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[[Kite Guitar Exercises|Exercises]] for the [[The Kite Guitar|Kite Guitar]] by [[Kite Giedraitis]], assumes the downmajor tuning. They are for a 6-string guitar, but can be adapted to a 7- or 8-string. Once you master them, there's no need to practice them further, because you'll naturally reinforce these skills in the course of singing and playing actual songs.
[[Kite Guitar Exercises and Techniques|Exercises and techniques]] for the [[The Kite Guitar|Kite Guitar]] by [[Kite Giedraitis]], assumes the downmajor tuning. Highest or top string means thinnest string, lowest or bottom string means thickest string.


== Exercises for Players ==
== Before You Get Your Kite Guitar ==
There are plenty of guitar exercises to make your fingers more agile or strong. They all apply to the Kite Guitar. These exercises help you navigate 41edo better.
You've ordered one, what to do while you wait for it? Learning your way around the major 3rds tuning is half the battle, and you can start right away! Take your 12-equal guitar and tune it in major 3rds as [http://ralphpatt.com/ Ralph Patt] did. Literally try to play everything you know in this tuning. When your Kite guitar arrives, you can jump in and play all the same shapes and patterns, with only slight adjustments for the increased number of frets.
 
== Exercises and Techniques for Players ==
There are plenty of guitar exercises to make your fingers more agile or strong. They all apply to the Kite Guitar. These exercises help you navigate 41-equal better. They are for a 6-string guitar, but can be adapted to a 7- or 8-string. For most of these, once you master them, there's no need to practice them further, because you'll naturally reinforce these skills in the course of singing and playing actual songs.


=== Vocal Exercises ===
=== Vocal Exercises ===
The best way to internalize 41-edo is to sing 41-edo! Get in the habit of singing what you play and playing what you sing.
The best way to internalize 41-equal is to sing 41-equal! Get in the habit of singing what you play and playing what you sing.


Beginning exercises:
Beginning exercises:
Line 15: Line 18:
* Make up your own exercises!
* Make up your own exercises!
Advanced exercises:
Advanced exercises:
* Play and sing a chromatic melody (steps of one fret).
* Play and sing a fretwise (trientonic) melody (steps of one fret).
* Play and sing a microtonal melody (steps of a half-fret).
* Play and sing a microtonal melody (steps of a half-fret).
* Play and sing a melody that uses the mid 2nd and/or the mid 3rd.
* Play and sing a melody that uses the mid 2nd and/or the mid 3rd.
* Play and sing a zigzag chromatic melody: P1 vm2 P1 ^m2 P1 vM2 P1 ^M2  P1.
* Play and sing a zigzag fretwise melody: P1 vm2 P1 ^m2 P1 vM2 P1 ^M2  P1.
* Play and sing a zigzag microtonal melody: P1 ^1 P1 vm2 P1 m2 P1 ^m2 P1 ~2 P1 vM2 P1 M2 P1.
* Play and sing a zigzag microtonal melody: P1 ^1 P1 vm2 P1 m2 P1 ^m2 P1 ~2 P1 vM2 P1 M2 P1.
As before, start by singing along with the guitar, then try singing first and checking yourself later with the guitar.
As before, start by singing along with the guitar, then try singing first and checking yourself later with the guitar.


=== Parallel Thirds ===
=== Parallel Thirds ===
For all your favorite scales, play ascending and descending lines harmonized in 3rds. If the two notes lie on the same string, use the scale's innate fuzziness to move one of the notes a half-fret up or down. The fuzzy notes are bolded:
For all your favorite scales, play ascending and descending lines harmonized in 3rds. If the two notes lie on the same string, use the scale's innate shiftiness to move one of the notes a half-fret up or down. The shifty notes are '''bolded''':
{| class="wikitable"
{| class="wikitable"
|+downmajor scale in descending 3rds
|+downmajor scale in descending 3rds
Line 46: Line 49:
|C
|C
|}
|}
Upminor with a raised 7th at the end, a sort of "macro-fuzziness":
Upminor with a raised 7th at the end, a sort of "macro-shiftiness":
{| class="wikitable"
{| class="wikitable"
|+upminor scale in descending 3rds
|+upminor scale in descending 3rds
Line 142: Line 145:
|G
|G
|}
|}
The harmonic and subharmonic pentatonic scales aren't fuzzy. They have a pleasing variety of intervals.
The harmonic and subharmonic pentatonic scales aren't shifty. They have a pleasing variety of intervals.
{| class="wikitable"
{| class="wikitable"
|+descending harmajor penta-3rds
|+descending harmajor penta-3rds
Line 246: Line 249:
=== Half-fret Bends ===
=== Half-fret Bends ===


The fact that each 41-edo note only occurs on every other string makes certain scales awkward to play, for example scales with pythagorean or neutral 3rds. But for 5-limit or 7-limit scales of low odd-limit, it usually works out that you're forced to move to the next string just about when you would want to anyway. For example, the downmajor scale is P1 -- M2 - vM3 - P4 -- P5 - vM6 -- vM7 - P8. The double dashes indicate where you have to move up a string.
The fact that each 41-equal note only occurs on every other string makes certain scales awkward to play, for example scales with pythagorean 3rds or neutral 3rds. But for 5-limit or 7-limit scales of low odd-limit, it usually works out that you're forced to move to the next string just about when you would want to anyway. For example, the downmajor scale is P1 -- M2 - vM3 - P4 -- P5 - vM6 -- vM7 - P8. The double dashes indicate where you have to move up a string.


There are however two problematic scenarios:  
There are however two problematic scenarios:  
* You're playing the 4th of the scale and you want to hammer on or slide up to the 5th.  
* You're playing the 4th of the scale and you want to hammer on or slide up to the 5th.  
* You run out of strings. You're playing the 4th on the top string, and you want to go up to the 5th (but see also unison leaps below)  
* You run out of strings. You're playing the 4th on the top string, and you want to go up to the 5th. (But see also unison leaps below.)
 
