5L 5s: Difference between revisions

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There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo|5edo]], and the generator reaches intervals of 5 ~~like~~ 6/5, 5/4, or 7/5.

There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29|blackwood]], in which intervals of the prime numbers [[3/1|3]] and [[7/1|7]] are all represented using steps of [[5edo|5edo]], and the generator reaches intervals of [[5/1|5]], such as [[6/5]], [[5/4]], and [[7/5]].

In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration [[MODMOS]]ses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

== Intervals ==

== Scale properties ==

=== Intervals ===

==Modes==

=== Modes ===

== Scale tree ==

=== Scale tree ===

{{MOS tuning spectrum

| 6/5 = Qintosec ↑

| 6/5 = [[Qintosec]] ↑

| 7/5 = Warlock

| 7/5 = [[Warlock]]

| 13/8 = Unnamed golden tuning

| 13/8 = Unnamed golden tuning (148.328{{c}})

| 7/4 = Quinkee

| 7/4 = [[Quinkee]]

| 2/1 = ~~Blacksmith is~~ optimal around here

| 2/1 = [[Blackwood]] (optimal around here)

| 9/4 = Trisedodge

| 9/4 = [[Trisedodge]]

| 13/5 = Unnamed golden tuning

| 13/5 = Unnamed golden tuning (173.666{{c}})

| 6/1 = Cloudtone ↓

| 6/1 = [[Cloudtone]] ↓

}}

[[Category:Pentawood| ]]

[[Category:Pentawood| ]]

[[Category:10-tone scales]]

~~~~

@@ Line 10: / Line 10: @@
 {{MOS intro}}
-There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo|5edo]], and the generator reaches intervals of 5 like 6/5, 5/4, or 7/5.
+There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29|blackwood]], in which intervals of the prime numbers [[3/1|3]] and [[7/1|7]] are all represented using steps of [[5edo|5edo]], and the generator reaches intervals of [[5/1|5]], such as [[6/5]], [[5/4]], and [[7/5]].
-In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.
+In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration [[MODMOS]]ses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.
-== Intervals ==
+== Scale properties ==
+{{TAMNAMS use}}
+=== Intervals ===
 {{MOS intervals}}
-==Modes==
+=== Modes ===
 {{MOS mode degrees}}
-== Scale tree ==
+=== Scale tree ===
 {{MOS tuning spectrum
-| 6/5 = Qintosec&nbsp;↑
+| 6/5 = [[Qintosec]]&nbsp;↑
-| 7/5 = Warlock
+| 7/5 = [[Warlock]]
-| 13/8 = Unnamed golden tuning
+| 13/8 = Unnamed golden tuning (148.328{{c}})
-| 7/4 = Quinkee
+| 7/4 = [[Quinkee]]
-| 2/1 = Blacksmith is optimal around here
+| 2/1 = [[Blackwood]] (optimal around here)
-| 9/4 = Trisedodge
+| 9/4 = [[Trisedodge]]
-| 13/5 = Unnamed golden tuning
+| 13/5 = Unnamed golden tuning (173.666{{c}})
-| 6/1 = Cloudtone&nbsp;↓
+| 6/1 = [[Cloudtone]]&nbsp;↓
 }}
-[[Category:Pentawood| ]]
+[[Category:Pentawood| ]] <!-- main article -->
 [[Category:10-tone scales]]
- <!-- main article -->