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! Degree
! Degree
! Cents
! Cents
! colspan="3" | [[Ups and Downs Notation|Up/down notation]]
! colspan="3" | [[Ups and downs notation|Up/down notation]]
! [[User:Inthar/Fox-Raven notation|Fox-Raven]] <br/> [[5L 3s]] <br/> Notation
! [[User:Inthar/Fox-Raven notation|Fox-Raven]] <br/> [[5L 3s]] <br/> Notation
! Category name
! Category name
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* 1143 can be used internally but not 1257.
* 1143 can be used internally but not 1257.
=== Diasem harmony ===
=== Diasem harmony ===
Diasem is an MV3 scale with step pattern either (left-handed) MLSLMLLSL or (right-handed) MLSLMLSLL which are non-superimposable mirror images. As its name suggests, it has qualities intermediate that of [[19edo]]'s [[diatonic]] mos and [[23edo]]'s [[semiquartal]] mos. 21edo diasem also has a non-chiral alteration 231323223, which, however, is only MV3 because of the specific step ratio 3:2:1 it has in 21edo.
[[Diasem]] is an MV3 scale with step pattern either (left-handed) MLSLMLLSL or (right-handed) MLSLMLSLL which are non-superimposable mirror images. As its name suggests, 21edo diasem has qualities intermediate that of [[19edo]]'s [[diatonic]] mos and [[23edo]]'s [[semiquartal]] mos. 21edo diasem also has a non-chiral alteration 231323223, which, however, is only MV3 because of the specific step ratio 3:2:1 it has in 21edo.


The basic Locrian 7th chord has a brighter version 0-343-629-1029 and a darker version 0-286-571-971. A more xen one can be made by lowering either 343 or 1029 by one step, which exists in some variant of diasem Locrian.
The basic Locrian 7th chord has a brighter version 0-343-629-1029 and a darker version 0-286-571-971. The bright version occurs in both diasem Locrians. A more xen one can be made by lowering either 343 or 1029 by one step, which exists in some variant of diasem Locrian. Unfortunately, the darker Locrian seventh chord doesn't appear in any unaltered diasem mode in 21edo. To remedy this one could split (add a comma step to) the tritone and the minor 2nd, yielding 11313113313.
==== Modes ====
Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. Fourteen of these modes are versions of diatonic modes which come in LH and RH pairs; four are more [[oneirotonic]]-like, sharing melodic segments with the oneirotonic scale in [[21edo]], and they lack either a perfect 4th or a perfect 5th.


The (right-handed) diasem Lydian 313323132 would benefit from the addition of the 629 cent tritone, yielding 3133113132.
{| class="wikitable"
|-
| style="text-align:center;" |
| style="text-align:center;" |Left-handed modes
| style="text-align:center;" |Right-handed modes
|-
| rowspan="5"|Modes with both a P4 and a P5
| | LSLMLLSLM <br/>LH Diasem Ionian
| | LSLMLSLLM <br/>RH Diasem Ionian
|-
| | LSLMLSLML <br/>LH Diasem Mixo
| | SLLMLSLML <br/>RH Diasem Mixo
|-
| | SLMLLSLML <br/>LH Diasem Dorian
| | LMLSLLMLS <br/>RH Diasem Dorian
|-
| | LMLSLMLLS <br/>LH Diasem Aeolian
| | LMLSLMLSL <br/>RH Diasem Aeolian
|-
| | MLLSLMLSL <br/>LH Diasem Phrygian
| | MLSLLMLSL <br/>RH Diasem Phrygian
|-
| rowspan=4|Modes lacking either a P4 or a P5
| | LLSLMLSLM <br/>LH Diasem Lydian
| | LSLLMLSLM <br/>RH Diasem Lydian
|-
| | LMLLSLMLS <br/>LH Diasem Darkened Dorian (Somewhat like Celdorian)
| | LLMLSLMLS <br/>RH Diasem Darkened Mixo (Somewhat like Illarnekian)
|-
| | SLMLSLMLL <br/>LH Diasem Brightened Aeolian (Somewhat like Hlanithian)
| | SLMLSLLML <br/>RH Diasem Brightened Dorian (Somewhat like Sardorian)
|-
| | MLSLMLLSL <br/>LH Diasem Locrian
| | MLSLMLSLL <br/>RH Diasem Locrian
|-
|}


Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. Modes with LLS are left-handed; modes with LLM are right-handed. Fourteen of these modes are versions of diatonic modes which come in LH and RH pairs; four are less diatonic-like.


==== Mode ====
Here, "brightened" (resp. "darkened") means that the diatonic scale is overall sharpened (resp. flattened) perfect 5th (resp. the perfect 4th) is missing. These may sound somewhat more like [[oneirotonic]] modes.
Diasem has 18 modes, 9 modes of LH diasem and 9 modes of RH diasem. 14 of these modes are versions of diatonic modes which come in LH and RH pairs; four are more [[oneirotonic]]-like.


