Xenharmonic Wiki

30edo: Difference between revisions

← Older editNewer edit →

Xenwolf (talk | contribs)

5 user groups
8,705 edits
VisualWikitext
Yourmusic Productions (talk | contribs)
autopatrolled, emailconfirmed
2,059 edits
m the the rain in spain falls mainly on the the plain.
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
linked to the scl info we already have; remove headings for scales of rank 2 temperament, as soon as there are more to distinguish, feel free to re-add headings :)
Line 1: Line 1:
__FORCETOC__
'''30edo''', the '''30 equal division''', divides the octave into 30 equal steps of precisely 40 cents each.  
= Theory =
 
The ''30 equal division'' divides the octave into 30 equal steps of precisely 40 cents each. Its [[Patent_val|patent val]] is a doubled version of the patent val for [[15edo|15edo]] through the 11-limit, so 30 can be viewed as a [[contorted|contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic_clan#Quindecic|quindecic temperament]].
== Theory ==
Its [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted|contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[Trienstonic_clan#Quindecic|quindecic temperament]].


However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
However, 5\30 is 200 cents, which is a good (and familiar) approximation for 9/8, and hence 30 can be viewed inconsistently, as having a 9' at 95\30 as well as a 9 at 96\30. Instead of the 18\30 fifth of 720 cents, 30 also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for pelogic (5-limit mavila), which tempers out 135/128. When 30 is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
Line 9: Line 10:
[[File:plot30.png|alt=plot30.png|plot30.png]]
[[File:plot30.png|alt=plot30.png|plot30.png]]


=Intervals=
== Intervals ==


{| class="wikitable"
{| class="wikitable"
|-
|-
! | '''Step'''
! Step
! | '''Cents'''
! Cents
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs]][[Ups_and_Downs_Notation| notation]]
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs]][[Ups_and_Downs_Notation| notation]]
|-
|-
Line 204: Line 205:
|}
|}


=Rank Two Temperaments=
== Rank Two Temperaments ==


As 30edo is highly composite, only 7, 11 and 13 steps create mode of symmetry scales that cover every interval using one period per octave. 7/30 produces [[Chromatic_pairs#Lovecraft|Lovecraft]], in which 2 generators is a moderately sharp [[11/8]], 3 a near perfect [[13/8]] and 5 the familiar mildly flat [[9/8]] from [[12edo]], creating the possibility of ignoring the 3rd & 5th entirely to use those harmonics as the primary building blocks of harmony in a similar way to [[orgone]]. 11 produces a flat [[sensi]] scale. 13 is an excellent higher order [[Pelogic_family#Mavila|Mavila]] tuning that functions the closest to the familiar diatonic scale you can get in this edo.  
As 30edo is highly composite, only 7, 11 and 13 steps create mode of symmetry scales that cover every interval using one period per octave. 7/30 produces [[Chromatic_pairs#Lovecraft|Lovecraft]], in which 2 generators is a moderately sharp [[11/8]], 3 a near perfect [[13/8]] and 5 the familiar mildly flat [[9/8]] from [[12edo]], creating the possibility of ignoring the 3rd & 5th entirely to use those harmonics as the primary building blocks of harmony in a similar way to [[orgone]]. 11 produces a flat [[sensi]] scale. 13 is an excellent higher order [[Pelogic_family#Mavila|Mavila]] tuning that functions the closest to the familiar diatonic scale you can get in this edo.  


=Scales=
; MOS scales:
 
=MOS scales=
Lovecraft[5] - 77772
 
Lovecraft[9] - 525252522
 
Lovecraft[13] - 3223223223222
 
Lovecraft[17] - 22221222122212221
 
Sensi[5] - 83838
 
Sensi[8] - 53353353
 
Sensi[11] - 33323332332
 
Sensi[19] - 2121212212121221212
 
Mavila[5] - 94944
 
Mavila[7] - 5445444
 
Mavila[9] - 444414441
 
Mavila[16] - 3131313113131311
 
Mavila[23] - 21121121121112112112111
 


* [[Lovecraft5|Lovecraft[5]]] - 77772
* [[Lovecraft9|Lovecraft[9]]] - 525252522
* [[Lovecraft13|Lovecraft[13]]] - 3223223223222
* Lovecraft[17] - 22221222122212221
* [[Sensi5|Sensi[5]]] - 83838
* [[Sensi8|Sensi[8]]] - 53353353
* [[Sensi11|Sensi[11]]] - 33323332332
* [[Sensi19|Sensi[19]]] - 2121212212121221212
* Mavila[5] - 94944
* Mavila[7] - 5445444
* Mavila[9] - 444414441
* Mavila[16] - 3131313113131311
* Mavila[23] - 21121121121112112112111


=Commas=
== Commas ==
30 EDO tempers out the following [[commas]]. (Note: This assumes the val < 30 48 70 84 104 111 | .)
30 EDO tempers out the following [[commas]]. (Note: This assumes the val < 30 48 70 84 104 111 | .)


Line 429: Line 415:
|}
|}


=Music=
== Music ==


[http://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces Fifteen Short Pieces] by Todd Harrop
[http://spectropolrecords.bandcamp.com/track/todd-harrop-fifteen-short-pieces Fifteen Short Pieces] by Todd Harrop


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:inconsistent]]
[[Category:Inconsistent]]
[[Category:pelogic]]
[[Category:Pelogic]]
[[Category:todo:unify_precision]]
[[Category:Zeta]]
[[Category:zeta]]
 
{{Todo
| unify precision
| cleanup
}}
Retrieved from "https://en.xen.wiki/w/30edo"