Moving the bridge hack - Revision history

ArrowHead294 at 18:36, 13 March 2025

2025-03-13T18:36:22Z

← Older revision		Revision as of 18:36, 13 March 2025
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	If you have a [[~~12edo\|~~12edo]] guitar, or other fretted [[~~string_instruments\|~~string instrument]], and you want to play in an EDO that is numerically near 12 (e.g. [[~~11edo\|~~11edo]] or [[~~13edo\|~~13edo]]), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?		If you have a [[12edo]] guitar, or other fretted [[string instrument]], and you want to play in an EDO that is numerically near 12 (e.g. [[11edo]] or [[13edo]]), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?

	...well, actually, no. The frets form a geometric series of lengths that converges at a specific point, which is where the bridge ought to be. (That's what an EDO is—a geometric sequence of frequencies, corresponding to a geometric sequence of string lengths.) If you move the bridge, the new string lengths no longer form a mathematically correct geometric sequence. However, depending on what range of the fretboard you want to be usable, and what accuracy you desire, a moving-the-bridge solution may be possible.		...well, actually, no. The frets form a geometric series of lengths that converges at a specific point, which is where the bridge ought to be. (That's what an EDO is—a geometric sequence of frequencies, corresponding to a geometric sequence of string lengths.) If you move the bridge, the new string lengths no longer form a mathematically correct geometric sequence. However, depending on what range of the fretboard you want to be usable, and what accuracy you desire, a moving-the-bridge solution may be possible.

ArrowHead294 at 18:36, 13 March 2025

2025-03-13T18:36:02Z

← Older revision		Revision as of 18:36, 13 March 2025
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	If you have a [[12edo\|12edo]] guitar, or other fretted [[string_instruments\|string instrument]], and you want to play in an EDO that is numerically near 12 (e.g. [[11edo\|11edo]] or [[13edo\|13edo]]), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?		If you have a [[12edo\|12edo]] guitar, or other fretted [[string_instruments\|string instrument]], and you want to play in an EDO that is numerically near 12 (e.g. [[11edo\|11edo]] or [[13edo\|13edo]]), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?

	...well, actually, no. The frets form a geometric series of lengths that converges at a specific point, which is where the bridge ought to be. (That's what an EDO ~~is - a~~ geometric sequence of frequencies, corresponding to a geometric sequence of string lengths.) If you move the bridge, the new string lengths no longer form a mathematically correct geometric sequence. However, depending on what range of the fretboard you want to be usable, and what accuracy you desire, a moving-the-bridge solution may be possible.		...well, actually, no. The frets form a geometric series of lengths that converges at a specific point, which is where the bridge ought to be. (That's what an EDO is—a geometric sequence of frequencies, corresponding to a geometric sequence of string lengths.) If you move the bridge, the new string lengths no longer form a mathematically correct geometric sequence. However, depending on what range of the fretboard you want to be usable, and what accuracy you desire, a moving-the-bridge solution may be possible.

	== Derivation of the resulting scale ==		== Derivation of the resulting scale ==
	Let the EDO number of the original instrument be N (so very often N=12). Let the original scale length of the instrument (distance from bridge to nut) be 1. In other words we're measuring all lengths relative to the original scale length. Then the playable string lengths of the unmodified instrument are		Let the EDO number of the original instrument be ''N'' (so very often {{nowrap\|''N'' {{=}} 12}}). Let the original scale length of the instrument (distance from bridge to nut) be 1. In other words we're measuring all lengths relative to the original scale length. Then the playable string lengths of the unmodified instrument are

	<math>2^{-i/N} \text{ for } i = 0, 1, 2, 3\dots</math>		<math>2^{-i/N} \text{ for } i = 0, 1, 2, 3\dots</math>

	If the bridge is moved so that the new scale length is x, this adds (x-1) to all string lengths, so the new string lengths are simply		If the bridge is moved so that the new scale length is ''x'', this adds ({{nowrap\|''x'' − 1}}) to all string lengths, so the new string lengths are simply

	<math>2^{-i/N} + x - 1 \text{ for } i = 0, 1, 2, 3\dots</math>		<math>2^{-i/N} + x - 1 \text{ for } i = 0, 1, 2, 3\dots</math>

	The frequencies are inversely proportional to the string lengths. If we plug in i=0 to the above formula, we get x, so the frequency ratios relative to the open string are		The frequencies are inversely proportional to the string lengths. If we plug in {{nowrap\|''i'' {{=}} 0}} to the above formula, we get ''x'', so the frequency ratios relative to the open string are

	<math>\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 0, 1, 2, 3\dots</math>		<math>\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 0, 1, 2, 3\dots</math>

ArrowHead294 at 18:34, 13 March 2025

2025-03-13T18:34:51Z

Show changes

TallKite: added charts, added a link in "see also"

2024-11-21T23:55:05Z

added charts, added a link in "see also"

← Older revision		Revision as of 23:55, 21 November 2024
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	Converting those frequency ratios into cents in the usual way (taking the log to base 2 and multiplying by 1200) gives the new scale in cents.		Converting those frequency ratios into cents in the usual way (taking the log to base 2 and multiplying by 1200) gives the new scale in cents.

