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User:VectorGraphics/Latitude: Difference between revisions

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Medial pairs with a higher latitude than ±45° tend to sound more dissonant against the axis or root than lower-latitude medials, and extremely low-latitude interval pairs may not sound distinct from each other. Higher latitude enables "cross-tonality", where both intervals in the pair can be played at once in the same chord, as in suspended or [[Arto and tendo theory|arto/tendo]] chords.
Medial pairs with a higher latitude than ±45° tend to sound more dissonant against the axis or root than lower-latitude medials, and extremely low-latitude interval pairs may not sound distinct from each other. Higher latitude enables "cross-tonality", where both intervals in the pair can be played at once in the same chord, as in suspended or [[Arto and tendo theory|arto/tendo]] chords.


Here is a table of the latitude of medials up to ±45° in various EDOs, with respect to their fifth as the axis:
Here is a table of the latitude of medials up to ±30° in various EDOs, with respect to their fifth as the axis:
 
{| class="wikitable"
!Fifth size in edosteps
!Edos
!Latitude (±n°)
|-
|3
|5
|30
|-
|4
|7
|0
|-
|5
|9
|18
|-
|6
|10
|0, 30
|-
|7
|12
|12.8
|-
|8
|13, 14
|0, 22.5
|-
|9
|15, 16
|10, 30
|-
|10
|17, 18
|0, 18
|-
|11
|18, 19
|8.2, 24.5
|-
|13
|22, 23
|6.9, 20.8
|-
|14
|23, 24, 25
|0, 12.8, 25.7
|-
|15
|25, 26, 27
|6, 18, 30
|-
|16
|26, 27, 28
|0, 11.3, 22.5
|-
|17
|28, 29, 30
|5.3, 15.9, 26.5
|-
|18
|30, 31, 32
|0, 10, 20, 30
|-
|20
|33, 34, 35, 36
|0, 9, 18, 27
|-
|24
|39, 40, 41, 42, 43
|0, 7.5, 15, 22.5, 30
|-
|31
|51, 52, 53, 54, 55, 56
|2.9, 8.7, 14.5, 20.3, 26.1
|}


(rescue table from earlier revision)
== Latitude-based interval regions ==
== Latitude-based interval regions ==
Names can be given to intervals based on latitude. A table is provided here for fifths:
Names can be given to intervals based on latitude. A table is provided here for fifths:
{| class="wikitable"
{| class="wikitable"
|+
|+
!Contrastiveness
!Latitude
!Major name
!Major name
!Minor name
!Minor name
Line 25: Line 100:
!Type
!Type
|-
|-
|0% to 2.9%
|±0 to 3°
|(Tendo)-neutral third
|(Tendo)-neutral third
|(Arto)-neutral third
|(Arto)-neutral third
Line 31: Line 106:
| rowspan="7" |Third
| rowspan="7" |Third
|-
|-
|2.9% to 7.1%
|±3 to 7°
|Submajor third
|Submajor third
|Supraminor third
|Supraminor third
|Intraclassical thirds
|Intraclassical thirds
|-
|-
|7.1% to 12.9%
|±7 to 12°
|Classical major third
|Classical major third
|Classical minor third
|Classical minor third
|Classical thirds
|Classical thirds
|-
|-
|12.9% to 17.1%
|±12 to 16°
|Pythagorean major third
|Pythagorean major third
|Pythagorean minor third
|Pythagorean minor third
|Pythagorean thirds
|Pythagorean thirds
|-
|-
|17.1% to 21.4%
|±16 to 20°
|Neogothic major third
|Neogothic major third
|Neogothic minor third
|Neogothic minor third
|Neogothic thirds
|Neogothic thirds
|-
|-
|21.4% to 25.7%
|±20 to 24°
|Septimal major third, supermajor third
|Septimal major third, supermajor third
|Septimal minor third, subminor third
|Septimal minor third, subminor third
|Septimal thirds
|Septimal thirds
|-
|-
|25.7% to 30%
|±24 to 28°
|Tendo third, ultramajor third
|Tendo third, ultramajor third
|Arto third, inframinor third
|Arto third, inframinor third
|Tridecimal thirds/[[Interseptimal interval|interseptimals]]
|Tridecimal thirds/[[Interseptimal interval|interseptimals]]
|-
|-
|30% to 35.7%
|±28 to 32°
|Major paraslendric
|Major paraslendric
|Minor paraslendric
|Minor paraslendric
Line 67: Line 142:
| rowspan="6" |Second/fourth
| rowspan="6" |Second/fourth
|-
|-
|35.7% to 40%
|±32 to 36°
|Supraslendric
|Supraslendric
|Subslendric
|Subslendric
|Extraslendrics
|Extraslendrics
|-
|-
|40% to 44.3%
|±36 to 40°
|Major suspended
|Major suspended
|Minor suspended
|Minor suspended
|Suspendeds
|Suspendeds
|-
|-
|44.3% to 47.1%
|±40 to 44°
|Suprasuspended
|Suprasuspended
|Subsuspended
|Subsuspended
|Extrasuspendeds
|Extrasuspendeds
|-
|-
|47.1% to 52.9%
|±44 to 48°
|Major paratetracot
|Major paratetracot
|Minor paratetracot
|Minor paratetracot
|Paratetracots
|Paratetracots
|-
|-
|>52.9%
|Beyond ±48°
| colspan="3" | -
| colspan="3" | -
|}
|}


