Skip fretting system 34 2 9 - Revision history

Yourmusic Productions: Categories, temperament basis

2023-04-25T08:27:31Z

Categories, temperament basis

← Older revision		Revision as of 08:27, 25 April 2023
Line 1:		Line 1:
	One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5.		One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5.

	Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.)		Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.) Since it makes playing music composed using [[keemun]] temperament particularly easy, it could also be called a Keemun or Kleismic guitar.

	== Where the first primes intervals lie ==		== Where the first primes intervals lie ==
Line 7:		Line 7:
	=== As a diagram ===		=== As a diagram ===

	In the ~~folowing~~ the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.		In the following the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

	headstock on this side		headstock on this side
Line 16:		Line 16:
	- - - - - -		- - - - - -
	bass - - 11 - 1 - treble		bass - - 11 - 1 - treble
	side - - 23 7 - 5 side		side 1 - 23 7 - 5 side
	- 5 3 - - 21		- 5 3 - - 21
	- 21 - 15 9 -		- 21 - 15 9 -
Line 68:		Line 68:
	From these, the location of most compound intervals can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.		From these, the location of most compound intervals can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.

	[[Category:Skip fretting]]		[[Category:Skip fretting]] [[Category:34edo]] [[Category:Kleismic_family]]

Jeff Brown: fix a diagram, hopefully

2023-04-23T18:47:31Z

fix a diagram, hopefully

← Older revision		Revision as of 18:47, 23 April 2023
Line 9:		Line 9:
	In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.		In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

	~~bass side treble side~~		headstock on this side
			- 15 9 - 13 -
	headstock on this side		13 - 19 - - -
	- 15 9 - 13 -		- - - - - 17
	13 - 19 - - -		- 17 - - - -
	- - - - - 17		- - - - - -
	- 17 - - - -		bass - - 11 - 1 - treble
	- - - - - -		side - - 23 7 - 5 side
	- - 11 - 1 -		- 5 3 - - 21
	1 - 23 7 - 5		- 21 - 15 9 -
	- 5 3 - - 21		9 - 13 - 19 -
	- 21 - 15 9 -		19 - - - - -
	9 - 13 - 19 -		bridge on this side
	19 - - - - -
	bridge on this side

	=== As a table ===		=== As a table ===

Jeff Brown: Fix a diagram

2023-04-23T18:46:07Z

Fix a diagram

← Older revision		Revision as of 18:46, 23 April 2023
Line 8:		Line 8:

	In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.		In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

			bass side treble side

	headstock on this side		headstock on this side
Line 14:		Line 16:
	- - - - - 17		- - - - - 17
	- 17 - - - -		- 17 - - - -
	~~bass~~ - - - - - - ~~treble~~		- - - - - -
	~~strings~~ - - 11 - 1 - ~~strings~~		- - 11 - 1 -
	1 - 23 7 - 5		1 - 23 7 - 5
	- 5 3 - - 21		- 5 3 - - 21

Jeff Brown at 18:44, 23 April 2023

2023-04-23T18:44:57Z

@@ Line 3: / Line 3: @@
 Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.)
-Here is where all the primes intervals lie:
+== Where the first primes intervals lie ==
 {| class="wikitable"
@@ Line 46: / Line 66: @@
 |}
-From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.
+From these, the location of most compound intervals can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.
 [[Category:Skip fretting]]

Xenwolf: add category

2021-05-02T16:58:31Z

add category

← Older revision		Revision as of 16:58, 2 May 2021
Line 47:		Line 47:

	From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.		From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.

			[[Category:Skip fretting]]

Jeff Brown: start

2021-05-02T03:43:32Z

start

New page

One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5.

Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.)

Here is where all the primes intervals lie:

{| class="wikitable"
! note
! fretboard position
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 34 steps = 2 % 1
| string 4 fret - 1
|-
| 20 steps = 3 % 2
| string 2 fret 1
|-
| 11 steps = 5 % 4
| string 1 fret 1
|-
| 27 steps = 7 % 4
| string 3 fret 0
|-
| 16 steps = 11 % 8
| string 2 fret - 1
|-
| 24 steps = 13 % 8
| string 2 fret 3
|-
| 3 steps = 17 % 16
| string - 1 fret 6
|-
| 8 steps = 19 % 16
| string 0 fret 4
|-
| 18 steps = 23 % 16
| string 2 fret 0
|-
| 29 steps = 29 % 16
| string 3 fret 1
|-
| 32 steps = 31 % 16
| string 4 fret - 2
|}

From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.