{"id":954,"date":"2015-09-04T15:30:02","date_gmt":"2015-09-04T20:30:02","guid":{"rendered":"http:\/\/android-originals.com\/tulsasound\/?page_id=954"},"modified":"2015-09-04T15:30:02","modified_gmt":"2015-09-04T20:30:02","slug":"calculating-string-spacing","status":"publish","type":"page","link":"http:\/\/android-originals.com\/tulsasound\/tutorials\/calculating-string-spacing\/","title":{"rendered":"Calculating String Spacing"},"content":{"rendered":"

Sheets 2, 3, 4 & 5 in the spreadsheet, 2015-08-25 base length and nut spacing calc<\/a>.xls, calculate the nut, bridge and tailpiece string spacing for a guitar using a Golden Gate S-96FV neck, and a string set of 0.010\u201d, 0.013\u201d, 0.017\u201d, 0.030\u201d, 0.042\u201d and 0.050\u201d diameters, with the base length and fret spacings fitted to measurements in Sheet 1.\u00a0 As noted in the spreadsheet:<\/p>\n

1)\u00a0\u00a0 \u00a0Measurements are in inches, or in decimal fractions of the spacing between strings.
\n2)\u00a0\u00a0 \u00a0\u201cString span\u201d = center of the 6-string to the center of the 1-string.
\n3)\u00a0\u00a0 \u00a0\u201cString separation\u201d = distance from the side of one string to the side of the next.
\n4)\u00a0\u00a0 \u00a0\u201cFret effective width\u201d = distance across the top of the fret, between side bevels.
\n5)\u00a0\u00a0 \u00a0\u201cRelief fraction\u201d = distance from the outer sides of the outer strings to the ends of the fret effective widths in terms of a fraction of the string separation.
\n6)\u00a0\u00a0 \u00a0The blue cells are input cells, measurements and choices.
\n7)\u00a0\u00a0 \u00a0The red cells are calculation output cells, and should not be changed.
\n8)\u00a0\u00a0 \u00a0\u201cSpan factor\u201d = factor increase in the string span per inch going from the nut to the neck (inch\/inch).<\/p>\n

Sheet 2<\/strong><\/p>\n

\"2015-09-04<\/a><\/p>\n

Row 6 begins with the base length, 25.445\u201d, and the string diameters.\u00a0 Cell C8 is the effective width of fret 1, 1.525\u201d, and cell 9 is the relief distance (not fraction), 0.080\u201d.\u00a0 In row 11, the string spacing across the top of fret 1, from the string 6 end, taking string diameters into account, so that the spacing between the sides of any two adjacent strings is equal, 0.241\u201d, and the distance from strings 1 and 6 to the effective ends of the fret are 0.080\u201d.\u00a0 Row 12 makes the same calculations from the string 1 end.\u00a0 The resulting fret 1 string spacing, center 6 to center 1, is 1.335\u201d.<\/p>\n

To calculate the angular spread of the strings to the nut, bridge and tailpiece, one more set of string spacing must be calculated.\u00a0 In Sheet 2, that is determined by the effective width of fret 12 and the fraction of side relief, 0.500s time the string spacing.\u00a0 Using these two numbers and the string diameters, Sheet 2 calculates the string spacing on fret 12 in rows 18 and 19, using the same methods for rows 11 and 12.\u00a0 It also calculates the string spacing on fret 12 as 0.287\u201d and the string span as 1.565\u201d.<\/p>\n

The fret 1 to fret 12 \u201cspan factor\u201d is then the difference between the fret 12 span and the fret 1 span, divided by the distance from fret 1 to fret 12.\u00a0 This span factor then determines the decrease in span from fret 1 back to the nut, and the increase in span from the nut to the bridge and the nut to the tailpiece.\u00a0 Given that span at each position, Sheet 2 again uses the string diameters and the span to calculate equal distances between the sides of the strings, and equal distances between the sides of the 1 and 6 strings to the ends of the nut, bridge and tailpiece, respectively.\u00a0 Not being fretted by the player, the nut, bridge and tailpiece are not taken to have bevels on their ends that affect the calculations.<\/p>\n

