Kite Guitar originals: Difference between revisions

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===Note names ===

The octave is divided into 41 equal steps, a tuning called 41-equal or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:

The octave is divided into 41 equal steps, a tuning called '''41-equal''' or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:

{| class="wikitable center-all"

|+

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In the table above, D is the '''anchor note''' that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But C, G, A and E have also been used.

Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.

Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. Thus 4 arrows = a sharp. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.

~~{| class="wikitable left-3 center-all"~~

|+

A major 2nd is 7 arrows. In this table, the plain notes are bolded.

~~!arrows~~

~~!frets~~

~~!interval~~

~~!equivalence~~

|-

|1

~~|half a fret~~

~~|a quarter-sharp/flat or a desc. dim 2nd~~

~~|^C = B#~~

|-

|2

~~| 1 fret~~

~~|half a sharp/flat~~

~~|^^C = vvC#~~

|-

|3

~~| 1.5 frets~~

~~|a minor 2nd~~

~~|^^^C = Db~~

|-

~~| 4~~

~~|2 frets~~

~~| 1 sharp/flat = an augmented unison~~

~~|^^^^C = C#~~

|}

~~Since a minor 2nd and an augmented unison add up to a~~ major 2nd~~, there are~~ 7 arrows ~~from C to D~~. In this table, the plain notes are bolded.

{| class="wikitable center-all"

|+

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The interval from C# to Db is a diminished 2nd. Since this interval is 0¢ in 12-equal, musicians don't think about it much. But in 41-equal, a diminished 2nd is actually -30¢, and a <u>descending</u> dim 2nd = 1 arrow.

{| class="wikitable left-3 center-all"

|+

!arrows

!frets

!interval

!equivalence

|-

|1

|half a fret

|a quarter-sharp or a descending dim 2nd

|^C = B#

|-

|2

| 1 fret

|half a sharp

|^^C = vvC#

|-

|3

| 1.5 frets

|a minor 2nd

|^^^C = Db

|-

| 4

|2 frets

| 1 sharp, i.e. an augmented unison

|^^^^C = C#

|}

In 12-equal, there are 3 "versions" of a note, for example Db, D and D# (not counting the occasional Dbb or D##). In 41-equal, there are 15 versions, running from vvDb to ^^D# (counting ^^Db and vvD separately even though they are the same note, likewise with ^^D and vvD#).

{| class="wikitable right-all"

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vD vE F vG vA Bb C vD

|}

Upmajor and downminor work similarly.

The quadruple stack always has the exact same shape: two above and two below. This unchanging shape enables one to parse the stack as a whole. The only question is whether the arrows point up or down, and whether they are single or double. The triple stack (two above, one below) can likewise be parsed as a whole.

The quadruple stack always has the exact same shape: two below and two above. Likewise, the triple stack is always one below, two above. The only differences are whether the arrows point up or down, and whether they are single or double. The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's ~~quite~~ easy to deduce the tonic. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.

The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's easy to deduce the tonic from either stack. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.

Modal key signatures are possible, e.g. G downmixolydian is G A vB C D vE vF G.

@@ Line 40: / Line 40: @@
 ===Note names ===
-The octave is divided into 41 equal steps, a tuning called 41-equal or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:
+The octave is divided into 41 equal steps, a tuning called '''41-equal''' or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:
 {| class="wikitable center-all"
 |+
@@ Line 80: / Line 80: @@
 In the table above, D is the '''anchor note''' that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But C, G, A and E have also been used.
-Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.
+Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. Thus 4 arrows = a sharp. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.
-{| class="wikitable left-3 center-all"
-|+
+A major 2nd is 7 arrows. In this table, the plain notes are bolded.
-!arrows
-!frets
-!interval
-!equivalence
-|-
-|1
-|half a fret
-|a quarter-sharp/flat or a desc. dim 2nd
-|^C = B#
-|-
-|2
-| 1 fret
-|half a sharp/flat
-|^^C = vvC#
-|-
-|3
-| 1.5 frets
-|a minor 2nd
-|^^^C = Db
-|-
-| 4
-|2 frets
-| 1 sharp/flat = an augmented unison
-|^^^^C = C#
-|}
-Since a minor 2nd and an augmented unison add up to a major 2nd, there are 7 arrows from C to D. In this table, the plain notes are bolded.
 {| class="wikitable center-all"
 |+
@@ Line 140: / Line 114: @@
 The interval from C# to Db is a diminished 2nd. Since this interval is 0¢ in 12-equal, musicians don't think about it much. But in 41-equal, a diminished 2nd is actually -30¢, and a <u>descending</u> dim 2nd = 1 arrow.
+{| class="wikitable left-3 center-all"
+|+
+!arrows
+!frets
+!interval
+!equivalence
+|-
+|1
+|half a fret
+|a quarter-sharp or a descending dim 2nd
+|^C = B#
+|-
+|2
+| 1 fret
+|half a sharp
+|^^C = vvC#
+|-
+|3
+| 1.5 frets
+|a minor 2nd
+|^^^C = Db
+|-
+| 4
+|2 frets
+| 1 sharp, i.e. an augmented unison
+|^^^^C = C#
+|}
 In 12-equal, there are 3 "versions" of a note, for example Db, D and D# (not counting the occasional Dbb or D##). In 41-equal, there are 15 versions, running from vvDb to ^^D# (counting ^^Db and vvD separately even though they are the same note, likewise with ^^D and vvD#).
 {| class="wikitable right-all"
@@ Line 572: / Line 572: @@
 vD vE F vG vA Bb C vD
 |}
 Upmajor and downminor work similarly.
+The quadruple stack always has the exact same shape: two above and two below. This unchanging shape enables one to parse the stack as a whole. The only question is whether the arrows point up or down, and whether they are single or double. The triple stack (two above, one below) can likewise be parsed as a whole.
-The quadruple stack always has the exact same shape: two below and two above. Likewise, the triple stack is always one below, two above. The only differences are whether the arrows point up or down, and whether they are single or double. The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's quite easy to deduce the tonic. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.
+The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's easy to deduce the tonic from either stack. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.
 Modal key signatures are possible, e.g. G downmixolydian is G A vB C D vE vF G.