Magic Guitar - Revision history

X31eq: Maybe EADGBE is only known as Spanish tuning to me

2021-06-20T08:18:22Z

Maybe EADGBE is only known as Spanish tuning to me

← Older revision		Revision as of 08:18, 20 June 2021
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	=== Standard Tuning ===		=== 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. 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.		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.		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.

X31eq: Actually say how to tune it

2021-05-17T05:54:55Z

Actually say how to tune it

← Older revision		Revision as of 05:54, 17 May 2021
Line 13:		Line 13:
	=== Standard Tuning ===		=== 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. 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.		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. 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.		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.

X31eq: typo

2021-05-17T05:39:51Z

typo

← Older revision		Revision as of 05:39, 17 May 2021
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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.		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 inconsistent with a harmonic seventh.		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.		The two tunings of the A string give every pitch of 41-edo between them somewhere on the fretboard.

X31eq: Add magic category

2021-05-16T16:02:08Z

Add magic category

← Older revision		Revision as of 16:02, 16 May 2021
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	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.		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:Guitar]]
	[[Category:Skip fretting]]		[[Category:Skip fretting]]
	[[Category:41edo]]		[[Category:41edo]]

X31eq: Say why to look at standard tuning

2021-05-16T16:00:14Z

Say why to look at standard tuning

← Older revision		Revision as of 16:00, 16 May 2021
Line 13:		Line 13:
	=== Standard Tuning ===		=== 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 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. 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.

	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.		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.

X31eq: Consistent use of n-edo

2021-05-16T15:57:51Z

Consistent use of n-edo

← Older revision		Revision as of 15:57, 16 May 2021
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	== Guitars Designed for Magic Temperament ==		== 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 ===		=== Fretting Options ===

X31eq: More tunings

2021-05-16T15:56:43Z

More tunings

@@ Line 26: / Line 26: @@
 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 inconsistent with a harmonic seventh.
 [[Category:Guitar]]
 [[Category:Skip fretting]]
 [[Category:41edo]]

X31eq: A bit on harmonic sevenths

2021-05-16T15:41:37Z

A bit on harmonic sevenths

← Older revision		Revision as of 15:41, 16 May 2021
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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.		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 inconsistent with a harmonic seventh.

	[[Category:Guitar]]		[[Category:Guitar]]
	[[Category:Skip fretting]]		[[Category:Skip fretting]]
	[[Category:41edo]]		[[Category:41edo]]

X31eq: More on standard tuning

2021-05-16T15:31:22Z

X31eq: Basic page on magic tempered guitars

2021-05-16T14:14:57Z

Basic page on magic tempered guitars

New page

== 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.

=== Fretting Options ===

A simple Magic fretting can follow either a 19 note (Pengcheng) or 22 note (Haizhou) MOS. A Pengcheng fretting is good ergonomically because the frets will be spaced at intervals of (approximately) two or three steps from 41-edo. It is poor for playing diatonic music because it allows for no comma shifts. A Haizhou fretting has a few frets spaced a comma apart and still allows the 19 notes of the Pengcheng scale to be played on frets spaced a semitoe, 2 steps from 41-edo, apart.

Most frets on either a Haizhou or Pengcheng are spaced a semitoe apart. In both cases, there are three discontinuities to an octave. An isomorphic fretting with equal semitoes right down the neck is possible. In the general case, each string sits on a different foot of [[Tripod Notation]]. With equal temperament, a string can morph from one foot to another to become a skip fretting. Given 41-edo, this leads to a fret spacing of 2 steps from 41-edo or 20½-edo or the [[Kite Guitar]].

[[Category:Guitar]]
[[Category:Skip fretting]]
[[Category:41edo]]