The solution to both issues is to move 3 frets up from the 4th to the down-5th and do a half-fret bend. It's a good idea to practice doing accurate half-fret bends. Here are some exercises that involve playing an off-perfect interval and bending it into tune. No need to practice them all, just find a few that you like.
 
1a) Play a note on the 6th fret and simultaneously play the next higher string open. This is an up-unison. Bend the 6th fret note up a half-fret to make it a unison.
 
1b) Same as 1a, but played up the neck. Put your 1st finger up the neck far enough that 6 frets is not too big a stretch. Put your 4th finger 1 string lower and 6 frets higher. Bend the lower (4th finger) note up.
 
1c) Same as 1b, but your 4th finger is 7 frets up. Bend the lower (1st finger) note up. You'll probably have to pull towards the treble side of the fretboard, instead of the usual push towards the bass side.
 
2a) Play a note on the 5th fret and simultaneously play the next lower string open. This is a down-5th. Bend the 5th fret note up a half-fret to make a perfect 5th. Again, pull don't push.
 
2b) Same as 2a, but played up the neck. Put your 1st finger on any fret. Put your 4th finger 1 string higher and 5 frets higher. Bend the higher (4th finger) note up. Pull don't push.
 
2c) Same as 2b, but your 4th finger is 6 frets up. Bend the lower (1st finger) note up.


The solution to both is to move 3 frets up from the 4th to the down-5th and do a half-fret bend. It's a good idea to practice doing accurate half-fret bends. Here are some exercises that involve playing an off-perfect interval and bending it into tune. No need to practice them all, just find one or two you like.
3a) Play a note on the 7th fret and simultaneously play the open string two strings lower. This is a down-8ve. Bend the 7th fret note up a half-fret to make a perfect 8ve.  


1) Play a note on the 6th fret and simultaneously play the next highest string open. This is an up-unison. Bend the 6th fret note up a half-fret to make it a unison.  
3b) Same as 3a, but played up the neck. Put your 1st finger on any fret. Put your 4th finger 2 strings and 7 frets higher. Bend the higher (4th finger) note up.  


2) Same as #1, but played up the neck. Put your 4th finger up the neck far enough that 6 frets is not too big a stretch. Put your 1st finger 1 string higher and 6 frets back. Bend the lower (4th finger) note up.
3c) Same as 2b, but your 4th finger is 8 frets up. Bend the lower (1st finger) note up.  


3) Same as #2, but your 1st finger is 7 frets back. Bend the higher (1st finger) note up.
4a) Play a note on the 4th fret and simultaneously play the open string two strings higher. This is an up-4th. Bend the 4th fret note up a half-fret to make a perfect 4th.  


4) Put your 1st finger on any fret. Put your 4th finger 5 frets higher on the next string up. Play as an interval, this is a down-5th. Now bend the higher (4th finger) note up half a fret to make a good 3/2.  
4b) Same as 4a, but played up the neck. Put your 1st finger on any fret. Put your 3rd finger 2 strings lower and 4 frets higher. Bend the lower (3rd finger) note up.


5) Put your 4th finger on any fret. Put your 1st finger 2 strings higher and 5 frets lower. This is a down-4th, so bend the higher (1st finger) note up half a fret.
4c) Same as 4b, but your 3rd finger is 5 frets higher. Bend the higher (1st finger) note up.


6) Same as #3, but your 1st finger is only 4 frets lower to make an up-4th. Now bend the lower (4th finger) note up.
Exactly how far you have to push the string sideways depends on your location on the neck. The most amount of travel is needed halfway up the neck, around the 5th dot (the [[KDF Fret Numbering|mid double]] dot). Closer to the nut or the bridge, you'll need less travel. Therefore be sure to include some of the "b" and "c" exercises.


In [[The Kite Guitar|relative tab]], these exercises are unison = (+1,-6.5), 5th = (+1,+5.5) and 4th = (+2,-4.5).
Half-fret bends can be notated in tablature by putting an up before the fret number. For example, exercise 1a can be written x x ^6 0 x x. This is consistent with an up meaning one edostep of 41. (In Musescore, to add an up, select Staff/Part Properties, then Advanced Style Properties, then Show Fingerings In Tablature. Then ups can be entered as fingerings.)


Exactly how far you have to push the string sideways depends on your location on the neck. The most amount of travel is needed halfway up the neck, around the 5th dot. Closer to the nut or the bridge, you'll need less travel.  
In [[The Kite Guitar|relative tab]], exercises 1a, 1b & 1c use the unison at (-1,+^6). Exercises 2a, 2b & 2c use the 5th at (+1,+^5). Exercises 3a, 3b & 3c use the 8ve at (+2,+^7). Exercises 4a, 4b & 4c use the 4th at (+2,-^5).


=== The Circle of 5ths ===
=== The Circle of 5ths ===
Line 279: Line 296:
* Move up a 4th the same way to Gb. This puts you on the 4th string.
* Move up a 4th the same way to Gb. This puts you on the 4th string.
* Move down a 5th by (-2,+1) to return to the 6th string.
* Move down a 5th by (-2,+1) to return to the 6th string.
* Continue cycling through the lowest 3 strings, 6th --> 5th --> 4th --> 6th, until you reach the 4th dot.
* Continue cycling through the lowest 3 strings, 6th --> 5th --> 4th --> 6th, until you reach the 4th dot (mid single).
* Move down a 5th by leaping down 3 dots, which is (0,-12) or (0,-3+0).
* Move down a 5th by leaping down 3 dots, which is (0,-12) or (0,-3+0).
* Continue as before, cycling through the lowest 3 strings and steadily moving up.
* Continue as before, cycling through the lowest 3 strings and steadily moving up.
* Whenever you reach the 4th dot (or overshoot it by 1 fret), leap down as before.
* Whenever you reach the mid single dot (or overshoot it by 1 fret), leap down as before.
After 5 leaps, you should return to where you started.
After 5 leaps, you should return to where you started.


