30edo: Difference between revisions

Line 1:

== Theory ==

~~=== Harmonics ===~~

30edo's [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.

~~{{Harmonics in equal|~~30}}

[[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]

However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.

~~=== RTT ===~~

Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for [[mavila]], which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

~~''See~~ [[~~regular temperament~~]] for ~~more about what all this means and how to use it~~.''

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]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.

=== Odd harmonics ===

~~However, 5\30 is 200~~{{c}}~~, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.~~

Instead of the 18\30 fifth of 720 cents, 30edo 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 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.

=== Subsets and supersets ===

30edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15}} and it is a [[largely composite]] edo.

30edo has subset edos {{EDOs| 1, 2, 3, 5, 6, 10, 15 }} and it is a [[largely composite]] edo.

30edo is the 3rd {{w|primorial}} edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.

Line 300:

Line 297:

== Regular temperament properties ==

=== Rank-2 temperaments ===

~~''See [[regular temperament]] for more about what all this means and how to use it.''~~

As 30edo is largely composite, only 7, 11 and 13 steps create [[MOS scale]]s that cover every interval using one period per octave.

7/30 produces [[No-threes subgroup temperaments#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.

=== Commas ===

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{ED intro}}
 == Theory ==
-=== Harmonics ===
+edo's [[patent val]] is a doubled version of the patent val for [[15edo]] through the 11-limit, so 30 can be viewed as a [[contorted]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.
-{{Harmonics in equal|30}}
 [[File:Plot30.png|alt=plot30.png|thumb|A plot of the Z function around 30.]]
+However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.
-=== RTT ===
+Instead of the 18\30 fifth of 720 cents, 30edo also makes available a 17\30 fifth of 680 cents. This is an ideal tuning for [[mavila]], which tempers out 135/128. When 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
-''See [[regular temperament]] for more about what all this means and how to use it.''
-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]] version of 15. In the 13-limit it supplies the optimal patent val for [[quindecic]] temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|30}}
-However, 5\30 is 200{{c}}, which is a good (and familiar) approximation for 9/8, and hence 30edo can be viewed inconsistently, as having a 9/1 at 95\30 as well as 96\30.
-Instead of the 18\30 fifth of 720 cents, 30edo 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 30edo is used for pelogic, 5\30 can again be used inconsistently as a 9/8.
 === Subsets and supersets ===
-edo has subset edos {{EDOs|1, 2, 3, 5, 6, 10, 15}} and it is a [[largely composite]] edo.
+edo has subset edos {{EDOs| 1, 2, 3, 5, 6, 10, 15 }} and it is a [[largely composite]] edo.
 edo is the 3rd {{w|primorial}} edo, being the product of first three primes and thus the smallest number with three distinct prime factors. As a corollary, 30edo is the smallest EDO that supports [[perfectly balanced]] scales that are minimal and not equally spaced. See the article on perfect balance.
@@ Line 300: / Line 297: @@
 == Regular temperament properties ==
 === Rank-2 temperaments ===
-''See [[regular temperament]] for more about what all this means and how to use it.''
 As 30edo is largely composite, only 7, 11 and 13 steps create [[MOS scale]]s that cover every interval using one period per octave.
 /30 produces [[No-threes subgroup temperaments#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]].
 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.
 === Commas ===