
=== Decatonic Notation ===
The decatonic notation is based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern. The system is based on two chains of fifths: one represented by Latin letters, the other by Greek. The two chains can be looked at as two juxtaposed pentatonic scales.
Chain 1: C G D A E
Chain 2: γ δ α ε β
The alphabet is, in ascending order: C δ D ε E γ G α A β C
In this alphabet, a chain of fifths is preserved because equivalent Greek letters also represent fifths if they are the same as their Latin counterparts. For example G-D is a fifth, and so is γ-δ.
=== Sagittal Notation ===
When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:
[[File:22edo.png|alt=22edo.png|22edo.png]]
This notation is consistent with Sagittal's notation of 5-limit JI harmony: "major" 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.
The division of the apotome into three syntonic commas also indicates 22's tempering out of the [[250/243|porcupine comma]] (which is equivalent to three syntonic commas minus a Pythagorean apotome).
We also have, from the appendix to [[The Sagittal Songbook]] by [[JacobBarton|Jacob A. Barton]], this diagram of how to notate 22-EDO in the Revo flavor of Sagittal:
[[File:22edo Sagittal.png|800px]]
=== Ups and Downs Notation ===
Treating [[Ups and Downs Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately:
[[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]]
Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:
[[File:Tibia_22edo_ups_and_downs_guide_2.png|alt=Tibia 22edo ups and downs guide 2.png|800x150px|Tibia 22edo ups and downs guide 2.png]]
A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.
[[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]
Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.
<gallery mode="slideshow">
File:Tibia in G CORRECTED-1.png|alt=Tibia in G CORRECTED-1.png|Tibia in G (page 1)
File:Tibia in G CORRECTED-2.png|alt=Tibia in G CORRECTED-2.png|Tibia in G (page 2)
</gallery>
=== Comparison of 22edo Notation Systems ===


{| class="wikitable center-all right-2"
{| class="wikitable center-all right-2"
Line 491: Line 540:
|}
|}


=== Decatonic Notation ===
=== Chord names ===
The decatonic notation is based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern. The system is based on two chains of fifths: one represented by Latin letters, the other by Greek. The two chains can be looked at as two juxtaposed pentatonic scales.
 
Chain 1: C G D A E
 
Chain 2: γ δ α ε β
 
The alphabet is, in ascending order: C δ D ε E γ G α A β C
 
In this alphabet, a chain of fifths is preserved because equivalent Greek letters also represent fifths if they are the same as their Latin counterparts. For example G-D is a fifth, and so is γ-δ.
 
=== Sagittal Notation ===
When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:
 
[[File:22edo.png|alt=22edo.png|22edo.png]]
 
This notation is consistent with Sagittal's notation of 5-limit JI harmony: "major" 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.
 
The division of the apotome into three syntonic commas also indicates 22's tempering out of the [[250/243|porcupine comma]] (which is equivalent to three syntonic commas minus a Pythagorean apotome).
 
We also have, from the appendix to [[The Sagittal Songbook]] by [[JacobBarton|Jacob A. Barton]], this diagram of how to notate 22-EDO in the Revo flavor of Sagittal:
 
[[File:22edo Sagittal.png|800px]]
 
=== Ups and Downs Notation ===
 
Treating [[Ups and Downs Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately:
 
[[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]]
 
Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:
 
[[File:Tibia_22edo_ups_and_downs_guide_2.png|alt=Tibia 22edo ups and downs guide 2.png|800x150px|Tibia 22edo ups and downs guide 2.png]]
 
A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.
 
[[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]
 
Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.
 
<gallery>
Tibia in G CORRECTED-1.png|alt=Tibia in G CORRECTED-1.png|200px|thumb|left|Tibia in G (page 1)
Tibia in G CORRECTED-2.png|alt=Tibia in G CORRECTED-2.png|200px|thumb|center|Tibia in G (page 2)
</gallery>
 
== Chord names ==
 
See also [[22 EDO Chords]], [[Chords of orwell]].
See also [[22 EDO Chords]], [[Chords of orwell]].


Retrieved from "https://en.xen.wiki/w/22edo"