Line 289: Line 306:
Once you get the general idea, test yourself by counting the notes out loud as you go. If you say (or sing) "one" for Ab, "two" for the next note, etc., you should return to Ab just as you say "42", which is after all [[wikipedia:Phrases_from_The_Hitchhiker's_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life,_the_Universe,_and_Everything_(42)|The Answer to the Ultimate Question of Life, the Universe, and Everything]]!  
Once you get the general idea, test yourself by counting the notes out loud as you go. If you say (or sing) "one" for Ab, "two" for the next note, etc., you should return to Ab just as you say "42", which is after all [[wikipedia:Phrases_from_The_Hitchhiker's_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life,_the_Universe,_and_Everything_(42)|The Answer to the Ultimate Question of Life, the Universe, and Everything]]!  


Get to the point where you can play this 42-note bass line in under 15 seconds. The final step is to play an actual chord over each of these bass notes. It can be a v7 chord or an ^m7 chord, or really any chord you want to practice. Use an open voicing for root-6 chords, a close voicing for root-4 chords, and either for root-5 chords.
Get to the point where you can play this 42-note bass line in under 15 seconds. The final step is to play an actual chord over each of these bass notes. It can be a v7 chord or an ^m7 chord, or really any chord you want to practice. Use a close voicing for root-4 chords, a hi3 voicing for root-5 chords, and a hi35 voicing for root-6 chords. (See [[hi-lo notation]].)


If you're really obsessed with music theory, rather than counting to 42, say the actual note names:
If you're really obsessed with music theory, rather than counting to 42, say the actual note names:
Line 307: Line 324:
* vF vC vG vD vA vE vB vF#=Gb
* vF vC vG vD vA vE vB vF#=Gb
* Db Ab
* Db Ab
Because 41 is a prime number, any one of 41edo's intervals will generate a similar circle (except the octave of course).  
Because 41 is a prime number, any one of 41-equal's intervals will generate a similar circle (except the octave of course). 
 
=== Moving by Plain Minor 2nds ===
When translating from 12-equal to 41-equal, one may need to move by a major 2nd in two equal or nearly equal root movements. For example, the 12-equal chords might be IV7 -- #IV7 -- V7 or VIm -- bVIm -- V. Assuming the roots translate to IV, V and vVI, the former will involve splitting a plain major 2nd and the latter, a downmajor 2nd.
 
To split a <u>plain</u> major 2nd, one moves by two frets then jumps to the final chord, e.g. IVv7 -- #IVv7 -- Vv7. Or one jumps to a root two frets from the final chord first, then moves two frets, as in IVv7 -- bVv7 -- Vv7. Either way, this jump is a plain minor 2nd, which is 3 half-frets. Jump up 1 string and back 5 frets, which in relative tab is (+1,-5). Splitting an <u>upmajor</u> 2nd is even easier, since each of the two moves is a simple two-fret move.
 
But splitting a <u>downmajor</u> 2nd in half is trickier. One must jump twice, and one of the jumps must backtrack by 8 frets. If one jump is (+1,-5), the other must be (-1,+8). If descending, they must be (-1,+5) and (+1,-8). This is not very intuitive, and it's worthwhile to practice rapidly executing these two jumps. Since the jumps can come in either order, practice both routes. Start with playing single notes, then play entire chords on each root.
 
* Play a note not too close to the nut or heel and not on the highest or lowest string, for example D on the 5th string, 8th fret
* Jump up (+1,-5) (-1,+8) then jump back down the same way i.e. (+1,-8) (-1,+5), making for example D Eb vE Eb D
* Jump up (-1,+8) (+1,-5) then jump back down the same way
* Repeat both exercises, but descending from D, making D C# ^C C# D
 
Practicing 3 consecutive jumps will train you to split a vm3 into three equal moves (e.g. vbVIIv7 -- vVIv7 -- bVIv7 -- Vv7).
 
* Play a note not too close to the nut and not on the highest or lowest string, for example D on the 5th string, 8th fret
* Jump up (+1,-5) (-1,+8) (+1,-5) then jump back down the same way = D Eb vE vF vE Eb D
* Descending: jump down (-1,+5) (+1,-8) (-1,+5) then jump back up the same way = D C# ^C ^B ^C C# D
 
These two exercises will cover 90-95% of the cases. But for notes near the nut, the backtracking jump must come first.
 
* Play a note near the nut, for example, B on the 5th string, 3rd fret
* Jump up (-1,+8) (+1,-5) (+1,-5) then back down the same way = B C vC# vD vC# C B
 
Ascending from a note on the 1st string requires two backtracking jumps.
 
* Play a note on the 1st string, for example E on the 6th fret
* Jump up (-1,+8) (+1,-5) (-1,+8) then back down the same way = E F Gb vG Gb F E
 
Descending from a note on the lowest string also requires two backtracking jumps. Note that this exercise is impossible if starting on the lowest string too close to the nut, or the 1st string too close to the heel.
 
Multiple ascending backtracking jumps will walk you through a complex zone and put you in the next higher rainbow zone. In general it's better to stay in one rainbow zone. But sometimes you may want to move to a higher range, and this maneuver avoids a large leap (see the next exercise).
 
Moving exclusively by plain minor 2nds and upminor 2nds aka aug unisons = (0,+2) can imitate the sound of 12-equal quite closely. The exact order of the steps doesn't matter too much, just do whatever is comfortable. Try traversing these intervals:
 
* The 4th = 3 m2's + 2 ^m2's
* The 5th = 4 m2 + 3 ^m2
* The 8ve = 7 m2's + 5 ^m2's = the sum of the 4th and 5th
 
To change zones, try traversing the 5th (+1,-5) (0,+2) (-1,+8) (0,+2) (+1,-5) (0,+2) (-1,+8).


=== Leaping by 5ths, 8ves and Unisons ===
=== Leaping by 5ths, 8ves and Unisons ===
Line 314: Line 371:
* Move up one fret to vvA, leap up to vvE and back down.
* Move up one fret to vvA, leap up to vvE and back down.
* Move up to A, leap up and down, move up to ^^A, leap, etc.
* Move up to A, leap up and down, move up to ^^A, leap, etc.
Try to get a steady rhythm going. Keep going up fret by fret until you run out of room, then move down fret by fret. A complimentary exercise starts at Eb on the 4th dot, leaps down to Ab and back up. Then go up one fret and continue.
Try to get a steady rhythm going. Keep going up fret by fret until you run out of room, then move down fret by fret. A complimentary exercise starts at Eb on the mid single dot (4th dot), leaps down to Ab and back up. Then go up one fret and continue.