The modes arranged in cyclic order:
{| class="wikitable"
{| class="wikitable"
|-
|-
| style="text-align:center;" |
| style="text-align:center;" |Left-handed modes
| style="text-align:center;" |Left-handed modes
| style="text-align:center;" |Right-handed modes
| style="text-align:center;" |Right-handed modes
|-
|-
| rowspan="7"|Diatonic-like modes
| | LSLMLSLML <br/>LH Diasem Mixo
| | LLSLMLSLM LH Diasem Lydian
| | LMLSLMLSL <br/>RH Diasem Aeolian
| | LSLLMLSLM RH Diasem Lydian
|-
|-
| | LSLMLLSLM LH Diasem Ionian
| | SLMLSLMLL <br/>LH Diasem Brightened Aeolian
| | LSLMLSLLM RH Diasem Ionian
| | MLSLMLSLL <br/>RH Diasem Locrian
|-
|-
| | LSLMLSLML LH Diasem Mixo
| | LMLSLMLLS <br/>LH Diasem Aeolian
| | SLLMLSLML RH Diasem Mixo
| | LSLMLSLLM <br/>RH Diasem Ionian
|-
|-
| | SLMLLSLML LH Diasem Dorian
| | MLSLMLLSL <br/>LH Diasem Locrian
| | LMLSLLMLS RH Diasem Dorian
| | SLMLSLLML <br/>RH Diasem Brightened Dorian
|-
|-
| | LMLSLMLLS LH Diasem Aeolian
| | LSLMLLSLM <br/>LH Diasem Ionian
| | LMLSLMLSL RH Diasem Aeolian
| | LMLSLLMLS <br/>RH Diasem Dorian
|-
|-
| | MLLSLMLSL LH Diasem Phrygian
| | SLMLLSLML <br/>LH Diasem Dorian
| | MLSLLMLSL RH Diasem Phrygian
| | MLSLLMLSL <br/>RH Diasem Phrygian
|-
|-
| | MLSLMLLSL LH Diasem Locrian
| | LMLLSLMLS <br/>LH Diasem Darkened Dorian
| | MLSLMLSLL RH Diasem Locrian
| | LSLLMLSLM <br/>RH Diasem Lydian
|-
|-
| rowspan=2|The odd ones out
| | MLLSLMLSL <br/>LH Diasem Phrygian
| |SLMLSLMLL LH Diasem Pseudo-Hlanithian
| | SLLMLSLML <br/>RH Diasem Mixo
| |LLMLSLMLS RH Diasem Pseudo-Illarnekian
|-
|-
| |LMLLSLMLS LH Diasem Pseudo-Celdorian
| | LLSLMLSLM <br/>LH Diasem Lydian
| |SLMLSLLML RH Diasem Pseudo-Sardorian
| | LLMLSLMLS <br/>RH Diasem Darkened Mixo
|}
|}
Here follow some snippets I've written in some diasem modes.
 
Here follow snippets I've written in various diasem modes.
===== RH Diasem Lydian =====
===== RH Diasem Lydian =====
[[File:RH Diasem Lydian Example 21edo.mp3]]
[[File:RH Diasem Lydian Example 21edo.mp3]] [[:File:Diasem Lydian Example Score.pdf|Score]]
===== LH Diasem Dorian =====
[[File:LH Diasem Dorian Example 21edo.mp3]]
===== RH Diasem Dorian =====
===== RH Diasem Dorian =====
[[File:RH Diasem Dorian Example 21edo.mp3]]
[[File:RH Diasem Dorian Example 21edo.mp3]] [[:File:RH Diasem Dorian Example Score.pdf|Score]]
===== LH Diasem Phrygian =====
[[File:Diasem Phrygian Example 21edo.mp3]]
 
===== LH Diasem Locrian =====
===== LH Diasem Locrian =====
[[File:LH Diasem Locrian Example 21edo.mp3]]
[[File:LH Diasem Locrian Example 21edo.mp3]] [[:File:Diasem Locrian Example.pdf|Score]]
===== RH Diasem Locrian =====
[[File:RH Diasem Sample 21edo.mp3]]
===== LH Diasem Pseudo-Celdorian =====
===== RH Diasem Pseudo-Illarnekian =====
==== Altered diasem modes ====
* 233231313 Oneiro-Diasem Locrian
* 231322213 Diasem Locrian "#6"


=== Other diatonic scales ===
=== Other diatonic scales ===
* 0 229 400 629 686 914 1086 1200: 21edo Bright Lydian
* 0 229 400 629 686 914 1086 1200: 21edo Bright Lydian (not contained in diasem)
* 0 171 400 571 686 857 1086 1200: 21edo Dark Lydian
== Free 21edo ==
[[File:21edo Fugue Expo.mp3]]


== Oneirotonic harmony ==
== Oneirotonic harmony ==
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Miracle is a good mapping.
Miracle is a good mapping.
[[Category:21edo]]
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