7L 3s: Difference between revisions

(11 intermediate revisions by 5 users not shown)

Line 1:

7L 3s represents ~~temperaments~~ such as [[mohajira]]/[[mohaha]]/[[mohoho]], among others, whose generators are around a neutral ~~3rd~~. The [[Mohaha7|seven]] and [[Mohaha10|ten-note]] forms of mohaha/mohoho form a [[Chromatic pairs#Mohaha|chromatic pair]].

7L 3s represents [[temperament]]s such as [[mohajira]]/[[mohaha]]/[[mohoho]], among others, whose generators are around a neutral third. The [[Mohaha7|seven]] and [[Mohaha10|ten-note]] forms of mohaha/mohoho form a [[Chromatic pairs#Mohaha|chromatic pair]].

==Name==

== Name ==

TAMNAMS ~~suggests the temperament-agnostic~~ name ~~'''dicoid''' (from dicot, an exotemperament) for the name of this scale.~~

==~~Intervals and degrees~~==

== Scale properties ==

~~:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''~~

Names for this scale's [[degrees]], the positions of the scale's tones, are called '''mosdegrees'''. Its [[Interval|intervals]], the pitch difference between any two tones, are based on the number of large and small steps between the two tones and are thus called '''mossteps'''. Per TAMNAMS, both mosdegrees and mossteps are ''0-indexed'', and may be referred to as '''dicodegrees''' and '''dicosteps'''. Ordinal names, such as mos-1st instead of 0-mosstep, are discouraged for non-diatonic MOS scales.

~~==Theory==~~

=== ~~Presence of neutral~~ intervals ===

=== Intervals ===

7L 3s combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals, thus making it compatible with Arabic and Turkish scales, but not with traditional Western scales. Notable intervals include:

*The '''perfect 3-mosstep''', the scale's dark generator, whose range is around that of a neutral third.

*The '''perfect 7-mosstep''', the scale's bright generator, the inversion of the perfect 3-mosstep, whose range is around that of a neutral sixth.

=== Generator chain ===

*The '''minor mosstep''', or '''small step''', which ranges form a quartertone to a minor second.

* The '''major mosstep''', or '''large step''', which ranges from a submajor second to a [[sinaic]] or trienthird (around ~~128¢~~).

*The '''major 4-mosstep''', whose range coincides with that of a perfect fourth;

=== Modes ===

*The '''minor 6-mosstep''', the inversion of the major 4-mosstep, whose range coincides with that of a perfect 5th.

== Theory ==

=== Neutral intervals ===

7L 3s combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals, thus making it compatible with [[Arabic, Turkish, Persian|Arabic]] and [[Arabic, Turkish, Persian|Turkish]] scales, but not with traditional Western scales. Notable intervals include:

* The '''perfect 3-mosstep''', the scale's dark generator, whose range is around that of a neutral third.

* The '''perfect 7-mosstep''', the scale's bright generator, the inversion of the perfect 3-mosstep, whose range is around that of a neutral sixth.

* The '''minor mosstep''', or '''small step''', which ranges form a [[quartertone]] to a minor second.

* The '''major mosstep''', or '''large step''', which ranges from a submajor second to a [[sinaic]], or trienthird (around 128{{c}}).

* The '''major 4-mosstep''', whose range coincides with that of a perfect fourth.

* The '''minor 6-mosstep''', the inversion of the major 4-mosstep, whose range coincides with that of a perfect 5th.

=== Quartertone and tetrachordal analysis===

Due to the presence of quartertone-like intervals, Graham Breed has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L 3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as ''T-t-T-t-T-t-t'', but Breed states that non-MOS patterns are possible, such as ''T-t-t-T-t-t-T''.

Due to the presence of [[quartertone]]-like intervals, [[Graham Breed]] has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L 3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as {{dash|''T, t, T, t, T, t, t''}}, but Breed states that non-MOS patterns are possible, such as {{dash|''T, t, t, T, t, t, T''}}.

Additionally, due to the presence of fourth and fifth-like intervals, 7L 3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones ({{dash|''T'', ''t'', ''t''}}), or an augmented step, small tone, and quartertone ({{dash|''A'', ''t'', ''q''}}).

Additionally, due to the presence of fourth and fifth-like intervals, 7L 3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones (''T''-''t''-''t''), or an augmented step, small tone, and quartertone (''A''-''t''-''q'').