Leaping up an octave is useful when switching from chording to soloing. Start at the low Ab, leap up (+1,+3+2) to Ab and back down. Go up 1 fret and continue. A complimentary exercise starts high, leaps down and leaps back up. Then go up 1 fret and continue.
Leaping up an octave is useful when switching from chording to soloing. Start at the low Ab, leap up (+1,+3+2) to Ab and back down. Go up 1 fret and continue. A complimentary exercise starts high, leaps down and leaps back up. Then go up 1 fret and continue.
Line 327: Line 384:
If you have enough frets, you can combine any leaping exercise with the circle of 5ths exercise. For example, start at Ab, leap up a 5th or an 8ve, leap back, move up a 4th to Db, leap up and down, move on to Gb, etc. Or start on Ab, leap up an 8ve, move up a 4th to Db, leap down, move up a 4th to Gb, etc.
If you have enough frets, you can combine any leaping exercise with the circle of 5ths exercise. For example, start at Ab, leap up a 5th or an 8ve, leap back, move up a 4th to Db, leap up and down, move on to Gb, etc. Or start on Ab, leap up an 8ve, move up a 4th to Db, leap down, move up a 4th to Gb, etc.


You can leap up an octave using a half-fret bend by a move of (+2,+7.5). Finally, you can combine this with the circle of 5ths exercise by repeatedly leaping up, leaping down, and moving up a 4th.
You can leap up an octave using a half-fret bend by a move of (+2,+^7). Finally, you can combine this with the circle of 5ths exercise by repeatedly leaping up, leaping down, and moving up a 4th.


You can add a vocal exercise to all this by singing what you play.
You can add a vocal exercise to all this by singing what you play.
=== Alternate Fingering Techniques ===
==== Cross-fret barre ====
When looking for a fingering, often a cross-fret barre (aka diagonal barre) is the solution. The closer fret spacing of the Kite guitar makes this much easier than it is on the 12-equal guitar. For example, 4 2 3 1 might be fingered as 3 1 2 1, and 2 4 4 3 1 as 1 3 4 2 1.
==== Harmonics ====
The 3rd harmonic is written in guitar tablature as <12>, meaning the 12th-fret harmonic. The 2nd harmonic falls midway between the 20th and 21st frets, and is written as <^20> or <v21>. The latter is preferable because one must place one's finger just behind the 21st fret, exactly as if the tab were 21. In other words, a guitarist is used to seeing "21" and placing their finger in the proper spot for <v21>. Furthermore ^20 without the angle brackets means bend the 20th-fret note up a half-fret. While ^20 and <^20> do look different, ^20 and <v21> are easier to distinguish.
The 5th harmonic falls between the 6th and 7th fret, but closer to the 7th. It's written here as <6.6> for greater accuracy, but in tablature it will usually be rounded off to <v7>. (In Musescore, to add an up, select Staff/Part Properties, then Advanced Style Properties, then Show Fingerings In Tablature. Then ups can be entered as fingerings.)
Here are all the places harmonics 1-12 occur, excluding those above the 41st fret. Be sure to pluck on an [[wikipedia:Node_(physics)|anti-node]]!
{| class="wikitable"
|+
Harmonics 1-12 on the Kite guitar
!harmonic -->
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
! colspan="2" |11
!12
|-
! rowspan="5" |fret
|open
|<v21>
|<12>
|<v9>
|<6.6>
|<5.4>
|<v5>
|<4>
|<v4>
|<3.1>
|<2.8>
|<17.9>
|<2.6>
|-
|
|
|<v33>
|<41>
|<15.1>
|
|<10>
|<13.9>
|<v8>
|<v11>
|<5.9>
|<23.3>
|<15.9>
|-
|
|
|
|
|<27.1>
|
|<v17>
|<29>
|<v18>
|<35.6>
|<9.4>
|<29.9>
|<25.9>
|-
|
|
|
|
|
|
|<25>
|
|<24>
|
|<13.4>
|<38.4>
|
|-
|
|
|
|
|
|
|<37>
|
|
|
| colspan="2" |
|
|-
!combo
|
|
|
|
|
|2nd + 3rd
|
|
|
|2nd + 5th
| colspan="2" |
|3rd + 4th
|}
The last row of the table indicates combo-harmonics. These let you play a harmonic by node-ing twice. For example, the 6th harmonic can be played by node-ing both the 2nd and 3rd harmonic simultaneously, e.g. <v21> with <12>, or <v21> with <v33>.
These harmonics, along with open strings, provide alternative fingerings for notes on the 13th, 14th and 15th frets:
{| class="wikitable"
|+
!13th fret
!14th fret
!15th fret
|-
|13 x x = x x 0
|x 14 = <v21> x
|x x x 15 = <v9> x x x
|-
|x x x 13 = <12> x x x
|
|x x x x x 15 = <15.1> x x x x x
|}
In the last equation, the harmonic is ~6¢ sharp of the 41-equal note.


=== Quarter-fret Bends, Sixth-fret Bends, etc. ===
=== Quarter-fret Bends, Sixth-fret Bends, etc. ===
When soloing over an ^m7 chord, a sustained 4th creates an innate-comma pentad. The effect is subtle but noticeable, and once you hear it, it's hard to unhear. The comma can be tamed by splitting the difference. Play the plain 4th, then bend it up a quarter-fret to a <u>half-up</u> 4th. The bend needn't be exact. Unlike bending the down-5th a half-fret up to the 5th, the end result isn't to lock into a specific ratio. In fact, rather than play a static half-up 4th, a moving bend that starts at the plain 4th and goes up <u>past</u> the half-up 4th and then back down sounds better. This is called a fuzzy 4th, specifically an upfuzzy 4th. But over a vm7 chord, we want a downfuzzy 4th. Either play the <u>down</u> 4th and bend it up, or play the plain 4th and bend it down (harder, see below).  
When soloing over an ^m7 chord, a sustained 4th creates an innate-comma pentad. The effect is subtle but noticeable, and once you hear it, it's hard to unhear. The comma can be tamed by splitting the difference. Play the plain 4th, then bend it up a quarter-fret to a <u>half-up</u> 4th. The bend needn't be exact. Unlike bending the down-5th a half-fret up to the 5th, the end result isn't to lock into a specific ratio. In fact, rather than play a static half-up 4th, a moving bend that starts at the plain 4th and goes up <u>past</u> the half-up 4th and then back down sounds better. This is called a fuzzy 4th, specifically an upfuzzy 4th. But over a vm7 chord, we want a downfuzzy 4th. Either play the <u>down</u> 4th and bend it up, or play the plain 4th and bend it down (harder, see below).  


