Magic Guitar: Difference between revisions

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== Guitars Designed for Magic Temperament ==

[[Magic|Magic Temperament]] is a good, mainstream choice for an unequal guitar fretting. It's almost as simple as [[Meantone]] but with much improved 9-limit harmony. It can be close enough to just intonation to sound clean within the inherent imprecision of a physical guitar. It has well tuned perfect fifths that will be familiar from 12 ~~note equal temperament~~. It can be tuned to 41-edo while minimizing the number of frets spaced by a single step. As it isn't a Meantone, it will have comma problems when playing conventional music. Magic supports full 11-limit harmony with acceptable tuning within the appropriate gamut for a guitar.

[[Magic|Magic Temperament]] is a good, mainstream choice for an unequal guitar fretting. It's almost as simple as [[Meantone]] but with much improved 9-limit harmony. It can be close enough to just intonation to sound clean within the inherent imprecision of a physical guitar. It has well tuned perfect fifths that will be familiar from 12-edo. It can be tuned to 41-edo while minimizing the number of frets spaced by a single step. As it isn't a Meantone, it will have comma problems when playing conventional music. Magic supports full 11-limit harmony with acceptable tuning within the appropriate gamut for a guitar.

=== Fretting Options ===

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=== Standard Tuning ===

Old Spear's standard tuning of the open strings follows the standard guitar tuning, also known as ~~Spanish tuning or~~ EADGBE or EBGDAE, adapted to magic temperament. The highest four strings (corresponding to the strings on a ukulele) are tuned to an Em⁷ chord, giving a poor voicing of Em⁷ on the open strings while allowing for E minor or G major chords across three strings and transpositions on other frets. The low E is naturally two octaves from the high E. This leaves the tuning of the A string wild. It must have a wolf with either E or D. You can choose the tuning for the key you want to play. Either way, some chords won't work with their conventional shapes and others will work but give you no choice about how to resolve comma shifts.

Old Spear's standard tuning of the open strings follows the standard guitar tuning, also known as EADGBE or EBGDAE, adapted to magic temperament. The highest four strings (corresponding to the strings on a ukulele) are tuned to an Em⁷ chord, giving a poor voicing of Em⁷ on the open strings while allowing for E minor or G major chords across three strings and transpositions on other frets. The low E is naturally two octaves from the high E. This leaves the tuning of the A string wild. It must have a wolf with either E or D. You can choose the tuning for the key you want to play. Either way, some chords won't work with their conventional shapes and others will work but give you no choice about how to resolve comma shifts. Of course, the advantage of a standard tuning variant is that you put your fingers roughly where you expect given experience of a standard guitar. With your electronic tuner, make B and E and maybe A about 20 cents flat relative to D and G and maybe A. If tuning to 41-edo, the fifths should also be widened slightly relative to 12-edo, and your ears can probably guide you with this.

In [[Tripod Notation|Tricycle Notation]] with wheel numbers as subscripts, the open strings from the bass are E₂ A D₂ G₃ B₁ E₂. Tuning A as A₃ gives perfect fourths in the bass and places the wolf between A₃ and D₂. Where B is played on the A string, Old Spear's comma-doubled frets give two different tunings a comma apart. An E major chord takes the higher B using the narrowly spaced frets, an E on the D string using the other whole tone fret, and G♯ obviously on the first fret of the G string. A G major chord uses the same pitch. An A minor chord works with the open E and A strings, E on the wider-spaced whole tone fret on the D string, A on the same fret on the G string, and C on the obvious second fret on the B string. An A major chord has three pitches all on the same whole tone fret. A D minor chord can't use the open A string and so is restricted to 4 strings.

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The alternative tuning of A gives E₂ A₁ D₂ G₃ B₁ E₂. The wolf is now between E₂ and A₁. Chords that use B₁ now keep the 10/9 fret on the A string. D chords can be played in tune. A major can be used with the open A string but it means shoving three fingers between the comma-spaced frets. E chords only use the first three frets, so these chord shapes work on 10 different Pengcheng and 13 different Haizhou roots.

E major chords can also be played with an added harmonic seventh fretted to turn B₁ into the semitoe below D₂. The same fret gives a C harmonic seventh chord. In both cases, the approximate 7/6 fret turns a 6 into a 7. Sadly, the standard shape for G7 is inconsistent with a harmonic seventh.

