4L 3s: Difference between revisions

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4L 3s can be thought of as a [[Warped diatonic|warped diatonic scale]], because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).

4L 3s has several temperament interpretations:

# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a L/s ratio between 3/2 and 6/5.

# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a L/s ratio between 3 and 2.

# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a L/s ratio between 4 and 3.

There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 notes in the generator chain are not enough to contain the most concordant chords in these temperaments; you would need to use a [[MODMOS]] or use a larger MOS gamut.

== Standing assumptions ==

The [[TAMNAMS]] system is used in this article to name 4L 3s intervals and step size ratios and step ratio ranges.

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== Names ==

The [[TAMNAMS]] MOS naming system (used in this article) uses the name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this pattern. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.

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~~4L 3s has several temperament interpretations:~~

~~# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a L/s ratio between 3/2 and 6/5.~~

~~# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a L/s ratio between 3 and 2.~~

~~# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a L/s ratio between 4 and 3.~~

There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 notes in the generator chain are not enough to contain the most concordant chords in these temperaments; you would need to use a [[MODMOS]] or use a larger MOS gamut.

~~-->~~

== Intervals ==

{| class="wikitable center-all"

@@ Line 12: / Line 12: @@
 L 3s can be thought of as a [[Warped diatonic|warped diatonic scale]], because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).
+L 3s has several temperament interpretations:
+# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a L/s ratio between 3/2 and 6/5.
+# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a L/s ratio between 3 and 2.
+# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a L/s ratio between 4 and 3.
+There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 notes in the generator chain are not enough to contain the most concordant chords in these temperaments; you would need to use a [[MODMOS]] or use a larger MOS gamut.
 == Standing assumptions ==
 The [[TAMNAMS]] system is used in this article to name 4L 3s intervals and step size ratios and step ratio ranges.
@@ Line 23: / Line 31: @@
 == Names ==
 The [[TAMNAMS]] MOS naming system (used in this article) uses the name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this pattern. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.
-<!--
-L 3s has several temperament interpretations:
-# With generator size between 5\18 (333.3c) and 11\39 (338.5c): [[Sixix]], corresponding to a L/s ratio between 3/2 and 6/5.
-# With generator size between 4\15 (320.0c) and 3\11 (327.3c): [[Orgone]], corresponding to a L/s ratio between 3 and 2.
-# With generator size between 5\19 (315.8c) and 4\15 (320.0c): [[Kleismic]], corresponding to a L/s ratio between 4 and 3.
-There are also other temperaments in the 4L 3s range, particularly [[amity]] and [[myna]], but 7 notes in the generator chain are not enough to contain the most concordant chords in these temperaments; you would need to use a [[MODMOS]] or use a larger MOS gamut.
--->
 == Intervals ==
 {| class="wikitable center-all"