Any chord that has two notes an upmajor or downmajor 2nd apart will create a fuzzy note:  
Any chord that has two notes an upmajor or downmajor 2nd apart will create a fuzzy note. In practice, this 2nd may be voiced as a 7th or 9th.  
{| class="wikitable"
{| class="wikitable"
|+
|+
fuzzy notes
! colspan="2" |if the chord has both...
! colspan="2" |if the chord has both...
! rowspan="2" |what to bend
! rowspan="2" |soloist
! colspan="6" rowspan="2" |example chords
must bend
! colspan="8" rowspan="2" |example chords
|-
|-
!plain
!plain
Line 353: Line 543:
|^d^7
|^d^7
|vdv7
|vdv7
|^9
|v9
|-
|-
|4th
|4th
Line 359: Line 551:
|^m,4
|^m,4
|vm,4
|vm,4
| colspan="4" |
| colspan="6" |
|-
|-
|5th
|5th
Line 368: Line 560:
|^m6
|^m6
|vm6
|vm6
| colspan="2" rowspan="2" |
| colspan="4" |
|-
|-
|9th
|9th
Line 377: Line 569:
|^M9
|^M9
|vM9
|vM9
|^9
|v9
| colspan="2" |
|}
|}
Both the top and bottom rows of the table apply to the dominant 9th chord, thus it has <u>two</u> fuzzy notes.
Both the top and bottom rows of the table apply to the dominant 9th chord, thus it has <u>two</u> fuzzy notes.


The next use of quarter-fret bends is less essential. One can hide pitch shifts by sharpening an entire chord by some fraction of an edostep. Obviously it won't work if a chord uses open strings. Play a progression with a pitch shift, e.g. Iv - vVI^m - vII^m - Vv7 - Iv. The 3rd chord has vD and the 4th chord has D. Bend the entire 3rd chord up a quarter-fret by ear, so that its vD becomes a half-down D. This creates another pitch shift, because the chord now has a half-down A which differs from the previous chord's vA. However, two small 15¢ shifts are better than one large 30¢ one. Alternatively, bend the 2nd chord up a '''sixth-fret''' and the 3rd chord up a '''third-fret''', to create three pitch shifts of 10¢ each.
The next use of quarter-fret bends is less essential. One can hide pitch shifts by sharpening an entire chord by some fraction of a half-fret. Obviously it won't work if a chord uses open strings. Play a progression with a pitch shift, e.g. Iv - vVI^m - vII^m - Vv7 - Iv. The 3rd chord has vD and the 4th chord has D. Bend the entire 3rd chord up a quarter-fret by ear, so that its vD becomes a half-down D. This creates another pitch shift, because the chord now has a half-down A which differs from the previous chord's vA. However, two small 15¢ shifts are better than one large 30¢ one. Alternatively, bend the 2nd chord up a '''sixth-fret''' and the 3rd chord up a '''third-fret''', to create three pitch shifts of 10¢ each.


To practice such bends, do one of the half-fret bend exercises in two or three stages.
To practice such bends, do one of the half-fret bend exercises in two or three stages.


In 41-edo, 5-over intervals like 5/4 and 5/3 are about 6¢ flat. This issue is even more subtle than the innate-comma pentad, but still noticeable. One can correct this by applying a '''tenth-fret''' bend to certain notes of the chord. This sounds hard, but fortunately there are only a few chord shapes to apply this to. One quickly gets in the habit of "leaning on" certain notes in these shapes.  
In 41-equal, 5-over intervals like 5/4 and 5/3 are about 6¢ flat. This issue is even more subtle than the innate-comma pentad, but still noticeable. One can correct this by applying a '''tenth-fret''' bend to certain notes of the chord. This sounds hard, but fortunately there are only a few chord shapes to apply this to. One quickly gets in the habit of "leaning on" certain notes in these shapes.  


For example, in a downmajor chord in R-5-3 voicing, bend the 3rd up slightly with your pinkie. Listen closely for interference beats that slow down as you bend up. It may help to play the actual coinciding harmonics first. If your chord is 4 x 3 x 5, play matching harmonics at 11 x x x 26, and also at  x x 10 x 17. Except for the last one at fret 17, touch the string just behind the fret. IOW fret 11 is really fret 10.5. For a 4 x 3 5 5 voicing, to bend the 3rd up, you'll need to pull your pinkie down towards the treble side of the fretboard. For a 1st inversion x 4 3 5 x voicing, push your finger up towards the bass side. It's rather difficult to bend the 3rd in a close 4 4 3 5 voicing.  
For example, with a downmajor chord in R-5-10 (aka hi3) voicing, bend the 3rd up slightly with your pinkie. Listen closely for interference beats that slow down as you bend up. It may help to play the actual coinciding harmonics first. As you play 4 x 3 x 5 x, play matching artificial harmonics at <v11> x x x <v26> x, and also at  x x <v10> x <17> x (see Harmonics above). For a 4 x 3 5 5 x voicing, to bend the 3rd up, you'll need to pull your pinkie down towards the treble side of the fretboard. For a 1st inversion x 4 3 5 x x voicing, push your finger up towards the bass side. It's rather difficult to bend the 3rd in a close 4 4 3 5 x x voicing.  