The two tunings of the A string give every pitch of 41-edo between them somewhere on the fretboard.

There are variations of standard tuning that retune the two bass strings to fit the home key and tend not to fret them, giving temporary drones. Logic like this is fine with a magic fretting. If you're going to retune the A string to suit the key, why not go the whole hog and tune them how you like so that you only have 4 strings to think about fretting?

=== Major Thirds Tuning ===

The simplest tuning for magic temperament is to tune the open strings to the 5:4 major third that generates the temperament. This minimizes the discrepancies between the strings. Old Spear considers this to be interesting theoretically but tricky in practice. It uses the same chord shapes as on the first three frets of the Kite Guitar. However, most Kite Guitar chords use more than the first three frets, so Old Spear's magic frettings work better with different tunings.

An alternative is to tune three strings to 5:4 and set pairs of three strings an octave apart. This is simpler yet and corresponds more closely to the lines of Tripod Notation.

=== Open Tunings ===

Open tunings will generally work with a magic guitar. You know that at least one chord will work. The frets are chosen to give approximations to simple JI intervals which means that other notes of the key should be there.

As a variation, you could fret a guitar to just intonation ratios that the magic guitar approximates and then tune the open strings to just intonation. For example, frets at 25/24, 16/15, 10/9, 9/8, 7/6, 6/5, 5/4, 4/3, etc, or equivalents with 225:224 tempered out. This will work for a few chords relative to an open tuning but break some transpositions (in the sense of being a little bit out of tune).

=== Fourths Tuning ===

Sorry, fourths tuning doesn't really work with Magic Temperament. Chaining Fourths like that assumes Meantone. Old Spear's Standard Tunings work because they break the chain low down and keep a major third between G and B. You can also include a wolf in a fourths tuning but doing that breaks the isomorphic pattern you wanted and only complicates matters.

[[Category:Magic]]

[[Category:Guitar]]

[[Category:Skip fretting]]

[[Category:41edo]]

