User:Moremajorthanmajor/7L 3s (15/7-equivalent): Difference between revisions

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|Tuning=7L 3s<15/7>}}

~~'''~~7L 3s<15/7>~~''' refers to the structure of [[MOSScales|moment of symmetry scales]] built from a 10-tone chain of major thirds:~~

~~L s L L L s L L s L~~

Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:

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==Intervals==

The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a ~~neutral or~~ major third.

The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a major third.

2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s|diatonic]] subminor sixths.

The "large step" will fall between 188.5 cents (1\7) and ~~132~~ cents (1\10), ranging from a small major second to a [[sinaic]].

The "large step" will fall between 188.5 cents (1\7) and 131.9 cents (1\10), ranging from a small major second to a [[sinaic]].

The "small step" will fall between 0 cents and ~~132~~ cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.

The "small step" will fall between 0 cents and 131.9 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.

The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.

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|3L+1s

| -2

|6

|6v

|minor 6-step

|4L+2s

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|-

|8

|6^

|6

|major 6-step

|5L+1s

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The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:

The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].

@@ Line 2: / Line 2: @@
 |Tuning=7L 3s<15/7>}}
-'''7L 3s<15/7>''' refers to the structure of [[MOSScales|moment of symmetry scales]] built from a 10-tone chain of major thirds:
+{{MOS intro|Scale Signature=7L 3s<15/7>}}
-L s L L L s L L s L
 Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:
@@ Line 13: / Line 11: @@
 ==Intervals==
-The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a neutral or major third.
+The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a major third.
 g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s|diatonic]] subminor sixths.
-The "large step" will fall between 188.5 cents (1\7) and 132 cents (1\10), ranging from a small major second to a [[sinaic]].
+The "large step" will fall between 188.5 cents (1\7) and 131.9 cents (1\10), ranging from a small major second to a [[sinaic]].
-The "small step" will fall between 0 cents and 132 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.
+The "small step" will fall between 0 cents and 131.9 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.
 The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.
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 |3L+1s
 | -2
-|6
+|6v
 |minor 6-step
 |4L+2s
@@ Line 109: / Line 107: @@
 |-
 |8
-|6^
+|6
 |major 6-step
 |5L+1s
@@ Line 196: / Line 194: @@
 The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:
-{{Scale tree|7L 3s <15/7>}}
+{{MOS tuning spectrum|Scale Signature=7L 3s <15/7>}}
 The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].