It's also possible to correct the 6¢ sharpness of 5-under intervals by bending a note slightly <u>down</u>. Press the string firmly against the fingerboard and push it towards the bridge. This is harder to do by the nut, because bending down stretches the string behind the fret, and there's very little to stretch there.  
It's also possible to correct the 6¢ sharpness of 5-under intervals by bending a note slightly <u>down</u>. Press the string firmly against the fingerboard and push it towards the bridge. This is harder to do by the nut, because bending down stretches the string behind the fret, and there's very little to stretch there.  


== Exercises for Composers and Arrangers ==
==== Primes 11 and 13 ====
These are not playing exercises for your fingers, but musical exercises for your mind.  
Whereas primes 5 and 7 are tuned slightly flat in 41-equal (5.8¢ and 3.0¢ respectively), primes 11 and 13 are slightly sharp (4.8¢ and 8.3¢ respectively). Thus ratios that have either 5 or 7 on one side and either 11 or 13 on the other are doubly mistuned. Bending up to ratios using 11 or 13 lets us fine-tune them. When primes 5 or 7 are present, best to underbend a bit, to match their flatness. This also makes ratios with primes 11 and 13 more physically accessible. For 13/8, the ^m6 is much easier to reach than the ~6. 11/6, 11/9 and 13/12 also become easier.
 
11-over and 13-over ratios require just under a half-fret bend. 11-under and 13-under ones require just over a half-fret bend. Both are denoted here with an up, e.g. ^4.
{| class="wikitable"
|+Augmented triads using primes 11 or 13
!chord
! colspan="2" |color name
!41-equal name
!example
!frets
!fingering
|-
|7:9:11
|ru loru-5
|r(1or5)
|up-downsharp5
|C^(v#5) = C ^E vG#
|4 5 ^4
|1 3 2
|-
|8:10:13
|yo tho-6 no5
|y,3o6no5
|down-upsharp5
|Cv(^#5) = C vE ^G#
|4 4 ^5
|1 2 3
|}
 
== Exercises and Techniques for Composers and Arrangers ==
These are not physical exercises for your fingers, but mental exercises for your mind.  


=== Interesting Root Movements ===
=== Interesting Root Movements ===
Given a chord, what chord can you move to that has at least 2 notes in common? Root movement intervals tend to be not plain. Harmonic chords tend to be followed by subharmonic chords and vice versa. The ^9 chord can often have its root omitted, becoming a vdv7 or ^m6 chord. These tables list only some of the possibilities.  
Given a chord, what chord can you move to that has at least 2 notes in common? Root movement intervals will tend to be not plain. Harmonic chords will tend to be followed by subharmonic chords and vice versa. The ^9 chord can often have its root omitted, becoming a vdv7 or ^m6 chord. These tables list only some of the possibilities.  
{| class="wikitable"
{| class="wikitable"
|+from the down7 chord
|+from the down7 chord
Line 453: Line 678:
|-
|-
| rowspan="2" |root & 7th
| rowspan="2" |root & 7th
| rowspan="2" |Iv7 -- vbVI^9 or
|Iv7 -- vbVI^9
Iv7 -- vbIII^m6
|  - 4 4 3 1
|  - 4 4 3 1
|3 4 2 1 1
|3 4 2 1 1
|vbVI^9 leads nicely into the Vv7 chord
|leads nicely into the Vv7 chord
|-
|-
|Iv7 -- vbIII^m6
|4 - - 1 5 4 -
|4 - - 1 5 4 -
| - 2 - 5 3 2 2
| - 2 - 5 3 2 2
|vbIII^m6 leads nicely into the IVv7 chord
|leads nicely into the IVv7 chord
|-
|-
|5th & 7th
|5th & 7th
Line 523: Line 748:
|one of my favorites, even though 3 common tones
|one of my favorites, even though 3 common tones
|}
|}
These are similar to [https://viva.pressbooks.pub/openmusictheory/chapter/neo-riemannian-triadic-progressions/ neo-Riemannian progressions], but using 41-equal 7-limit tetrads not 12-equal 5-limit triads. A more exact extension of the 12-equal case would allow only two tetrads, the v7 (harmonic) and vdv7 (subharmonic) ones. Interestingly, just as in the 5-limit 12-equal case, you can get from one tetrad to any other in five steps or less (four if the first and last chord have the same quality). Thus one can modulate to any key in 41edo fairly quickly.


=== Harmonizing Chromatic Melodies ===
=== Harmonizing Fretwise Melodies ===
Write a melody with steps of vm2 (one fret), with perhaps an occasional m2 for string-hopping. Write chords under it. See if you can improve on my attempt:
Write a melody with steps of vm2 (one fret), with perhaps an occasional m2 for string-hopping. Write chords under it. See if you can improve on my attempt:


Line 544: Line 770:


=== Rotations aka Inversions ===
=== Rotations aka Inversions ===
In music theory, the word [[wikipedia:Inversion_(music)|inversion]] has distinct, but related, meanings when applied to intervals, chords, voices (in counterpoint), and melodies. These exercises cover melodic-style inversions, i.e. flipping things upside down. Similar to what Jacob Collier calls negative harmony. To avoid confusion, we'll call them '''rotations''', for reasons that will become obvious.  
In music theory, the word [[wikipedia:Inversion_(music)|inversion]] has distinct, but related, meanings when applied to intervals, chords, voices (in counterpoint), and melodies. These exercises are not about chord inversions in the sense of putting the 3rd or 5th in the bass. Rather, they use melodic inversions, i.e. flipping everything upside down. It's similar to what Jacob Collier calls negative harmony. To avoid confusion, we'll call them '''rotations''', for reasons that will become obvious.  