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 == Guitars Designed for Magic Temperament ==
-[[Magic|Magic Temperament]] is a good, mainstream choice for an unequal guitar fretting.  It's almost as simple as [[Meantone]] but with much improved 9-limit harmony.  It can be close enough to just intonation to sound clean within the inherent imprecision of a physical guitar.  It has well tuned perfect fifths that will be familiar from 12 note equal temperament.  It can be tuned to 41-edo while minimizing the number of frets spaced by a single step.  As it isn't a Meantone, it will have comma problems when playing conventional music.  Magic supports full 11-limit harmony with acceptable tuning within the appropriate gamut for a guitar.
+[[Magic|Magic Temperament]] is a good, mainstream choice for an unequal guitar fretting.  It's almost as simple as [[Meantone]] but with much improved 9-limit harmony.  It can be close enough to just intonation to sound clean within the inherent imprecision of a physical guitar.  It has well tuned perfect fifths that will be familiar from 12-edo.  It can be tuned to 41-edo while minimizing the number of frets spaced by a single step.  As it isn't a Meantone, it will have comma problems when playing conventional music.  Magic supports full 11-limit harmony with acceptable tuning within the appropriate gamut for a guitar.
 === Fretting Options ===
@@ Line 13: / Line 13: @@
 === Standard Tuning ===
-Old Spear's standard tuning of the open strings follows the standard guitar tuning, also known as Spanish tuning or EADGBE or EBGDAE, adapted to magic temperament.  The highest four strings (corresponding to the strings on a ukulele) are tuned to an Em⁷ chord, giving a poor voicing of Em⁷ on the open strings while allowing for E minor or G major chords across three strings and transpositions on other frets.  The low E is naturally two octaves from the high E.  This leaves the tuning of the A string wild.  It must have a wolf with either E or D.  You can choose the tuning for the key you want to play.  Either way, some chords won't work with their conventional shapes and others will work but give you no choice about how to resolve comma shifts.
+Old Spear's standard tuning of the open strings follows the standard guitar tuning, also known as EADGBE or EBGDAE, adapted to magic temperament.  The highest four strings (corresponding to the strings on a ukulele) are tuned to an Em⁷ chord, giving a poor voicing of Em⁷ on the open strings while allowing for E minor or G major chords across three strings and transpositions on other frets.  The low E is naturally two octaves from the high E.  This leaves the tuning of the A string wild.  It must have a wolf with either E or D.  You can choose the tuning for the key you want to play.  Either way, some chords won't work with their conventional shapes and others will work but give you no choice about how to resolve comma shifts.  Of course, the advantage of a standard tuning variant is that you put your fingers roughly where you expect given experience of a standard guitar.  With your electronic tuner, make B and E and maybe A about 20 cents flat relative to D and G and maybe A.  If tuning to 41-edo, the fifths should also be widened slightly relative to 12-edo, and your ears can probably guide you with this.
 In [[Tripod Notation|Tricycle Notation]] with wheel numbers as subscripts, the open strings from the bass are E₂ A D₂ G₃ B₁ E₂.  Tuning A as A₃ gives perfect fourths in the bass and places the wolf between A₃ and D₂.  Where B is played on the A string, Old Spear's comma-doubled frets give two different tunings a comma apart.  An E major chord takes the higher B using the narrowly spaced frets, an E on the D string using the other whole tone fret, and G♯ obviously on the first fret of the G string.  A G major chord uses the same pitch.  An A minor chord works with the open E and A strings, E on the wider-spaced whole tone fret on the D string, A on the same fret on the G string, and C on the obvious second fret on the B string.  An A major chord has three pitches all on the same whole tone fret.  A D minor chord can't use the open A string and so is restricted to 4 strings.
@@ Line 25: / Line 25: @@
 The alternative tuning of A gives E₂ A₁ D₂ G₃ B₁ E₂.  The wolf is now between E₂ and A₁.  Chords that use B₁ now keep the 10/9 fret on the A string.  D chords can be played in tune.  A major can be used with the open A string but it means shoving three fingers between the comma-spaced frets.  E chords only use the first three frets, so these chord shapes work on 10 different Pengcheng and 13 different Haizhou roots.
+E major chords can also be played with an added harmonic seventh fretted to turn B₁ into the semitoe below D₂.  The same fret gives a C harmonic seventh chord.  In both cases, the approximate 7/6 fret turns a 6 into a 7.  Sadly, the standard shape for G7 is inconsistent with a harmonic seventh.
+The two tunings of the A string give every pitch of 41-edo between them somewhere on the fretboard.
+There are variations of standard tuning that retune the two bass strings to fit the home key and tend not to fret them, giving temporary drones.  Logic like this is fine with a magic fretting.  If you're going to retune the A string to suit the key, why not go the whole hog and tune them how you like so that you only have 4 strings to think about fretting?
+=== Major Thirds Tuning ===
+The simplest tuning for magic temperament is to tune the open strings to the 5:4 major third that generates the temperament.  This minimizes the discrepancies between the strings.  Old Spear considers this to be interesting theoretically but tricky in practice.  It uses the same chord shapes as on the first three frets of the Kite Guitar.  However, most Kite Guitar chords use more than the first three frets, so Old Spear's magic frettings work better with different tunings.
+An alternative is to tune three strings to 5:4 and set pairs of three strings an octave apart.  This is simpler yet and corresponds more closely to the lines of Tripod Notation.
+=== Open Tunings ===
+Open tunings will generally work with a magic guitar.  You know that at least one chord will work.  The frets are chosen to give approximations to simple JI intervals which means that other notes of the key should be there.
+As a variation, you could fret a guitar to just intonation ratios that the magic guitar approximates and then tune the open strings to just intonation.  For example, frets at 25/24, 16/15, 10/9, 9/8, 7/6, 6/5, 5/4, 4/3, etc, or equivalents with 225:224 tempered out.  This will work for a few chords relative to an open tuning but break some transpositions (in the sense of being a little bit out of tune).
+=== Fourths Tuning ===
+Sorry, fourths tuning doesn't really work with Magic Temperament.  Chaining Fourths like that assumes Meantone.  Old Spear's Standard Tunings work because they break the chain low down and keep a major third between G and B.  You can also include a wolf in a fourths tuning but doing that breaks the isomorphic pattern you wanted and only complicates matters.
+[[Category:Magic]]
 [[Category:Guitar]]
 [[Category:Skip fretting]]
 [[Category:41edo]]