# ExMI’s Free-Bar Length Calculator

### Software designed by Peter van Gorder

User notes by Bart Hopkin

**Click here ****to skip the notes and go straight to the Equal Temperament calculator**

**Click here ****to skip the notes and go straight to the Just Intonation calculator**

**Click here ****to view detailed notes on the calculators and how they work. (Or just read on for a less detailed version.)**

Free bars are musical bars or tubes such as those used in marimbas and xylophones, vibraphones, wind chimes and other tubular chimes, tubulons (metal-tube marimbas), and similar instruments. This software will tell you how long to make the bars to get the pitches or scale you want.

**Two important limitations**

*Limitation #1*: This software only works for bars, tubes or rods that are regular in shape. The bars have to be uniform in thickness and shape over their length — no indentations or lumps or other irregularities. Unfortunately, this means you can’t use this software with marimba bars that are tuned by thinning the underside of the center of the bar.

What it can be used for: any instrument using uniformly rectangular or cylindrical bars, rods or tubes which are not reshaped for tuning.

The results will be very accurate for bars made of metal and other materials manufactured to close tolerances.

For wood, with its natural variations in density and rigidity, the results will be more approximate.

More detailed info on this limitations

*Limitation #2*: Before using this software, you may have to cut, tune and measure a sample bar made from the same material the rest of the bars will be made from. This gives the software a starting point for comparison, allowing it to calculate lengths for all the remaining bars.

An alternative approach is to specify a fictional sample bar of length 1. In that case the software won’t give you absolute lengths, but it will give you a set of multipliers telling you how long to make your bars relative to one another in order to get your desired scale.

More info on this option

Notice that there are two versions of the calculator!

The upper one is for equal tempered scales, including the standard western 12-tone scale. Use this version of the calculator if you wish to tune to the standard western chromatic scale. You can also use it if you wish to tune to a set of notes that are a subset of the chromatic scale, such as a standard major or minor scale. In addition, more adventurous instrument makers can use this version for non-12 equal temperaments.

The lower version of the calculator is for just intonation scales. Use this version if you wish to tune to a just scale.

More info on Equal Temperament and Just Intonation

More info on choosing what scale to tune to

Two Ways of Using the Calculators

As mentioned above, you can use the free bar calculator either of two ways:

*Method 1 — the sample bar method.* Use this method to calculate actual lengths for your instrument’s bars. First, cut and tune a sample bar using the same type of material you’ll be using for the bars. Tune this bar to any of the notes in your intended scale. Enter this bar’s length into the appropriate space in the calculator. Also enter the information requested for the scale you want. When you click “calculate,” the software will calculate bar lengths for the remaining notes of your scale.

More info on tuning sample bars

*Method 2 — the relative lengths method; no sample bar needed*: Use this method to get relative lengths for your bars. In the appropriate space in the calculator, input a value of 1 for the sample bar length. (In the JI version of the calculator, enter the 1 in the space for the first note, leaving the others blank.) Then eEnter the information requested for the scale you want. Click “calculate.”

The calculator will come back with a set of length values relative to 1. For instance, imagine you put in the 1 for what is to be your instrument’s lowest note, and for some other note of your scale the calculator came back with a length value of 1.5. Then the bar for that other note should be made 1.5 times as long as the “1″ note.

User Notes

You may find that you can use the calculator without referring to the more extensive user notes, but you’ll get more out of it if you do review them.

**Free-Bar Length Calculator Version 1
E Q U A L – T E M P E R E D C A L C U L A T O R**

**Use this version of the calculator if you want to tune your instrument to any of the following scales**:

- The standard western chromatic scale (12-tone equal temperament)
- A standard major or minor scale, pentatonic scale, or any other scale that is a subset of the standard chromatic scale.
- Any other equal temperament, such as 19-tone or 31-tone equal temperament.

More info on choosing your scale

The Input Fields

*Number of Tones Per Octave*

For the standard chromatic scale or subsets of that scale, enter 12. For 19-tone equal temperament enter 19; for 31 on put 31; etc.

Sample Bar Length

Option One: If you have cut and tuned a sample bar, enter its length here (see notes above, and more detail here, if you need more explanation of the sample bar idea). It doesn’t matter what units of measure you use (inches or centimeters), as long as you stick with that unit throughout the bar tuning process.

Option Two: Enter a 1. In this case, the calculator will give you a set of numbers representing the lengths of the bars relative to one another. (See notes above, and more detail here, if you need more explanation of this.)

*
Number of Steps to Calculate Up the Scale* and

*Number of Steps to Calculate Down the Scale*

If you cut a sample bar, use these fields to indicate how many notes you want calculated above and below the sample bar. For example, if you tuned your sample bar to middle C and you want the range of the instrument to extend from the C below that to the C above, you would enter 12 for “up the scale” and 12 for “down the scale. The calculator would then give you lengths for the octave above and for the octave below your sample bar at middle C.

If you didn’t cut a sample bar and entered “1″ for the sample bar length, enter the total number of bars you want in the “up the scale” field, and enter 0 in the “down the scale” field.

**Free-Bar Length Calculator Version 2
J U S T I N T O N A T I O N C A L C U L A T O R**

Use this version of the calculator for tuning to just intonation scales.

The Input Fields

*Frequency Ratios*

Because just scales use frequency ratios to indicate the pitch relationships of the scale, with this version of the calculator you provide frequency ratios as input. Enter the ratios for your intended scale, numerator on the left of the slash, denomonator on the right.

Example: the most common form of a major scale in just intonation uses these ratios for a scale of one octave: 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1. To enter this scale, you’d type 1 and 1 in the two top most fields, 9 and 8 below that, etcetera. If you fill all the available spaces and need more, click “add another bar” to create spaces for more notes.

More information on frequency ratios

*Sample Bar Lengths*

* *Option One: If you have cut and tuned a sample bar to one of the notes in your scale, enter its length alongside the ratio for that note. (See notes above, and more detail here, if you need more explanation of the sample bar idea). It doesn’t matter what units of measure you use (inches or centimeters), as long as you stick with that unit throughout the bar cutting and tuning process.

Example: suppose you want a one-octave just major scale starting on middle C. You have entered the ratios for that scale in the calculator as described above, and you have tuned a sample bar to middle C. In the bar lengths column along side 1/1, enter the length of that sample bar. Leave the other bar lengths blank. Click calculate. The calculator will return lengths for the remaining bars.

Another example: in the above example, imagine that you tuned the sample bar not to C but to to the G above, corresponding to ratio: 3/2. Fill in the sample bar’s length alongside 3/2 in the chart, and leave the other bar lengths blank. Click calculate. The calculator will return lengths for the remaining bars.

Option Two: No sample bar. Enter a 1 in the bar length space alongside your 1/1 ratio or in the topmost space. Click calculate. In this case, the calculator will give you a set of numbers representing the lengths of the bars relative to one another. (See notes above, and more detail here, if you need more explanation of this.)

**Tip: **For the most accurate results, cut your bars a bit longer than the software’s calculated lengths and then tune them up to pitch (by shortening them) by ear or with an electronic tuner. With wooden bars, due to the inconsistencies of the material, this this approach is recommended. With metal bars manufactured to close tolerances, it’s probably not be necessary.

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