Chapter 26

Moving Signifiers between Spines

In many types of tasks is it useful to be able to transfer signifiers from one spine to another. In this chapter we will discuss two commands. The rend command makes it possible to split characters in a single spine and distribute them across two or more spines. The cleave command does the reverse: it allows characters that are distributed across two or more spines to be gathered into a single new spine. These two commands provide opportunities to create Humdrum spines that contain precisely the information of interest to the user.

The rend Command

The rend command allows a Humdrum spine to be broken apart into two or more spines. Different pieces of information can be distributed to the individual output spines. Consider for example the following spine containing pitch data:


The rend command might be used to structure this as three independent spines:

**octave	**note	**accidental
3	Ab	b
4	F#	#
5	C	.
*-	*-	*-

The operation of rend requires a reassignment file where each line contains an output exclusive interpretation, followed by a tab, followed by a regular expression. In the above case, the reassignment file (reassign) contained the following:

**octave	[0-9]
**note	[A-Gb#x]
**accidental	[b#x]

The first line tells rend that any signifiers matching the character-class 0-9 should be output in a spine labelled octave. The second line causes signifiers matching the upper-case letters A to G and the b, # and x signifiers to be output in a spine labelled note. The third line causes signifiers matching just b, # and x to be output in a spine labelled accidental.

The above output was generated by invoking the following command:

rend -i '**pitch' -f reassign inputfile

Note that the i and f options are mandatory. The i option tells rend which input spines to process and the f option tells rend the name of the file containing the spine-reassignments.

The rend command is typically paired with a subsequent cleave command.

The cleave Command

The cleave command amalgamates concurrent data tokens in two or more spines into a single data spine. In effect, cleave does the opposite of rend. By way of example, cleave can be used to transform the following:

**A	**B	**C
a	b	c
*-	*-	*-



Specifically, the above “cleaving” would be done using the following command:

cleave -i '**A,**B,**C' -o '**new' inputfile

Both the i and o options are mandatory. The i option tells cleave which exclusive interpretations should be cleaved together. In the above case, we have provided a list of three types of data. The o option tells cleave what to call the resulting cleaved spine. In this case, we’ve simply called the result new.

Suppose that we would like to automatically add key-velocities to some MIDI data that reflect the normal accents arising from the meter. For example, in 4/4 meter, we would like the first note in each measure to be strongest, the third beat to be next most strongest and so on. Recall that MIDI data tokens consist of three elements: (1) the duration in MIDI clock ticks, (2) the key number (also on/off indication), and (3) the key velocity. In order to add accents, we need to change the key velocity values. The maximum MIDI key velocity value is 127; the minimum value is 0; and the default value is 64.

Consider the following hypothetical input file:


The metpos command can be used to identify the metric position of various note onsets. Before using metpos however, we must use the timebase command to create an isorhythmic record structure. Since the shortest note is an eighth-note, the appropriate command is as follows.

timebase -t 8 scale > scale.tb

Using the timebased output, we can then invoke the metpos command:

metpos scale.tb > scale.met

The resulting output contains both the original input (on the left) and the metric position spine (on the right):

**kern	**metpos
*M4/4	*M4/4
*tb8	*tb8
=1-	=1-
4c	1
.	4
8d	3
8e	4
8f	2
8g	4
8a	3
8b	4
=2	=2
2cc	1
.	4
.	3
.	4
*-	*-

Let’s now eliminate the null data tokens introduced by timebase. Using humsed, we delete each data record beginning with a period character:

humsed '/^\./d' scale.met > scale.tmp

Next, we can use the recode command to change the metric position values to appropriate MIDI key velocities. We might use the following reassignment file (named accent):

==1	100
==2	80
==3	60
==4	40
else	error

In applying recode we will take care to avoid processing measure numbers using the s (skip) option:

recode -f accent -s ^= -i '**metpos' scale.tmp > scale.acc

The output will now appear as follows:

**kern	**metpos
*M4/4	*M4/4
*tb8	*tb8
=1-	=1-
4c	100
8d	60
8e	40
8f	80
8g	40
8a	60
8b	40
=2	=2
2cc	100
*-	*-

Now we can use the midi command to generate MIDI data:

midi scale.acc > scale.mid

The result is given below:

