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Time Signatures and Rhythmic Units

AudioMulch supports two concepts used to deal with musical rhythm: time signatures and rhythmic units (rhythmic durations). Time signatures are used for describing the grids used for rhythmic patterns and the automation timeline, rhythmic units are used in contraptions that deal with clock synchronized pulses, such as the Quantize setting on granulators or delay times in the tempo-synced SDelay contraption. AudioMulch uses numbers, fractions and ratios to describe these values rather than western music notation symbols.

Time Signatures

Rhythmic music is usually based on cycles of regular, counted beats or pulses. A time signature specifies how many beats there are in each rhythmic cycle. In western music each cycle is called a “bar.” A time signature also specifies the duration of each beat. Western pop music usually has four beats in a bar, but there are many other possibilities, found in classical and folk music.

A time signature is written as a fraction, for example:

The upper number (the numerator) is the number of beats in each bar, and the lower number (the denominator) forms a fraction representing the duration of each beat. The above example indicates bars comprising of 3 beats, each of which has the duration of a quarter note, i.e. 3 times 1/4.

Often the lower number is only important in understanding the relative duration of beats when the time signature changes. For example, when the time signature changes from 3/4 to 3/8, the duration of each beat halves (the effective beat-rate or tempo doubles). The lower number also determines the relationship of beats to the global tempo, and in AudioMulch to any external synchronization such as MIDI clock sync.

Grouping beats within a bar

There are common-practice rules for how beats are grouped within each bar. For example, 6/8 is usually grouped as two groups of three beats. In performed music this may determine how the performer accents each beat. However, in the computer there is no such interpretation – each beat is equal. That said, it may still be useful to group beats to make it easier to visually orient yourself within an bar – AudioMulch will draw grid lines with different weights to indicate the grouping, and with custom time signatures it is possible to explicitly specify how beats are grouped (see below).

Editing Time Signatures

AudioMulch uses time signatures whenever you specify a rhythmic pattern, such as in the Drums contraption or in the Automation timeline. The main use of time signatures is to select the grid used for snapping events and pattern lengths. Some contraptions also synchronize their mute/unmute controls to bar boundaries.

On each timeline, AudioMulch displays a Time Signature Channel. Click on the horizontal line in the center of the channel to create time signature changes. Clicking on the time signature numbers displays a popup context menu with a list of different time signatures that you can select. You can also choose Other... to specify a custom time signature (see below). By clicking on the dark bar line to the left of the time signature numbers you can drag time signature left or right to determine the time at which the time signature will change. As with other automation channels, you can delete a time signature by dragging it up or down off the channel.

When dragging time signatures they will snap to the beat boundaries of the preceeding time signature. The time signature channel displays special indicators when a time signature change is not aligned to a bar or beat boundary (which might cause a rhythmic glitch).

When the time signature change is beat-aligned but not aligned to a bar boundary an asterisk (*) is displayed at the start of the preceding bar. For example, in the image above notice how the second 4/4 bar only has 3 beats.

When a time signature change is not beat-aligned an indicator showing three vertical break marks is drawn at the left of the time signature change. Usually this happens when you change the preceding time signature so the next one is no longer beat aligned.

Custom Time Signatures

Selecting Other... from the time signature's popup context menu displays a dialog box that lets you specify a custom time signature. Two text boxes let you type in the numbers for the upper and lower part of the time signature fraction. You can enter any integers you like into these boxes, for example 13/27 is a valid time signature in AudioMulch. Using unusual numbers in the denominator (lower number) is most useful when creating multiple patterns with beats with different relative durations. For example, two Drums contraptions might be set up with time signatures of 13/27 and 13/26, resulting in a complex but predictable relationship between rhythms in each.

Once a custom time signature has been created it will be displayed at the top of the popup list of time signatures so you can select it from any other time signature editor in AudioMulch. Custom time signatures are stored with the document, and only remain in the list while they are being used. Unused time signatures are discarded when the document is closed.

Grouping beats

It is possible to explicitly specify groupings of beats within a bar. For example 5/4 can be written as 2+3/4 or 3+2/4 as shown below. More complex groupings such as (3+2+2)+(3+2+2)+(2+2+3+2+2), the 25 pulse Bulgarian Sedi Donka, are also possible. AudioMulch indicates the groupings by drawing grid lines with different thicknesses.

You can group beats by using a combination of plus signs + and brackets (). Nested groups are also possible, eg 2 + (1+3 + (2+1))/4

Fractional Denominators

AudioMulch also allows the lower number (the denominator) to be specified as a fraction of two integers. This provides another way to create patterns with the same number of beats but with different durations for each beat.

For example, bars of 4/(8/3) are 1.5 times longer than bars of 4/4. In 4/(8/3) the beat duration is 1/(8/3) which simplifies to 3/8, or, 1.5/4 (although the latter isn't a valid AudioMulch time signature).

Rhythmic Units

AudioMulch lets you specify some rhythmic quantities as multiples of a rhythmic unit. For example: granulator contraption quantization periods, delay times, and automation snap resolutions. The popup context menus for selecting rhythmic units present the standard options, usually fractions of a whole note. These fractions are equivalent to the fractions formed by the denominators (lower numbers) of time signatures, as described above. Triplets are indicated by the [3:2] ratio next to the fraction.

As with time signatures, you can specify custom rhythmic units by selecting Other... from the drop down list. When you select Other..., a dialog box is displayed which allows you to specify the rhythmic unit as a fraction optionally combined with a tuplet ratio.

The tuplet ratio X:Y (where X and Y are integers) means “X pulses take the time of Y pulses specified by the rhythmic unit fraction". Common examples are 3:2 (three in the time of two, or triplets) and 5:2 (five in the time of two, or quintuplets), but more complex relationships are possible.

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