==== Motivating Example ====
==== Motivating Example ====
Line 553: Line 779:
x x 4 6 6 5
x x 4 6 6 5


We can derive an entirely different, yet vaguely similar chord progression from this one via rotation:
I can derive an entirely different, yet vaguely similar chord progression from this one by rotating everything 180 degrees:


x x 8 6 5 5
x x 8 6 5 5
Line 579: Line 805:
|}
|}
Notice how major intervals become minor and vice versa. Augmented becomes diminished and up becomes down. But not everything changes. Perfect stays perfect. 3-limit remains 3-limit, 5-limit remains 5-limit, 7-limit remains 7-limit, and 11-limit remains 11-limit. A highly consonant interval remains at least fairly consonant. A highly dissonant interval won't improve much.
Notice how major intervals become minor and vice versa. Augmented becomes diminished and up becomes down. But not everything changes. Perfect stays perfect. 3-limit remains 3-limit, 5-limit remains 5-limit, 7-limit remains 7-limit, and 11-limit remains 11-limit. A highly consonant interval remains at least fairly consonant. A highly dissonant interval won't improve much.
This is not about chord inversions in the sense of putting the 3rd or 5th in the bass. Rather it is about flipping all the notes upside-down.


==== Rotating a Melody ====
==== Rotating a Melody ====
Line 682: Line 906:
|low-3, add-low-5
|low-3, add-low-5
|}
|}
Not a very nice voicing. You can only take rotations so far. The basic rules of voicing and voice leading still hold. Good chord voicings imitate the harmonic series: larger intervals between the lower voices and smaller intervals between the upper voices. In accompaniments, Good bass melodies tend to have big leaps, and good melodies in the upper voices tend to have smaller steps. So a good voicing will often rotate to a bad one, and you'll often want to revoice after rotating.  
Not a very nice voicing. You can only take rotations so far. The basic rules of voicing and voice leading still hold. Good chord voicings imitate the harmonic series: larger intervals between the lower voices and smaller intervals between the upper voices. In accompaniments, good bass melodies tend to have big leaps, and good melodies in the upper voices tend to have smaller steps. So a good voicing will often rotate to a bad one, and you'll often want to revoice after rotating.  


* major rotates to minor
* major rotates to minor
Line 690: Line 914:
* the prime limit doesn't change
* the prime limit doesn't change


7th chords rotate to 6th chords, but every 6th chord has a 7th chord homonym. So 7th chords can rotate to 7th chords, as in out first example 4 4 3 1 --> 4 2 1 1. You can think of this as Cv7 becomes vEb^m6, or as Cv7 becomes Cvdv7.
7th chords rotate to 6th chords, but every 6th chord has a 7th chord [[Chord homonym|homonym]]. So 7th chords can rotate to 7th chords, as in our first example 4 4 3 1 --> 4 2 1 1. You can think of this as Cv7 becomes vEb^m6/C, or as Cv7 becomes Cvdv7.


==== Rotating a Chord Progression ====
==== Rotating a Chord Progression ====
Line 789: Line 1,013:
|I^m
|I^m
|}
|}
All these rotations work in 12-edo, or any tuning system, but unless your guitar is isomorphic, the fretboard shapes won't simply rotate.
All these rotations work in 12-equal, or any tuning system, but unless your guitar is isomorphic, the fretboard shapes won't simply rotate.
 
=== The Big Switcheroo ===
Like the previous exercise, this creates a new melody or chord progression from an old one. You simply swap up for down, so that upminor becomes downminor, etc. Swap intervals, not notes. The quality (major, minor, perfect, augmented or diminished) is unchanged. Plain and mid intervals are unchanged. (The reason mid is unchanged is that it's simultaneously both dupminor and dudmajor. But the former would become dudminor, and the latter dupmajor. Rather than changing to two things, which doesn't make any sense, it doesn't change at all.)
{| class="wikitable"
|+
! rowspan="2" |lyrics
! colspan="2" |original
! colspan="2" |swapped
|-
!melody
!chords
!melody
!chords
|-
|Happy
|P5
| rowspan="4" |Iv
 
|P5
| rowspan="4" |I^
 
|-
|Birth-
|vM6
|^M6
|-
|day
|P5
|P5
|-
|To
|P8
|P8
|-
|You
|vM7
| rowspan="5" |Vv
 
|^M7
| rowspan="5" |V^
 
|-
|Happy
|P5
|P5
|-
|Birth-
|M6
|M6
|-
|day
|P5
|P5
|-
|To
|M9
|M9
|-
|You
|P8
|Iv
|P8
|I^
|}
This swapping has the effect of interchanging prime 5 with prime 7 (i.e. 5-limit becomes 7-limit-no-fives), and harmonic with subharmonic. Rotations also exchange harmonic with subharmonic, so rotating followed by switching preserves this property.
{| class="wikitable"
|+
! rowspan="2" |lyrics
! colspan="2" |original
! colspan="2" |first rotated
! colspan="2" |then swapped
|-
!melody
!chords
!melody
!chords
!melody
!chords
|-
|Happy
|P5
| rowspan="4" |Iv
 
|P8
| rowspan="4" |I^m
|P8
| rowspan="4" |Ivm
|-
|Birth-
|vM6
|^m7
|vm7
|-
|day
|P5
|P8
|P8
|-
|To
|P8
|P5
|P5
|-
|You
|vM7
| rowspan="5" |Vv
 
|^m6
| rowspan="5" |IV^m
|vm6
| rowspan="5" |IVvm
|-
|Happy
|P5
|P8
|P8
|-
|Birth-
|M6
|^m7
|vm7
|-
|day
|P5
|P8
|P8
|-
|To
|M9
|P4
|P4
|-
|You
|P8
|Iv
|P5
|I^m
|P5
|Ivm
|}
 