**MIDI		**metpos
*Ch1		*
*M4/4		*M4/4
*tb8		*tb8
=1-		=1-
72/60/64	100
72/-60/64	72/62/64	60
36/-62/64	36/64/64	40
36/-64/64	36/65/64	80
36/-65/64	36/67/64	40
36/-67/64	36/69/64	60
36/-69/64	36/71/64	40
=2		=2
36/-71/64	36/72/64	100
144/-72/64	.
*-		*-

Before using cleave to join the new key velocity values to the MIDI data we need to delete the current key-down velocities. These are the values 64 preceding the tab character. The humsed command can be used as follows:

humsed 's/64<tab>/<tab>/' scale.mid > scale.tmp

The modified output will now be:

**MIDI		**metpos
*Ch1		*
*M4/4		*M4/4
*tb8		*tb8
=1-		=1-
72/60/		100
72/-60/64	72/62/	60
36/-62/64	36/64/	40
36/-64/64	36/65/	80
36/-65/64	36/67/	40
36/-67/64	36/69/	60
36/-69/64	36/71/	40
=2		=2
36/-71/64	36/72/	100
144/-72/	.
*-		*-

Finally, we use cleave to add the new key-down velocities.

cleave -i '**MIDI,**metpos' -o '**MIDI' scale.tmp > scale.mid

The final output is:

72/-60/64 72/62/60
36/-62/64 36/64/40
36/-64/64 36/65/80
36/-65/64 36/67/40
36/-67/64 36/69/60
36/-69/64 36/71/40
36/-71/64 36/72/100

Creating Mixed Representations

For some analytic tasks it is often useful to generate a special representation that combines all of the elements or types of data of interest to the researcher. For example, suppose we were working on a model of melodic organization that reduced melodies to three types of information: relative-duration context, gross pitch height, and scale step. Sample data tokens for our representation and their meanings are given in the following table. Notice that the order of signifiers is important:

token meaning
LSLHto long-short-long rhythm, high pitch, tonic
LLSLsd long-long-short rhythm, low pitch, subdominant
MLSMlt medium-long-short rhythm, medium pitch, leading tone
r rest

In Chapter 22 we learned how to use recode to classify various numerical ranges and humsed to classify non-numeric data. We already know how to create the elements of our new representation.

The scale degree information can be created by using deg and humsed can be used to transform the signifiers as in the following degree file:


We can classify the pitch ranges into high, medium, and low using the semits command, followed by recode. For example, we could transform the semits data using the following reassignment file:

<0	L
>16	H
>=0	M
else	r

Durations can be similarly classified into long (L), medium (M), and short (S) using the dur command, followed by recode.

>1.0	L
>0.5	M
>0	S

Using context -n 3 we could then create contextual triples so that data records contain three durations. Suppose also that we have used sed to change the names of the exclusive interpretations so they are more appropriate. As a result we have three spines that, when assembled together are organized as in Example 26.1

Example 26.1

**rhythm	**range	**scale-step
L S L	H	to
L L S	L	sd
M L S	M	lt
r	r	r
*-	*-	*-

We need to process the first spine with humsed again to eliminate the spaces in the multiple stops. The rhythm spine would be processed as follows:

humsed 's/ //g' rhythm >

We could assemble these spines using the assemble command:

assemble range scale.step > newfile

Finally we can use cleave to amalgamate all of the data into a single final spine.

cleave -i '**rhythm,**range,**scale-step' -o '**complex' \
     newfile > output

Having created our new representation, we can continue to process this new data with the various Humdrum tools. For example, we could generate inventories that answer questions such as “How often does a high subdominant note in a long-short-long rhythmic follow a low submediant in a long-long-short context?

A similar approach can be used to address other questions, such as whether large leaps involving chromatically-altered tones tend to have a longer duration on the altered tone. Etc.


In this chapter we have seen how rend and cleave can be used to take bits and pieces of signifiers from potentially many spines, and assemble a composite Humdrum spine that contains precisely the information of interest. Before amalgamating spines, you can use the humsed command to translate the characters/signifiers so that you use your preferred way of representing something.