==Scale tree==

{{~~Scale tree~~|~~Comments=~~6/5: [[Restles]] ↑;

{{MOS tuning spectrum

7/5: [[Beatles]];

| 6/5 = [[Restles]] ↑

3/2: [[~~Rastmic_clan#Suhajira |~~ Suhajira]] / ringo;

| 7/5 = [[Beatles]]

12/5: [[Hemif]] / [[hemififths]];

| 3/2 = [[Suhajira]] / ringo

5/2: [[Mohaha]] / [[neutrominant]];

| 12/5 = [[Hemif]] / [[hemififths]]

13/5: [[Hemif]] / [[salsa]] / [[karadeniz]];

| 5/2 = [[Mohaha]] / [[neutrominant]] / [[mohamaq]]

~~8/3: [[Mohaha]] / [[mohamaq]];~~

| 13/5 = [[Hemif]] / [[salsa]] / [[karadeniz]]

4/1: [[Mohaha]] / [[migration]] / [[mohajira]];

| 4/1 = [[Mohaha]] / [[migration]] / [[mohajira]]

6/1: [[Mohaha]] / [[ptolemy]];

| 6/1 = [[Mohaha]] / [[ptolemy]]

13/8: Golden [[suhajira]]}}

| 13/8 = Golden [[suhajira]]

}}

~~== See also==~~

*[http://x31eq.com/7plus3.htm Graham Breed's page on 7L 3s] (which covers 3L 7s to an extent)

== External links==

* [http://x31eq.com/7plus3.htm Graham Breed's page on 7L 3s] (which covers 3L 7s to an extent)

[[Category:10-tone scales]]

