Kite Guitar Exercises and Techniques by Kite Giedraitis: Difference between revisions
added the 12-equal Patt-tuning exercise, other minor changes |
|||
| (12 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
[[Kite Guitar Exercises and Techniques|Exercises and techniques]] for the [[The Kite Guitar|Kite Guitar]] by [[Kite Giedraitis]], assumes the downmajor tuning. | [[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. | ||
Highest or top string means thinnest string, lowest or bottom string means thickest string. | |||
== Before You Get Your Kite Guitar == | == Before You Get Your Kite Guitar == | ||
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 play all the same shapes and patterns, with slight adjustments. | 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 == | == 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. | 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 === | ||
| Line 251: | Line 249: | ||
=== Half-fret Bends === | === Half-fret Bends === | ||
The fact that each 41-equal 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 ( | * 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. | |||
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. | |||
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. | |||
3c) Same as 2b, but your 4th finger is 8 frets up. Bend the lower (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. | |||
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. | |||
4c) Same as 4b, but your 3rd finger is 5 frets higher. Bend the higher (1st 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. | |||
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.) | |||
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 294: | 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 | 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 317: | Line 329: | ||
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. | 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 | 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. | 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. | ||
| Line 344: | Line 356: | ||
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. | 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 | 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 | 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 4th = 3 m2's + 2 ^m2's | ||
| Line 372: | 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 | 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. | |||
For example, | |||
==== 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" | {| class="wikitable" | ||
|+ | |+ | ||
Harmonics on the Kite guitar | Harmonics 1-12 on the Kite guitar | ||
!harmonic --> | !harmonic --> | ||
!1 | !1 | ||
| Line 495: | Line 418: | ||
! rowspan="5" |fret | ! rowspan="5" |fret | ||
|open | |open | ||
|< | |<v21> | ||
|<12> | |<12> | ||
|< | |<v9> | ||
|<6.6> | |<6.6> | ||
|<5.4> | |<5.4> | ||
|< | |<v5> | ||
|<4> | |<4> | ||
|< | |<v4> | ||
|<3.1> | |<3.1> | ||
|<2.8> | |<2.8> | ||
|<17.9> | |<17.9> | ||
|<2. | |<2.6> | ||
|- | |- | ||
| | | | ||
| | | | ||
|< | |<v33> | ||
|<41> | |<41> | ||
|<15.1> | |<15.1> | ||
| Line 516: | Line 439: | ||
|<10> | |<10> | ||
|<13.9> | |<13.9> | ||
|< | |<v8> | ||
|< | |<v11> | ||
|<5.9> | |<5.9> | ||
|<23.3> | |<23.3> | ||
| Line 528: | Line 451: | ||
|<27.1> | |<27.1> | ||
| | | | ||
|< | |<v17> | ||
|<29> | |<29> | ||
|< | |<v18> | ||
|<35.6> | |<35.6> | ||
|<9.4> | |<9.4> | ||
| Line 577: | Line 500: | ||
|3rd + 4th | |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. < | 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: | These harmonics, along with open strings, provide alternative fingerings for notes on the 13th, 14th and 15th frets: | ||
| Line 587: | Line 510: | ||
|- | |- | ||
|13 x x = x x 0 | |13 x x = x x 0 | ||
|x 14 = < | |x 14 = <v21> x | ||
|x x x 15 = < | |x x x 15 = <v9> x x x | ||
|- | |- | ||
|x x x 13 = <12> x x x | |x x x 13 = <12> x x x | ||
| Line 594: | Line 517: | ||
|x x x x x 15 = <15.1> x x 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. === | |||
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. In practice, this 2nd may be voiced as a 7th or 9th. | |||
{| class="wikitable" | |||
|+ | |||
fuzzy notes | |||
! colspan="2" |if the chord has both... | |||
! rowspan="2" |soloist | |||
must bend | |||
! colspan="8" rowspan="2" |example chords | |||
|- | |||
!plain | |||
!upped or downed | |||
|- | |||
|root | |||
|minor 7th | |||
|the perfect 4th | |||
|^7 | |||
|v7 | |||
|^m7 | |||
|vm7 | |||
|^d^7 | |||
|vdv7 | |||
|^9 | |||
|v9 | |||
|- | |||
|4th | |||
|minor 3rd | |||
|the minor 7th | |||
|^m,4 | |||
|vm,4 | |||
| colspan="6" | | |||
|- | |||
|5th | |||
|major 6th | |||
|the major 2nd | |||
|^6 | |||
|v6 | |||
|^m6 | |||
|vm6 | |||
| colspan="4" | | |||
|- | |||
|9th | |||
|major 3rd | |||
|the major 6th | |||
|^,9 | |||
|v,9 | |||
|^M9 | |||
|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. | |||
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. | |||
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, 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. | |||
==== Primes 11 and 13 ==== | |||
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 == | == Exercises and Techniques for Composers and Arrangers == | ||
| Line 729: | 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 | === 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 750: | 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 | 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 759: | Line 779: | ||
x x 4 6 6 5 | x x 4 6 6 5 | ||
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 785: | 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. | ||
==== Rotating a Melody ==== | ==== Rotating a Melody ==== | ||
| Line 896: | 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 | 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 998: | Line 1,016: | ||
=== The Big Switcheroo === | === 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 | 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" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 1,060: | Line 1,078: | ||
|I^ | |I^ | ||
|} | |} | ||
This swapping has the effect of interchanging | 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" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 1,138: | Line 1,156: | ||
=== Modulation via Dim7 Chords === | === 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 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>'''. | 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" | {| class="wikitable" | ||
|+using a dim7 chord to modulate in 12-equal | |+using a dim7 chord to modulate in 12-equal | ||
| Line 1,176: | Line 1,194: | ||
|} | |} | ||
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 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. 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. | 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. | 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. | ||
| Line 1,200: | Line 1,218: | ||
|- | |- | ||
|A^d7 = A '''<u>^C</u>''' vD# F# | |A^d7 = A '''<u>^C</u>''' vD# F# | ||
|Bv7 = '''<u>vA</u>''' B vD# | |Bv,7 = A B vD# F# | ||
Bv7 = '''<u>vA</u>''' B vD# F# | |||
|E | |E | ||
|F#vm6 = '''<u>vA</u>''' C# vD# F# | |F#vm6 = '''<u>vA</u>''' C# vD# F# | ||
''(F# | ''(F#mv6 = A C# vD# F#)'' | ||
|C# | |C# | ||
|- | |- | ||
| Line 1,211: | Line 1,229: | ||
''(D,^7 = A ^C D F#)'' | ''(D,^7 = A ^C D F#)'' | ||
|G | |G | ||
|A^m6 = A ^C E '''<u>^F#</u>''' | |A^m,6 = A ^C E F# | ||
A^m6 = A ^C E '''<u>^F#</u>''' | |||
|E | |E | ||
|- | |- | ||
| Line 1,221: | Line 1,239: | ||
|^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. | Again, there are alternate interpretations for the new chord. | ||