			Each fret will raise the pitch by a different amount, as these charts show
			[[File:Bridge-sliding chart 1.jpg\|none\|thumb]]
			[[File:Bridge-sliding chart 2.jpg\|none\|thumb]]
			[[File:Bridge-sliding chart 3.jpg\|none\|thumb]]

	== Examples for converting a 12edo instrument ==		== Examples for converting a 12edo instrument ==
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	== Advanced tricks ==		== Advanced tricks ==
	By adjusting the nut in addition to the bridge, it may be possible to make a surprisingly large portion of the fretboard usable with good accuracy. This is because there is another degree of freedom to tweak. For decreasing the EDO number you would want to either raise the nut or move it away from the first fret, and for increasing the EDO number you would want to either lower it or move it towards the first fret.		By adjusting the nut in addition to the bridge, it may be possible to make a surprisingly large portion of the fretboard usable with good accuracy. This is because there is another degree of freedom to tweak. For decreasing the EDO number you would want to either raise the nut or move it away from the first fret, and for increasing the EDO number you would want to either lower it or move it towards the first fret.

			== See also ==
			[[Tuning A Kite Guitar To 31edo or 62edo]]

	[[Category:Guitar]]		[[Category:Guitar]]

Fredg999: Markup, misc. edits, categories

2022-10-11T01:36:33Z

Markup, misc. edits, categories

Show changes

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>keenanpepper: Imported revision 373260670 - Original comment:

2012-10-15T15:41:51Z

**Imported revision 373260670 - Original comment: **

← Older revision		Revision as of 15:41, 15 October 2012
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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-~~14 16~~:04:10 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-15 15:41:51 UTC</tt>.<br>
	: The original revision id was <tt>~~372908500~~</tt>.<br>		: The original revision id was <tt>373260670</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	[[math]]		[[math]]
	2^{-i/N} \text{ for } i = 1, 2, 3\dots		2^{-i/N} \text{ for } i = 0, 1, 2, 3\dots
	[[math]]		[[math]]

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	[[math]]		[[math]]
	2^{-i/N} + x - 1 \text{ for } i = 1, 2, 3\dots		2^{-i/N} + x - 1 \text{ for } i = 0, 1, 2, 3\dots
	[[math]]		[[math]]

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	[[math]]		[[math]]
	\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 1, 2, 3\dots		\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 0, 1, 2, 3\dots
	[[math]]		[[math]]

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	2^{-i/N} \text{ for } i = 1, 2, 3\dots&lt;br/&gt;[[math]]		2^{-i/N} \text{ for } i = 0, 1, 2, 3\dots&lt;br/&gt;[[math]]
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	<br />		<br />
	If the bridge is moved so that the new scale length is x, this adds (x-1) to all string lengths, so the new string lengths are simply<br />		If the bridge is moved so that the new scale length is x, this adds (x-1) to all string lengths, so the new string lengths are simply<br />
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	<!-- ws:start:WikiTextMathRule:1:		<!-- ws:start:WikiTextMathRule:1:
	[[math]]&lt;br/&gt;		[[math]]&lt;br/&gt;
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	--><script type="math/tex">2^{-i/N} + x - 1 \text{ for } i = 1, 2, 3\dots</script><!-- ws:end:WikiTextMathRule:1 --><br />		--><script type="math/tex">2^{-i/N} + x - 1 \text{ for } i = 0, 1, 2, 3\dots</script><!-- ws:end:WikiTextMathRule:1 --><br />
	<br />		<br />
	The frequencies are inversely proportional to the string lengths. If we plug in i=0 to the above formula, we get x, so the frequency ratios relative to the open string are<br />		The frequencies are inversely proportional to the string lengths. If we plug in i=0 to the above formula, we get x, so the frequency ratios relative to the open string are<br />
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	<!-- ws:start:WikiTextMathRule:2:		<!-- ws:start:WikiTextMathRule:2:
	[[math]]&lt;br/&gt;		[[math]]&lt;br/&gt;
	\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 1, 2, 3\dots&lt;br/&gt;[[math]]		\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 0, 1, 2, 3\dots&lt;br/&gt;[[math]]
	--><script type="math/tex">\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 1, 2, 3\dots</script><!-- ws:end:WikiTextMathRule:2 --><br />		--><script type="math/tex">\frac{x}{2^{-i/N} + x - 1} \text{ for } i = 0, 1, 2, 3\dots</script><!-- ws:end:WikiTextMathRule:2 --><br />
	<br />		<br />
	Converting those frequency ratios into cents in the usual way (taking the log to base 2 and multiplying by 1200) gives the new scale in cents.<br />		Converting those frequency ratios into cents in the usual way (taking the log to base 2 and multiplying by 1200) gives the new scale in cents.<br />