Diatonic and antidiatonic fifths can also be categorized by the contrastiveness of the medials they generate:
Diatonic and antidiatonic fifths can also be categorized by the latitude of the medials they generate:
{| class="wikitable"
{| class="wikitable"
|Third type
|Third type
Line 100: Line 175:
|Interseptimal
|Interseptimal
|Inframedio
|Inframedio
|654.6-661.4
|654.6-660.5
|11edo
|11edo
|-
|-
|Septimal
|Septimal
|Avila
|Avila
|661.4-665.3
|660.5-664.6
|29edo
|29edo
|-
|-
|Neogothic
|Neogothic
|Pelogic
|Pelogic
|665.3-669.3
|664.6-668.7
|9edo
|9edo
|-
|-
|Pythagorean
|Pythagorean
|Mediocratic
|Mediocratic
|669.3-673.3
|668.7-672.9
|25edo
|25edo
|-
|-
|Classical
|Classical
|Mavila
|Mavila
|673.3-678.7
|672.9-678.2
|16edo
|16edo
|-
|-
|Intraclassical
|Intraclassical
|Sharpmavila
|Sharpmavila
|678.8-682.9
|678.2-682.5
|30edo
|30edo
|-
|-
|Neutral
|Neutral
|Neutral
|Neutral
|682.9-688.5
|682.5-689
|7edo
|7edo
|-
|-
|Intraclassical
|Intraclassical
|Flattone
|Flattone
|688.5-692.8
|689-693.4
|26edo
|26edo
|-
|-
|Classical
|Classical
|Meantone
|Meantone
|692.8-698.5
|693.4-699
|19edo
|19edo
|-
|-
|Pythagorean
|Pythagorean
|Pythagorean
|Pythagorean
|698.5-702.9
|699-703.6
|12edo
|12edo
|-
|-
|Neogothic
|Neogothic
|Neogothic
|Neogothic
|702.9-707.3
|703.6-708.2
|17edo
|17edo
|-
|-
|Septimal
|Septimal
|Archy
|Archy
|707.4-711.9
|708.2-712.8
|22edo
|22edo
|-
|-
|Interseptimal
|Interseptimal
|Ultrapyth
|Ultrapyth
|711.9-720
|712.8-720
|5edo
|5edo
|}
|}
Line 167: Line 242:
[[Category:Terms]]
[[Category:Terms]]


== Superparticular triads ==
== Triads ==
A superparticuar triad, such as 3:4:5 or 4:5:6, is always "major"; how major it is can be characterized by latitude.
Just triads containing arithmetic frequency divisions are always "major"; how major it is can be characterized by latitude.
{| class="wikitable"
|+
!Name
!Triad
!Latitude of medial
|-
|
|1:3:5
|32.8°
|-
|
|1:2:3
|23.5°
|-
|
|3:5:7
|18.5°
|-
|
|2:3:4
|15.3°
|-
|
|5:7:9
|13°
|-
|Inverted major triad
|3:4:5
|11.4°
|-
|
|7:9:11
|10.1°
|-
|Major triad
|4:5:6
|9.1°
|-
|
|9:11:13
|8.2°
|-
|
|5:6:7
|7.5°
|-
|
|11:13:15
|7°
|-
|Quartal triad
|6:7:8
|6.5°
|-
|
|13:15:17
|6°
|-
|
|7:8:9
|5.6°
|-
|
|15:17:19
|5.3°
|-
|
|8:9:10
|5°
|}
Retrieved from "https://en.xen.wiki/w/User:VectorGraphics/Latitude"