@@ Line 1: / Line 1: @@
 {{Infobox MOS}}
 {{MOS intro|Scale Signature=7L 3s}}
-L 3s represents temperaments such as [[mohajira]]/[[mohaha]]/[[mohoho]], among others, whose generators are around a neutral 3rd. The [[Mohaha7|seven]] and [[Mohaha10|ten-note]] forms of mohaha/mohoho form a [[Chromatic pairs#Mohaha|chromatic pair]].
+L&nbsp;3s represents [[temperament]]s such as [[mohajira]]/[[mohaha]]/[[mohoho]], among others, whose generators are around a neutral third. The [[Mohaha7|seven]] and [[Mohaha10|ten-note]] forms of mohaha/mohoho form a [[Chromatic pairs#Mohaha|chromatic pair]].
-==Name==
+== Name ==
-TAMNAMS suggests the temperament-agnostic name '''dicoid''' (from dicot, an exotemperament) for the name of this scale.
+{{TAMNAMS name}}
-==Intervals and degrees==
+== Scale properties ==
-:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''
+{{TAMNAMS use}}
-Names for this scale's [[degrees]], the positions of the scale's tones, are called '''mosdegrees'''. Its [[Interval|intervals]], the pitch difference between any two tones, are based on the number of large and small steps between the two tones and are thus called '''mossteps'''. Per TAMNAMS, both mosdegrees and mossteps are ''0-indexed'', and may be referred to as '''dicodegrees''' and '''dicosteps'''. Ordinal names, such as mos-1st instead of 0-mosstep, are discouraged for non-diatonic MOS scales.
-{{MOS intervals|Scale Signature=7L 3s}}
-==Theory==
-=== Presence of neutral intervals ===
+=== Intervals ===
-L 3s combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals, thus making it compatible with Arabic and Turkish scales, but not with traditional Western scales. Notable intervals include:
+{{MOS intervals}}
-*The '''perfect 3-mosstep''', the scale's dark generator, whose range is around that of a neutral third.
-*The '''perfect 7-mosstep''', the scale's bright generator, the inversion of the perfect 3-mosstep, whose range is around that of a neutral sixth.
+=== Generator chain ===
-*The '''minor mosstep''', or '''small step''', which ranges form a quartertone to a minor second.
+{{MOS genchain}}
-* The '''major mosstep''', or '''large step''', which ranges from a submajor second to a [[sinaic]] or trienthird (around 128¢).
-*The '''major 4-mosstep''', whose range coincides with that of a perfect fourth;
+=== Modes ===
-*The '''minor 6-mosstep''', the inversion of the major 4-mosstep, whose range coincides with that of a perfect 5th.
+{{MOS mode degrees}}
+== Theory ==
+=== Neutral intervals ===
+L 3s combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals, thus making it compatible with [[Arabic, Turkish, Persian|Arabic]] and [[Arabic, Turkish, Persian|Turkish]] scales, but not with traditional Western scales. Notable intervals include:
+* The '''perfect 3-mosstep''', the scale's dark generator, whose range is around that of a neutral third.
+* The '''perfect 7-mosstep''', the scale's bright generator, the inversion of the perfect 3-mosstep, whose range is around that of a neutral sixth.
+* The '''minor mosstep''', or '''small step''', which ranges form a [[quartertone]] to a minor second.
+* The '''major mosstep''', or '''large step''', which ranges from a submajor second to a [[sinaic]], or trienthird (around 128{{c}}).
+* The '''major 4-mosstep''', whose range coincides with that of a perfect fourth.
+* The '''minor 6-mosstep''', the inversion of the major 4-mosstep, whose range coincides with that of a perfect 5th.
 === Quartertone and tetrachordal analysis===
-Due to the presence of quartertone-like intervals, Graham Breed has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L 3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as ''T-t-T-t-T-t-t'', but Breed states that non-MOS patterns are possible, such as ''T-t-t-T-t-t-T''.
+Due to the presence of [[quartertone]]-like intervals, [[Graham Breed]] has proposed the terms ''tone'' (abbreviated as ''t'') and ''quartertone'' (abbreviated as ''q'') as alternatives for large and small steps. This interpretation only makes sense for step ratios in which the small step approximates a quartertone. Additionally, Breed has also proposed a larger tone size, abbreviated using a capital ''T'', to refer to the combination of ''t'' and ''q''. Through this addition of a larger step, 7-note subsets of 7L&nbsp;3s can be constructed. Some of these subsets are identical to that of 3L 4s, such as {{dash|''T, t, T, t, T, t, t''}}, but Breed states that non-MOS patterns are possible, such as {{dash|''T, t, t, T, t, t, T''}}.
+Additionally, due to the presence of fourth and fifth-like intervals, 7L&nbsp;3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones ({{dash|''T'', ''t'', ''t''}}), or an augmented step, small tone, and quartertone ({{dash|''A'', ''t'', ''q''}}).
-Additionally, due to the presence of fourth and fifth-like intervals, 7L 3s can be analyzed as a [[tetrachord|tetrachordal scale]]. Since the major 4-dicostep, the fourth-like interval, is reached using 4 steps rather than 3 (3 tones and 1 quartertone), Andrew Heathwaite offers an additional step ''A'', for ''augmented second'', to refer to the combination of two tones (''t''). Thus, the possible tetrachords can be built as a combination of a (large) tone and two (regular) tones (''T''-''t''-''t''), or an augmented step, small tone, and quartertone (''A''-''t''-''q'').
 ==Scale tree==
-{{Scale tree|Comments=6/5: [[Restles]] ↑;
+{{MOS tuning spectrum
-/5: [[Beatles]];
+| 6/5 = [[Restles]]&nbsp;↑
-/2: [[Rastmic_clan#Suhajira | Suhajira]] / ringo;
+| 7/5 = [[Beatles]]
-/5: [[Hemif]] / [[hemififths]];
+| 3/2 = [[Suhajira]] / ringo
-/2: [[Mohaha]] / [[neutrominant]];
+| 12/5 = [[Hemif]] / [[hemififths]]
-/5: [[Hemif]] / [[salsa]] / [[karadeniz]];
+| 5/2 = [[Mohaha]] / [[neutrominant]] / [[mohamaq]]
-/3: [[Mohaha]] / [[mohamaq]];
+| 13/5 = [[Hemif]] / [[salsa]] / [[karadeniz]]
-/1: [[Mohaha]] / [[migration]] / [[mohajira]];
+| 4/1 = [[Mohaha]] / [[migration]] / [[mohajira]]
-/1: [[Mohaha]] / [[ptolemy]];
+| 6/1 = [[Mohaha]] / [[ptolemy]]
-/8: Golden [[suhajira]]}}
+| 13/8 = Golden [[suhajira]]
+}}
-== See also==
-*[http://x31eq.com/7plus3.htm Graham Breed's page on 7L 3s] (which covers 3L 7s to an extent)
+== External links==
+* [http://x31eq.com/7plus3.htm Graham Breed's page on 7L&nbsp;3s] (which covers 3L&nbsp;7s to an extent)
 [[Category:10-tone scales]]