Wikispaces>keenanpepper: Imported revision 372908500 - Original comment:

2012-10-14T16:04:10Z

**Imported revision 372908500 - Original comment: **

← Older revision		Revision as of 16:04, 14 October 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-14 13:12:15 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-14 16:04:10 UTC</tt>.<br>
	: The original revision id was <tt>~~372874772~~</tt>.<br>		: The original revision id was <tt>372908500</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	\|\| 15 \|\|> 1869.859 \|\|> 69.859 \|\|		\|\| 15 \|\|> 1869.859 \|\|> 69.859 \|\|

	Max error limited to 10 cents:		Max error limited to 10 cents (only the first 9 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 10edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 10edo \|\|
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	\|\| 19 \|\|> 2133.611 \|\|> 60.884 \|\|		\|\| 19 \|\|> 2133.611 \|\|> 60.884 \|\|

	Super-accurate, error limited to 1 cent:		Super-accurate, error limited to 1 cent (only the first 4 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 11edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 11edo \|\|
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	\|\| 23 \|\|> 2061.810 \|\|> -61.267 \|\|		\|\| 23 \|\|> 2061.810 \|\|> -61.267 \|\|

	Super-accurate, error limited to 1 cent:		Super-accurate, error limited to 1 cent (only the first 5 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 13edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 13edo \|\|
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	\|\| 21 \|\|> 1738.090 \|\|> -61.910 \|\|		\|\| 21 \|\|> 1738.090 \|\|> -61.910 \|\|

	Max error limited to 10 cents:		Max error limited to 10 cents (only the first 12 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 14edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 14edo \|\|
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	\|\| 21 \|\|> 1613.546 \|\|> -66.454 \|\|		\|\| 21 \|\|> 1613.546 \|\|> -66.454 \|\|

	Max error limited to 10 cents:		Max error limited to 10 cents (only the first 11 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 15edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 15edo \|\|
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	\|\| 21 \|\|> 1512.281 \|\|> -62.719 \|\|		\|\| 21 \|\|> 1512.281 \|\|> -62.719 \|\|

	Max error limited to 10 cents:		Max error limited to 10 cents (only the first 10 frets may be used):

	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 16edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 16edo \|\|
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	<br />		<br />
	Max error limited to 10 cents:<br />		Max error limited to 10 cents (only the first 9 frets may be used):<br />
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	<br />		<br />
	Super-accurate, error limited to 1 cent:<br />		Super-accurate, error limited to 1 cent (only the first 4 frets may be used):<br />
	<br />		<br />

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	<br />		<br />
	Super-accurate, error limited to 1 cent:<br />		Super-accurate, error limited to 1 cent (only the first 5 frets may be used):<br />
	<br />		<br />

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	<br />		<br />
	Max error limited to 10 cents:<br />		Max error limited to 10 cents (only the first 12 frets may be used):<br />
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	<br />		<br />
	Max error limited to 10 cents:<br />		Max error limited to 10 cents (only the first 11 frets may be used):<br />
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	<br />		<br />
	Max error limited to 10 cents:<br />		Max error limited to 10 cents (only the first 10 frets may be used):<br />
	<br />		<br />

Wikispaces>keenanpepper: Imported revision 372874772 - Original comment:

2012-10-14T13:12:15Z

**Imported revision 372874772 - Original comment: **

← Older revision		Revision as of 13:12, 14 October 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-14 13:05:45 UTC</tt>.<br>		: This revision was by author [[User:keenanpepper\|keenanpepper]] and made on <tt>2012-10-14 13:12:15 UTC</tt>.<br>
	: The original revision id was <tt>~~372873708~~</tt>.<br>		: The original revision id was <tt>372874772</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 11edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 11edo \|\|
	\|\| 0 \|\|> 0.000 \|\|> 0.000 \|\|		\|\| 0 (nut) \|\|> 0.000 \|\|> 0.000 \|\|
	\|\| 1 \|\|> 108.322 \|\|> -0.769 \|\|		\|\| 1 \|\|> 108.322 \|\|> -0.769 \|\|
	\|\| 2 \|\|> 217.183 \|\|> -0.998 \|\|		\|\| 2 \|\|> 217.183 \|\|> -0.998 \|\|
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	\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 13edo \|\|		\|\|~ Fret number \|\|~ Cents \|\|~ Deviation from 13edo \|\|
	\|\| 0 \|\|> 0.000 \|\|> 0.000 \|\|		\|\| 0 (nut) \|\|> 0.000 \|\|> 0.000 \|\|
	\|\| 1 \|\|> 93.001 \|\|> 0.693 \|\|		\|\| 1 \|\|> 93.001 \|\|> 0.693 \|\|
	\|\| 2 \|\|> 185.616 \|\|> 1.000 \|\|		\|\| 2 \|\|> 185.616 \|\|> 1.000 \|\|
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	\|\| 8 \|\|> 1246.229 \|\|> 75.768 \|\|		\|\| 8 \|\|> 1246.229 \|\|> 75.768 \|\|

