line2sine manual

Time

Currently, if a line changes time direction, all of the vertices of the line will be resorted so that they increase in time. It may be nice to change this property to the case where a time reversal in the line will create a new oscillator track. Anyway, here is what happens to a single line which changes time direction:

Line drawn as:

Will be interpreted as:

Note that the time-sorted line will not be drawn or visible in the Diagram window. Also note that you can create two lines which join at their ends which looks like the left diagram window above. In that case, there is no problem since there are no time reversals on either line, since they both only have two vertices each.

Increasing the width of the Diagram document

Frequency

In harmonic space, equal distances in linear space are mapped directly to frequency space. For example, any pair of lines in the Diagram document which are 1 centimeter apart will always have the same frequency separation no matter where along the y-axis direction they are placed. This means that equally spaced lines with respect to 0 Hertz will be equivalent to harmonics of a fundamental. You are not allowed to use negative frequencies but are allow to alias as much as you like. The sampling rate is hardwired to 44100 Hz.

In interval space, equal distances in linear space are mapped into equal size intervals. For example, any pair of lines in the Diagram document which are 1 centimeter apart will always have the same musical interval relation no matter where along the y-axis direction they are placed. When using Interval space, you cannot use frequencies below 20 Hz.

Separate frequency tracks

Amplitude

Global amplitude control

The line2sine program prompts for a global amplitude. This amplitude scales the amplitude of all sound in the output soundfile. Values greater than 1.0 will make the sound louder; values less than 1.0 will make the sound quieter.

The line2sine program also prompts for a default amplitude envelope. This envelope will be applied to all lines which do not have their own local amplitude envelope. See the envelope section below for how to make an envelope.

Local amplitude control

The thickness of a line controls the relative loudness of that line to other lines in the Diagram window. to change the thickness of a line, click the button on the toolbar at the top of the Diagram window. Then select a line to change the amplitude of, and select the button. This will open up the style inspector as shown below:

The amplitude units are specified in units of centimeters. You may be using other measurement units according to Preferences.app. If you would like to change to centimeters in the thickness window, then open /NextApps/Preferences.app (usually second icon in your dock), then click on the icon and set measurement units to centimeters. You will probably have to restart Diagram.app in order for the change to take place. The default thickness of a line is 0.035 cm.

The global amplitude envelope for lines can be overridden by attaching a local amplitude envelope to a line. double-click on a line to create a label:

Envelope

(0 0; 1 1; 2 0)

(0 0; 1000 1; s; 2000 0)

There are several types of interpolation available:

• L = Linear interpolation between points in the envelope.
• G = Geometric interpolation between points in the envelope. This is linear interpolation on a decibel scale or interval scale. You cannot include a zero point in the envelope when using this interpolation type.
• C = Constant interpolation. the envelope points are not interpolated, but instead each value is held until then next point in the envelope.

You can control the interpolation on two levels, the first being the default interpolation for the entire envelope, for example the envelope below will be geometrically interpolated:

     g(0 0.0001; 1 1; 2 0.0001)

The local interpolation between points can be controlled by placing the interpolation letter after the first pair to be interpolated:

     (0 0; 5 0.1 g; 50 1; 100 0)

Also, you can optionally use commas in time-value pairs:

     (0, 0; 1, 1; 2, 0)

Note there is a bug in the envelope string which will be fixed eventually: you must place a zero before the decimal point for numbers less than 1.

Tips

Coarse/Fine movement

Use command-, (command comma) to switch between coarse and fine movement in a Diagram document. You can control the coarseness by using command-# (command pound) and adjusting the grid spacing.

Making harmonics

The easiest way to make harmonics is to:
1. Set the number of page rows to two across.
2. Draw a horizontal line exactly at the base of the first page row. Use 200% magnification.
3. Copy the line with command-c, and then paste the line with command-v.
4. Move the pasted line to the position of the desired fundamental frequency. Make sure that the pasted line starts at exactly the same time as the original line.
5. Now press command-v for as many harmonics as desired.
6. Erase the original line.
7. Set the page rows back to one across.
8. When using line2sine, set the interpolation to frequencies (linear), and set the minimum frequency of the Window to 0 Hz. The upper limit frequency will determine the actual pitch of the note.

Making a musical "staff"

1. Type command-# to open the Grid panel.
2. Type command-P and select two page rows across so that you can see the lower limit of the top row of pages.
3. Select a grid size to represent enough chromatic steps. Make sure that the grid aligns exactly with the bottom of the first page row. You may want to set zoom to 200%, and you may also need to type in the grid size to do fine adjustment to the grid size.
4. Now each grid line represents a chromatic frequency (or quarter-tone, etc.).
5. When using line2sine, use interval interpolation, and set the minimum and maximum frequency range to particular notes on the grid. For example, if you have 12 squares in the vertical direction, then there are 13 grid lines. Each line stands for a chromatic note, so the relation between lower and upper frequency ranges will be an octave.

See Example 10 for an implementation of these directions. Here is a table of notes near middle C (C4):

A4 = 440.000 G#4 = 415.305 G4 = 391.995 F#4 = 369.994

F4 = 349.228 E4 = 329.628 D#4 = 311.127 D4 = 293.665

C#4 = 277.183 C4 = 261.626 B3 = 246.942 A#3 = 233.082 A3 = 220.000

How to rotate and scale lines

You can rotate and scale lines by grouping them. At least two lines can be grouped together by selecting them and then pressing command-g. To rotate the group press the button on the Diagram tool bar, Then press the position button and change the angle. To make the line group larger or smaller, highlight the group and them drag one of the corners or sides of the group. To ungroup a set of lines, press command-G.

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