Xenharmonic Reference - User contributions [en]

9edo

2026-07-24T05:52:16Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! colspan="3" |Notation
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:51:38Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! colspan="3" |Notation
!a
!b
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:47:17Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! Notation
!a
!b
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:46:27Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! Notation
!
!
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:45:19Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! colspan=“3” |Notation
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:44:45Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |[[JI]] approximation
! colspan=“3”|Notation
|-
!7-limit [[Ennealimmal]]-based (accurate)
!Coarse
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[27/25]]
|[[16/15]]
|E
|E
|^Eb
|-
|2
|266.67
|[[7/6]]
|[[8/7]]
|E#, Fb
|Eb, F#
|vF
|-
|3
|400
|[[63/50]]
|[[5/4]]
|F
|F
|F#
|-
|5
|533.33
|[[49/36]]
|[[4/3]], [[11/8]]
|G
|G
|^G
|-
|6
|666.67
|[[72/49]]
|[[3/2]], [[16/11]]
|A
|A
|vA
|-
|6
|800
|[[100/63]]
|[[8/5]]
|B
|B
|Bb
|-
|7
|933.33
|[[12/7]]
|[[7/4]]
|B#, Cb
|Bb, C#
|^B
|-
|6
|1066.67
|[[50/27]]
|[[15/8]]
|C
|C
|vC#
|-
|9
|1200
|[[2/1]]
|
|D
|D
|D
|}

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:29:31Z

CompactStar:

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan=“3”|Notation
|-
!11-limit
!Additional groups
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[16/15]], [[27/25]]
|
|D
|D
|D
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:25:01Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan=“3”|Notation
|-
!11-limit
!Additional groups
!Melodic antidiatonic
!Harmonic antidiatonic
![[36edo]] notation ([[ups and downs notation|ups and downs]])
|-
|0
|0
|[[1/1]]
|
|D
|D
|D
|-
|1
|133.33
|[[1/1]]
|
|D
|D
|D
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T05:19:10Z

CompactStar: /* Intervals and notation */

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan="3" |Notation
! colspan="4" |Name (optional)
|-
!Very rough [[11-limit]] JI ([[patent val]])
!Additional groups
!Melodic antidiatonic notation
![[36edo]] subset [[ups and downs notation]]
!
!System 1 (usually ADIN)
!System 2 (usually ups and downs, if meaningfully different)
!System 3 (usually neutral diatonic, if different)
!
|-
|0
|0
|[[1/1]]
|
|D
|D
|
|
|...
|...
|...
|-
|...
|...
|...
|...
|...
|...
|...
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T04:56:32Z

CompactStar:

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

9edo is probably best known for its very flat, muddy-sounding [[fifth]] interval and [[antidiatonic]] (2L 5s) scale, a version of the diatonic scale with inverted harmonic properties (such as major and minor intervals being flipped) when you use the circle of fifths. It does not represent small [[harmonic series|harmonics]] that well, but it has extremely accurate renditions of the just intonation intervals [[27/25]] and [[7/6]], which forms the basis of an ultra-precise [[regular temperament]] called [[ennealimmal]].

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan="3" |Notation
! colspan="4" |Bame (optional)
|-
!Group 1
!Additional groups
!Notation 1 (usually ups and downs)
!Notation 2 (usually neutral diatonic notation, if different))
!Additional notations
!System 1 (usually ADIN)
!System 2 (usually ups and downs, if meaningfully different)
!System 3 (usually neutral diatonic, if different)
!Additional systems
|-
|0
|XXX
|XX/XX
|XX/XX
|D
|D
|J
|...
|...
|...
|...
|-
|...
|...
|...
|...
|...
|...
|...
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T04:47:06Z

CompactStar:

{{stub}}
UNDER CONSTRUCTION

'''9edo''', or 9 equal divisions of the octave (sometimes called '''9-TET''' or '''9-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/9) = 133.333… [[Cent|cents]] exactly, 9 of which stack to the perfect octave [[2/1]].

[Overview of tuning properties for key intervals]

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|9|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan="3" |Notation
! colspan="4" |Bame (optional)
|-
!Group 1
!Additional groups
!Notation 1 (usually ups and downs)
!Notation 2 (usually neutral diatonic notation, if different))
!Additional notations
!System 1 (usually ADIN)
!System 2 (usually ups and downs, if meaningfully different)
!System 3 (usually neutral diatonic, if different)
!Additional systems
|-
|0
|XXX
|XX/XX
|XX/XX
|D
|D
|J
|...
|...
|...
|...
|-
|...
|...
|...
|...
|...
|...
|...
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==

9edo

2026-07-24T04:45:44Z

CompactStar: Created page with "{{stub}} UNDER CONSTRUCTION '''Xedo''', or X equal divisions of the octave (sometimes called '''X-TET''' or '''X-tone equal temperament'''), is the equal tuning featuring steps of (1200/X) = Y cents exactly, X of which stack to the perfect octave 2/1. [Overview of tuning properties for key intervals] == General theory == === Derivation === [Derivation by equal division of various key intervals or of interval qualities] === JI app..."

{{stub}}
UNDER CONSTRUCTION

'''Xedo''', or X equal divisions of the octave (sometimes called '''X-TET''' or '''X-tone equal temperament'''), is the [[Equal temperament|equal tuning]] featuring steps of (1200/X) = Y [[Cent|cents]] exactly, X of which stack to the perfect octave [[2/1]].

[Overview of tuning properties for key intervals]

== General theory ==

=== Derivation ===
[Derivation by equal division of various key intervals or of interval qualities]

=== JI approximation ===
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]{{Harmonics in ED|0|prime}}

=== Edostep interpretations ===
[Cover these in a list]

=== Intervals and notation ===
{| class="wikitable"
|+
! rowspan="2" |Edostep
! rowspan="2" |Cents
! colspan="2" |Intervals
! colspan="3" |Notation
! colspan="4" |Bame (optional)
|-
!Group 1
!Additional groups
!Notation 1 (usually ups and downs)
!Notation 2 (usually neutral diatonic notation, if different))
!Additional notations
!System 1 (usually ADIN)
!System 2 (usually ups and downs, if meaningfully different)
!System 3 (usually neutral diatonic, if different)
!Additional systems
|-
|0
|XXX
|XX/XX
|XX/XX
|D
|D
|J
|...
|...
|...
|...
|-
|...
|...
|...
|...
|...
|...
|...
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
|
|
|}
[Add solfege in a separate table, if applicable]

== Tempering properties ==

=== Tempered commas ===
[List commas with S-expressions and examples of what they equate]

=== Arithmetic progressions ===

=== Notable structural chains ===
[Generator chains]

== Compositional theory ==

=== Tertian structure ===
[Describe]
{| class="wikitable"
|+Thirds in Xedo
!Quality ([[ADIN]])
|'''Mosdiatonic Quality'''
|Quality
|-
!Cents
|'''XXX'''
|XXX
|-
!Just interpretation
|'''X/X'''
|X/X
|-
!Steps
|'''X'''
|X
|}
Diatonic thirds are bolded.

=== Scales ===
[if edo is composite, link to subset edos and discuss scales of subset edos there]

[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]

[Explain more complex scale theory topics here]

==== Tables of scales ====

=== Harmony ===
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]

[Explain systems of harmony here, this is how you put the chords together to make music]

[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]

[Use individual voices maybe?]

==== Tables of chords ====

== Instruments ==
[Put instruments and isomorphic layouts here]

== Supersets and subsets ==

== Comparisons to other tuning systems ==

== Music in Xedo ==

== See also ==