In rows 33 to 39 of Sheet 2, the bridge string span is calculated as 1.825\u201d, from the nut string span and the span factor of 0.020.\u00a0 Using the string diameters and a bridge side relief fraction of 0.750, Sheet 2 calculates a bridge width of 2.363\u201d with a string spacing of 0.339\u201d, side to side.\u00a0 Rows 38 and 39 show the spacing of string centers from one side of the bridge to the other, both ways.<\/p>\n

Sheet 2 repeats those calculations for a tailpiece positioned 27.781\u201d from the nut, with a side relief factor of 1.500.\u00a0 It gives and effective tailpiece width of 2.947\u201d with string spacings in rows 46 and 47.<\/p>\n

Sheet 3<\/strong><\/p>\n

\"2015-09-04<\/a><\/p>\n

Sheet 3 does the same thing as Sheet 2, but uses fret 21 instead of fret 12.\u00a0 It optimizes the fret 21 side relief factor to produce a bridge width of 2.25\u201d.<\/p>\n

Sheet 4<\/strong><\/p>\n

\"2015-09-04<\/a><\/p>\n

Sheet 4 does the same thing as Sheet 3, but changes the fret 21 side relief fraction (cell C16) from 0.691 to 0.660, and the bridge side relief fraction (cell C36) from 0.750 to 0.600.<\/p>\n

Sheet 5<\/strong><\/p>\n

\"2015-09-04<\/a><\/p>\n

Sheet 5 does the same thing as Sheet 4, but changes the fret 21 side relief fraction (cell C16) from 0.660 to 0.501 to get a bridge string span (cell C34) of 1.875; changes the bridge side relief fraction (cell C36) from 0.600 to 0.495 to get a bridge effective width (cell C37) of 2.25\u201d; and changes the tailpiece side relief fraction (cell C44) from 1.500 to 1.495 to get a tailpiece width of 3.000\u201d.\u00a0 For the prototype guitar in mind, this simplifies certain construction details.\u00a0 In this case, the bridge string span is about 1\/8\u201d to 3\/16\u201d smaller than the usual 2\u201d to 2-1\/16\u201d bridge spans, meant to provide a little more room for bending the 1 and 6 strings along the neck.<\/p>\n

Summary<\/strong><\/p>\n

The insertion of 17 different measurements and choices produces string spacings at five different locations, the nut, fret 1, fret 12 or 21, the bridge and the tailpiece.\u00a0 In practice the elements under construction, the nut, bridge and tailpiece, can be marked from each end towards the center with a dial caliper, three marks on a side.\u00a0 The spacings are compensated for string diameter, so that the spacing between the sides of the strings are equal, and from the sides of strings 1 and 6 to the ends are equal.<\/p>\n

Note – There are some small, unintentional errors in these calculations.\u00a0 The spacings at two points along the neck, frets 1 and 12 in Sheets 2, and frets 1 and 21 in Sheets 3 to 5, should have determined the spacings at the other locations without compensating for the diameters of the strings, merely by extending the angular projections of the strings up and down the neck.\u00a0 But these calculations came easier.\u00a0 So, when using compensated spacings at the nut and tailpiece to set the string spacing along the neck, the string spacings at frets 1 and 12 or frets 1 and 21 will be slightly off, but not a noticeable amount.\u00a0 It is not easy to file the nut and tailpiece slots perfectly on the marked string centers; those errors are likely more significant.<\/p>\n","protected":false},"excerpt":{"rendered":"

Sheets 2, 3, 4 & 5 in the spreadsheet, 2015-08-25 base length and nut spacing calc.xls, calculate the nut, bridge and tailpiece string spacing for a guitar using a Golden Gate S-96FV neck, and a string set of 0.010\u201d, 0.013\u201d, … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":947,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/954"}],"collection":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/comments?post=954"}],"version-history":[{"count":1,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/954\/revisions"}],"predecessor-version":[{"id":955,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/954\/revisions\/955"}],"up":[{"embeddable":true,"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/pages\/947"}],"wp:attachment":[{"href":"http:\/\/android-originals.com\/tulsasound\/wp-json\/wp\/v2\/media?parent=954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}