Skip fretting system 27 2 9 - Revision history

Yourmusic Productions: Fix math error.

2026-09-25T09:10:15Z

Fix math error.

← Older revision		Revision as of 09:10, 25 September 2026
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	\|-		\|-
	\| 21		\| 21
	\| ~~1755~~.519		\| 1775.519
	\| -91.146 (-2.258)		\| -91.146 (-2.258)
	\|-		\|-

Yourmusic Productions: Approximating this tuning with a regular guitar.

2026-09-25T08:58:14Z

Approximating this tuning with a regular guitar.

← Older revision		Revision as of 08:58, 25 September 2026
Line 51:		Line 51:
	From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).		From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

	[[Category:Skip fretting]] [[Category:27edo]] [[Category:Guitar]]		== Approximating using a standard guitar ==

			As 27ed4 is not that far from 12edo in step size, this tuning is quite amenable to the [[Moving the bridge hack]]. To do this, you will need an archtop guitar with a floating bridge with at least 2+1/2 inches of play behind the standard bridge position. (You could also entirely unscrew the bridge on another type of guitar and move it back, but this will require drilling new holes, making it a permanent modification that affects the appearance of your guitar.)

			As 27ed4 does not have a fret where the octave is, you cannot use that to check for intonation. Instead, the optimal way to tune it is to move the bridge far back enough that the 9th fret is 800 cents above the open tuning. (The precise length needed to do this on a 25.5" scale guitar is 27.9365", but you're unlikely to be able to get that level of precision with a floating bridge, so anywhere between 27.9 and 28 inches should give acceptable results.) This will let you check your intonation both by octaves on the string above and unisons on the string two steps up, allowing you to tweak the position until it sounds right.

			If done correctly, it will sound near identical to 27ed4 nearly all the way up to the cutaway, with inconsistent sweet spots at frets 17 and 21 where the notes are one or two steps below what a true 27ed4 guitar would give at that position that can still be highly useful.
			{\| class="wikitable right-2 right-3"
			\|-
			! Fret number
			! Cents
			! Deviation from 27ed4
			\|-
			\| 0 (nut)
			\| 0.000
			\| 0.000
			\|-
			\| 1
			\| 91.841
			\| 2.952
			\|-
			\| 2
			\| 181.608
			\| 3.830
			\|-
			\| 3
			\| 271.661
			\| 4.994
			\|-
			\| 4
			\| 361.189
			\| 5.634
			\|-
			\| 5
			\| 450.167
			\| 5.723
			\|-
			\| 6
			\| 538.562
			\| 5.229
			\|-
			\| 7
			\| 626.350
			\| 4.127
			\|-
			\| 8
			\| 713.504
			\| 2.393
			\|-
			\| 9
			\| 800
			\| 0.0
			\|-
			\| 10
			\| 885.805
			\| -3.083
			\|-
			\| 11
			\| 970.889
			\| -6.888
			\|-
			\| 12
			\| 1055.234
			\| -11.432
			\|-
			\| 13
			\| 1138.795
			\| -16.759
			\|-
			\| 14
			\| 1221.544
			\| -22.900
			\|-
			\| 15
			\| 1303.466
			\| -29.868
			\|-
			\| 16
			\| 1384.501
			\| -37.720 (+6.724)
			\|-
			\| 17
			\| 1464.643
			\| -46.467 (-2.023)
			\|-
			\| 18
			\| 1543.846
			\| -56.143 (-11.699)
			\|-
			\| 19
			\| 1622.081
			\| -66.807
			\|-
			\| 20
			\| 1699.315
			\| -78.461
			\|-
			\| 21
			\| 1755.519
			\| -91.146 (-2.258)
			\|-
			\| 22
			\| 1850.661
			\| -104.894
			\|}

			[[Category:Skip fretting]] [[Category:27edo]] [[Category:Guitar]] [[Category:Augmented]]

Yourmusic Productions: Restore text.

2025-04-24T07:32:11Z

Restore text.

← Older revision		Revision as of 07:32, 24 April 2025
Line 1:		Line 1:
	#~~REDIRECT [~~[~~User~~:~~MisterShafXen~~/~~Skip~~ fretting ~~system~~ 27 2 9]]		A good way to play [[27-edo]] on a 13.5-edo guitar is to tune each pair of adjacent strings 9/27 apart, or the familiar 400 cent major third shared with 12edo.

			Among the possible [[skip fretting]] systems for 27-edo, the (27, 2, 9) system is especially effective because it makes [[5-limit]] chords easy to play, every interval can be reached with a stretch of 4 frets or less (equivalent to 3.55 on a 12edo guitar) and it can be quickly & easily tuned using an ordinary 12edo guitar tuner, making it well suited to live performance. Since it makes it particularly easy to play music composed using [[Augmented_family#Augmented\|augmented]] temperament, it could also be called an augmented or [https://en.wikipedia.org/wiki/Major_thirds_tuning major thirds] guitar.

			It does limit your ability to play more complex septimal and higher-limit chords compared to a full 27edo guitar though, so you might want to use a partial system with the full set of frets in the lower octave and skip-fretting higher up, or have multiple instruments adding the more complex upper range harmonies.


			Here is where all the prime intervals lie.

			{\| class="wikitable"
			! note
			! fretboard position
			\|-
			\| 0 steps = 1 % 1
			\| string 0 fret 0
			\|-
			\| 27 steps = 2 % 1
			\| string 3 fret 0
			\|-
			\| 16 steps = 3 % 2
			\| string 2 fret -1
			\|-
			\| 9 steps = 5 % 4
			\| string 1 fret 0
			\|-
			\| 22 steps = 7 % 4
			\| string 2 fret 2
			\|-
			\| 12 steps = 11 % 8
			\| string 2 fret -3
			\|-
			\| 19 steps = 13 % 8
			\| string 3 fret -4
			\|-
			\| 2 steps = 17 % 16
			\| string 0 fret 1
			\|-
			\| 7 steps = 19 % 16
			\| string 1 fret -1
			\|-
			\| 14 steps = 23 % 16
			\| string 2 fret -1
			\|-
			\| 23 steps = 29 % 16
			\| string 3 fret -2
			\|-
			\| 26 steps = 31 % 16
			\| string 2 fret 4
			\|}

			From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

			[[Category:Skip fretting]] [[Category:27edo]] [[Category:Guitar]]

BudjarnLambeth: Changed redirect target from MisterShafXen/Skip fretting system 27 2 9 to User:MisterShafXen/Skip fretting system 27 2 9

2025-04-24T03:01:43Z

Changed redirect target from MisterShafXen/Skip fretting system 27 2 9 to User:MisterShafXen/Skip fretting system 27 2 9

← Older revision		Revision as of 03:01, 24 April 2025
Line 1:		Line 1:
	#REDIRECT [[MisterShafXen/Skip fretting system 27 2 9]]		#REDIRECT [[User:MisterShafXen/Skip fretting system 27 2 9]]

BudjarnLambeth: BudjarnLambeth moved page Skip fretting system 27 2 9 to MisterShafXen/Skip fretting system 27 2 9

2025-04-24T02:53:15Z

BudjarnLambeth moved page Skip fretting system 27 2 9 to MisterShafXen/Skip fretting system 27 2 9

New page

#REDIRECT [[MisterShafXen/Skip fretting system 27 2 9]]