=== Modulation via Dim7 Chords ===
This is analogous to 12-equal's Cdim7 --> B7 --> E (or EM7 or Em7). The idea is to lower one of the 4 notes in the dim7 chord by a semitone to transform it into a dom7 chord, then use a typical V7 - I cadence to arrive at one of 4 new keys. Thus the dim7 chord is sort of a "portal" to other keys. The following table uses a single 12-equal dim7 chord that is spelled 4 different ways for convenience. This starting chord is one of the three possible dim7 chords in 12-equal, thus two more tables would be needed to show all possible modulations. (Briefly, Gdim7 goes to D, F, Ab and B, and Bdim7 goes to F#, A, C and Eb.) The note that is lowered is '''<u>bolded</u>'''.
{| class="wikitable"
|+using a dim7 chord to modulate in 12-equal
! rowspan="2" |starting
dim7 chord
! colspan="2" |bolded note is lowered
! colspan="2" |bolded note is raised
|-
!new V7 chord
!new key
!new IVm6 chord
!new key
|-
|Adim7 = '''<u>A</u>''' C Eb Gb
|Ab7 = Ab C Eb Gb
|Db
|Ebm6 = Bb C Eb Gb
|Bb
|-
|B#dim7 = A '''<u>B#</u>''' D# F#
|B7 = A B D# F#
|E
|F#m6 = A C# D# F#
|C#
|-
|D#dim7 = A C '''<u>D#</u>''' F#
|D7 = A C D F#
|G
|Am6 = A C E F#
|E
|-
|F#dim7 = A C Eb '''<u>F#</u>'''
|F7 = A C Eb F
|Bb
|Cm6 = A C Eb G
|G
|}
 
The last two columns take this idea further. The bolded note is <u>raised</u> to make a min6 chord that resolves down a 4th to the new tonic. This IVm6 - I cadence is simply the [[Kite Guitar Exercises and Techniques by Kite Giedraitis#Rotations aka Inversions|rotation]] of V7 - I. Note that both cadences take you to the same 4 keys. Also, the chord that results from raising the note can be interpreted as a dom9noR chord, in which case it resolves the same as if the note had been lowered. In other words, instead of being lowered to become the root, the note is raised to become the ninth. For example, Ebm6 can resolve to Bb, but if heard as Ab9noR, it can resolve to Db. Likewise, the Ab7 chord can be interpreted as Ebm6,11no5, and thus can resolve to Bb. (This is perhaps more plausible in 41-equal than in 12-equal.) In all these cadences, the C-Gb dim 5th resolves inward to a 3rd.
 
Let's extend this idea to 41-equal. A plain dim7 chord is possible, but awkward on the Kite guitar. So we will focus on the ^dim7 and vdim7 chords. Neither of these are symmetrical, so 40 more tables would be needed! How much to raise/lower by? The bolded note has another chord note a tritone above it. The bolded note is either lowered to make that interval a perfect 5th, or raised to make a perfect 4th.
 
Sometimes another note in the chord needs to shift by a half-fret to make a low-odd-limit chord. When this happens, the shifting note is bolded in the "new chord" column. Without this shift, the new chord is more dissonant. But the down add-7 chord is a very familiar dissonance. Furthermore the vanishing [[225/224|Ruyoyo comma]] means the 45/32 downaug 4th is really a consonant 7/5 dim 5th. So it's listed in the 2nd row as an alternative to shifting. The upminor add6 chord is included as a possibility because it's a rotation of v,7, and has the same vanishing innate comma. But the other two non-shifting chords, F# minor add-down6 and D add-up7, are less plausible because of their dissonant plain 3rds. Those two are written in ''(italics)''.
{| class="wikitable"
|+using an updim7 chord to modulate in 41-equal
! rowspan="2" |starting
^d7 chord
! colspan="2" |bolded note is lowered
! colspan="2" |bolded note is raised
|-
!new V chord
!new key
!new IV chord
!new key
|-
|A^d7 = '''<u>A</u>''' ^C Eb ^Gb
|Ab^7 = Ab ^C Eb ^Gb
|Db
|Eb^m6 = Bb ^C Eb ^Gb
|Bb
|-
|A^d7 = A '''<u>^C</u>''' vD# F#
|Bv,7 = A B vD# F#
Bv7 = '''<u>vA</u>''' B vD# F#
|E
|F#vm6 = '''<u>vA</u>''' C# vD# F#
''(F#mv6 = A C# vD# F#)''
|C#
|-
|A^d7 = A ^C '''<u>Eb</u>''' F#
|D^7 = A ^C D '''<u>^F#</u>'''
''(D,^7 = A ^C D F#)''
|G
|A^m,6 = A ^C E F#
A^m6 = A ^C E '''<u>^F#</u>'''
|E
|-
|A^d7 = A ^C Eb '''<u>^Gb</u>'''
|^Fv7 = A ^C Eb ^F
|^Bb
|^Cvm6 = A ^C Eb ^G
|^G
|}
Note that unlike in 12-equal, the IV-I cadences take you to mostly different keys than the V-I cadences.
 
Again, there are alternate interpretations for the new chord.
 
* Ab^7 = Eb^m6,11no5
* Eb^m6 = Ab^9noR
* ^Fv7 = ^Cvm6,11no5
* ^Cvm6 = ^Fv9noR
 
Here's a similar table for the downdim7 chord. All the non-shifting chords contain mid intervals.
{| class="wikitable"
|+using a downdim7 chord to modulate in 41-equal
! rowspan="2" |starting
vd7 chord
! colspan="2" |bolded note is lowered
! colspan="2" |bolded note is raised
|-
!new V chord
!new key
!new IV chord
!new key
|-
|^Avd7 = '''<u>^A</u>''' C ^Eb Gb
|^Abv7 = ^Ab C ^Eb Gb
|^Db
|^Ebvm6 = ^Bb C ^Eb Gb
|^Bb
|-
|^Avd7 = ^A '''<u>C</u>''' D# vF#
|vB^7 = '''<u>A</u>''' vB D# vF#
''(vB^,~7 = ^A vB D# vF#)''
|vE
|vF#^m6 = '''<u>A</u>''' vC# D# vF#
''(vF#~,^6 = ^A vC#  D# vF#)''
|vC#
|-
|^Avd7 = ^A C '''<u>^Eb</u>''' vF#
|^Dv7 = ^A C ^D '''<u>F#</u>'''
''(^D~,v7 = ^A C ^D vF#)''
|^G
|^Avm6 = ^A C ^E '''<u>F#</u>'''
''(^Avm,~6 = ^A C ^E vF#)''
|^E
|-
|^Avd7 = ^A C ^Eb '''<u>Gb</u>'''
|F^7 = ^A C ^Eb F
|Bb
|C^m6 = ^A C ^Eb G
|G
|}
[[Category:Kite Guitar]]
[[Category:Kite Guitar]]
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