	If the open strings are tuned in 9/7s or 7/5s, this makes a perfectly playable BP guitar with fret error under 9 cents. The only restriction is that you should never play frets 6 or above, because they're increasingly out of tune.</pre></div>		If the open strings are tuned in 9/7s or 7/5s, this makes a perfectly playable BP guitar with fret error under 9 cents. The only restriction is that you should never play frets 6 or above, because they're increasingly out of tune.

			=Advanced tricks=

			By adjusting the nut in addition to the bridge, it may be possible to make a surprisingly large portion of the fretboard usable with good accuracy. This is because there is another degree of freedom to tweak. For decreasing the EDO number you would want to either raise the nut or move it away from the first fret, and for increasing the EDO number you would want to either lower it or move it towards the first fret.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Moving the bridge hack</title></head><body>If you have a <a class="wiki_link" href="/12edo">12edo</a> guitar, or other fretted <a class="wiki_link" href="/string%20instruments">string instrument</a>, and you want to play in an EDO that is numerically near 12 (e.g. <a class="wiki_link" href="/11edo">11edo</a> or <a class="wiki_link" href="/13edo">13edo</a>), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Moving the bridge hack</title></head><body>If you have a <a class="wiki_link" href="/12edo">12edo</a> guitar, or other fretted <a class="wiki_link" href="/string%20instruments">string instrument</a>, and you want to play in an EDO that is numerically near 12 (e.g. <a class="wiki_link" href="/11edo">11edo</a> or <a class="wiki_link" href="/13edo">13edo</a>), then rather than redoing the whole fretboard, you might be tempted simply to move the bridge. If you move the bridge so that the 13th fret is now precisely 2/1, the frets will play precisely 13edo, right?<br />
Line 1,121:		Line 1,125:
	</tr>		</tr>
	<tr>		<tr>
	<td>0<br />		<td>0 (nut)<br />
	</td>		</td>
	<td style="text-align: right;">0.000<br />		<td style="text-align: right;">0.000<br />
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	</tr>		</tr>
	<tr>		<tr>
	<td>0<br />		<td>0 (nut)<br />
	</td>		</td>
	<td style="text-align: right;">0.000<br />		<td style="text-align: right;">0.000<br />
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	<br />		<br />
	If the open strings are tuned in 9/7s or 7/5s, this makes a perfectly playable BP guitar with fret error under 9 cents. The only restriction is that you should never play frets 6 or above, because they're increasingly out of tune.</body></html></pre></div>		If the open strings are tuned in 9/7s or 7/5s, this makes a perfectly playable BP guitar with fret error under 9 cents. The only restriction is that you should never play frets 6 or above, because they're increasingly out of tune.<br />
			<br />
			<!-- ws:start:WikiTextHeadingRule:23:&lt;h1&gt; --><h1 id="toc10"><a name="Advanced tricks"></a><!-- ws:end:WikiTextHeadingRule:23 -->Advanced tricks</h1>
			<br />
			By adjusting the nut in addition to the bridge, it may be possible to make a surprisingly large portion of the fretboard usable with good accuracy. This is because there is another degree of freedom to tweak. For decreasing the EDO number you would want to either raise the nut or move it away from the first fret, and for increasing the EDO number you would want to either lower it or move it towards the first fret.</body></html></pre></div>

Wikispaces>keenanpepper: Imported revision 372873708 - Original comment:

2012-10-14T13:05:45Z

**Imported revision 372873708 - Original comment: **

Show changes

Moving the bridge hack - Revision history

ArrowHead294 at 18:36, 13 March 2025

ArrowHead294 at 18:36, 13 March 2025

ArrowHead294 at 18:34, 13 March 2025

TallKite: added charts, added a link in "see also"

Fredg999: Markup, misc. edits, categories

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>keenanpepper: **Imported revision 373260670 - Original comment: **

Wikispaces>keenanpepper: **Imported revision 372908500 - Original comment: **

Wikispaces>keenanpepper: **Imported revision 372874772 - Original comment: **

Wikispaces>keenanpepper: **Imported revision 372873708 - Original comment: **

Wikispaces>keenanpepper: Imported revision 373260670 - Original comment:

Wikispaces>keenanpepper: Imported revision 372908500 - Original comment:

Wikispaces>keenanpepper: Imported revision 372874772 - Original comment:

Wikispaces>keenanpepper: Imported revision 372873708 - Original comment: