Chapter 24: The Shell (III)

In Chapter 16 we learned about the**alias**feature of the shell. The**alias**command allowed us to create new commands by assigning a complex pipeline to a single-word command. In this chapter we will learn how to use the shell to write more complex programs. Shell programs allow users to reduce lengthy sequences of Humdrum commands to a single user-defined command.

Shell Programs

A shell program is simply a script consisting of one or more shell commands. Suppose we had a complex procedure consisting of a number of commands and pipelines:

``extract -i ‘**Ursatz’ inputfile | humsed ‘/X/d’

> >> | context -o Y -b Z > Ursatz`` > ``extract -i ‘**Urlinie’ inputfile | humsed ‘/X/d’

> >> | context -o Y -b Z > Urlinie > > assemble Ursatz Urlinie | rid -GLId | graph``

In the above hypothetical script, we have processed an input file called inputfile. It may be that this is a procedure we would like to apply to several different files. Rather than typing the above command sequence for each file, an alternative is to place the above commands in a file. Let’s assume that we put the above commands in a file called Schenker. In order to execute this file as a shell script, we need to assign execute permissions to the file. We can do this by invoking the UNIX**chmod**command.

chmod +x Schenker

The +x option causes**chmod**to add execute permissions to the file Schenker. Using**chmod**we can change modes related to executing a file, reading a file, and writing to a file. Possible mode changes include the following:

> +xadd execute permission > -xdeny execute permission > +radd read permission > -rdeny read permission > +wadd write permission > -wdeny write permission

Having added execute permissions to the file, we can now execute the shell script or program. This is done simply by typing the name of the file; in effect, the filename becomes a new command:

Schenker

Each time we type this command, our script will be executed anew. Notice that in our script, the final output has not been sent to a file. As a result, the output from our**Schenker**command will be sent to the screen (standard output). It is convenient not to specify an output file in the script since this is often something the user would like to specify. When typing our new command, we can use file-redirection to place the output in a user-specified file:

Schenker > outputfile

As currently written, our program can be applied only to an input file whose name is literally inputfile. If we wanted to, we could edit our script and update the name of the input filename every time we want to use the command. However, it would be more convenient to specify the input filename on the command line – as we can do for other commands. For example, it would be convenient to be able to type commands such as the following:

Schenker opus118 > opus118.out

In order to allow such a possibility, we can use a predefined feature of the shell. Whenever the shell receives a command, each item of information on the command line is assigned to a shell variable. The first item on the command line is assigned to the variable $0 (normally, this is the command name). For example, in the above example, $0 is assigned the string value “Schenker.” The variables $1, $2, $3, etc. are assigned to each successive item of information on the command line. So in the above example, $1 is assigned the string value “opus118.”

These shell variables can be accessed within the shell script itself. We need to revise the script so that each occurrence of the input file is replaced by the variable $1:

``extract -i ‘**Ursatz’ $1 | humsed ‘/X/d’

> >> | context -o Y -b Z > Ursatz`` > ``extract -i ‘**Urlinie’ $1 | humsed ‘/X/d’

> >> | context -o Y -b Z > Urlinie > > assemble Ursatz Urlinie | rid -GLId | graph``

This change means that our**Schenker**command can be applied to any user- specified input file – simply by typing the filename in the command.

Flow of Control: The if Statement

Suppose we wanted our**Schenker**command to apply only to tonal works – more specifically, to works with a known key. Before processing a work, we might want to have**Schenker**test for the presence of a tandem interpretation specifying the key.

Let’s begin by using grep to search for a key tandem interpretation. An appropriate grep command would be:

grep '^\*[A-Ga-g][#-]*:' $1

Recall that we can assign the output of any command to a shell variable by placing the command within back-quotes or greves, i.e. .... Let’s assign the key interpretation to the variable KEY:

KEY=`grep '^\*[A-Ga-g][#-]*:' $1

If no key indicator is found by grep, then the variable KEY will be empty. We can test for this condition using the shell**if**statement.

KEY=`grep '^\*[A-Ga-g][#-]*:' $1` if [ "$KEY" = "" ] then > >> echo "Sorry, this input file has no key." exit > > fi

Notice that we use the dollars sign prior to the variable to mean the contents of variable KEY. The double quotation marks allow a string comparison. Our test is whether the variable $KEY is equivalent to the empty or null string “”. If the test is true, then the commands following the then statement are executed. By convention, these commands are indented for clarity. In the above case, two commands are executed if the $KEY variable is empty. The**echo**command causes the quoted string to be output. The**exit**command causes the script to terminate. Notice the presence of the**fi**command (**if**backwards). This command simply indicates that the if-block has ended.

Of course, if there is a key designation, then it is appropriate to execute the rest of our**Schenker**script. The complete script would be as follows:

KEY=`grep '^\*[A-Ga-g][#-]*:' $1` if [ "$KEY" = "" ] then > >> echo "Sorry, this input file has no key." exit > > else > >``extract -i ‘**Ursatz’ $1 | humsed ‘/X/d’

>> >>> | context -o Y -b Z > Ursatz`` >> >``extract -i ‘**Urlinie’ $1 | humsed ‘/X/d’

>> >>> | context -o Y -b Z > Urlinie >> >> assemble Ursatz Urlinie | rid -GLId | graph > > fi``

Notice the addition of the**else**statement. The**else**statement delineates the block of commands to be executed whenever the**if**condition fails – that is, when the $KEY variable does not equal the null string. Once again, to make the script more readable, we indent the commands contained in the else-block.

The**if**command provides many other ways of testing some condition. For example, the shell provides ways to determine whether a file exists, and other features.

Flow of Control: The for Statement

In music research, a common task is to apply a particular process or script to a large number of score files. By way of illustration, suppose we wanted to know the maximum number of notes in any single folk melody in a collection of Czech folksongs. Suppose further that we are located in a directory containing a large number of Czech folksongs named czech01.krn, czech02.krn, czech03.krn, and so on.

We would like to run the census -k command on each file separately, but we’d prefer not to type the command for each score. The**for**statement provides a convenient way to do this. The following commands might be typed directly at the shell:

for J in czech*.krn > do > census -k $J | grep 'Number of notes:' > done | sort -n

The pattern czech*.krn will be expanded to all of the files in the current directory that it matches. The variable**J**will take on each name in turn. The commands between**do**and**done**will be executed for each value of the variable $J. That is, initially $J will have the value czech01.krn. Having completed the do-done block of commands, the value of $J will become czech02.krn, and the do-done block will be repeated. This will continue until the value of $J has taken on all of the possible matches for czech*.krn.

The output might appear as follows:

Number of notes: 31 Number of notes: 32 Number of notes: 32 Number of notes: 34 Number of notes: 35 Number of notes: 39 Number of notes: 39 Number of notes: 40 Number of notes: 48 Number of notes: 48 Number of notes: 55 Number of notes: 78 etc.

Incidentally, the output from a**for**construction such as above can be piped to further commands, so we might identify the maximum number of notes in a Czech melody by piping the output through sort -n.

A Script for Identifying Transgressions of Voice-Leading

Shell programs can be of arbitrary complexity. Below is a shell program (dubbed**leader**) whose purpose is to identify all instances of betrayals of nine classic rules of voice-leading for a two-part input. A number of refinements have been added to the program – including input file checking, and formatting of the output.

The program is invoked as follows:

``leader ``

The input is assumed to contain two voices, each in a separate **kern_ spine. The nominally lower voice should be in the first spine. For music containing more than two voices, the Humdrum |extract|_ command should be used to select successive pairs of voices for processing by**leader**.

``# LEADER # # A shell program to check for voice-leading infractions. # This command is invoked as: # # leader # # where is assumed to be a file containing two voices, each # in a separate **kern spine, where the nominally lower voice is in the # first spine.

# Before processing, ensure that a proper input file has been specified. if [ ! -f $1 ] then echo “leader: file $1 not found” exit fi if [ $# -eq 0 ] then echo “leader: input file not specified” exit fi

# 1. Record the ranges for the two voices. echo ‘Range for Upper voice:’ extract -f 2 $1 | census -k | egrep ‘Highest|Lowest’ | sed ‘s/^/ /’ echo ‘Range for Lower voice:’ extract -f 1 $1 | census -k | egrep ‘Highest|Lowest’ | sed ‘s/^/ /’

# 2. Check for augmented or diminished melodic intervals. extract -f 1 $1 | mint -b r | sed ‘/[[Ad][Ad]*]/d’ | egrep -n ‘^[^!*].*[Ad][^1]’ |sed ‘s/:/ (/;s/$/)/;s/^/Augmented or diminished melodic interval at line: /’ extract -f 2 $1 | mint -b r | sed ‘/[[Ad][Ad]*]/d’ | egrep -n ‘^[^!*].*[Ad][^1]’ |sed ‘s/:/ (/;s/$/)/;s/^/Augmented or diminished melodic interval at line: /’

# 3. Check for consecutive fifths and octaves. echo ‘P5’ > $TMPDIR/template; echo ‘P5’ >> $TMPDIR/template hint -c $1 | patt -f $TMPDIR/template -s = | sed ‘s/ of file.*/./;s/.*Pattern/Consecutive fifth/’ echo ‘P1’ > $TMPDIR/template; echo ‘P1’ >> $TMPDIR/template hint -c $1 | patt -f $TMPDIR/template -s = | sed ‘s/ of file.*/./;s/.*Pattern/Consecutive octave/’

# 4. Check for doubling of the leading-tone. deg $1 | extract -i ‘**deg’ | ditto -s = | sed ‘s/^=.*/=/’ | egrep -n ‘^7.*7|^[^!*].*7.*7’ | egrep -v ‘7[-+]’ | sed ‘s/:.*/./;s/^/Leading-tone doubled at line: /’

# 5. Check for unisons. semits -x $1 | ditto -s = | awk ‘{if($0~/[^0-9t-]/)next}{if($1==$2) print “Unison at line: ” NR}’

# 6. Check for the crossing of parts. semits -x $1 | ditto -s = | sed ‘s/^=.*/=/’ | awk ‘{if($0~/[^0-9t-]/)next}{if($1>$2) print “Crossed parts at line: ” NR}’

# 7. Check for more than an octave between the two parts. semits -x $1 | ditto -s = | awk ‘{if($0~/[^0-9t-]/)next} {if($2-$1>12) print “More than an octave between parts at line: ” NR}’

# 8. Check for overlapping parts. extract -f 2 $1 | sed ‘s/^=.*/./’ | context -n 2 -p 1 -d XXX | rid -GL | humsed ‘s/XXX.*//’ > $TMPDIR/upper extract -f 1 $1 | sed ‘s/^=.*/./’ > $TMPDIR/lower assemble $TMPDIR/lower $TMPDIR/upper | semits -x | ditto | awk ‘{if($0~/[^0-9t-]/)next}{if($1>$2) print “Parts overlap at line: ” NR}’ extract -f 1 $1 | sed ‘s/^=.*/./’ | context -n 2 -p 1 -d XXX | rid -GL | humsed ‘s/XXX.*//’ > $TMPDIR/lower extract -f 2 $1 | sed ‘s/^=.*/./’ > $TMPDIR/upper assemble $TMPDIR/lower $TMPDIR/upper | semits -x | ditto | awk ‘{if($0~/[^0-9t-]/)next}{if($1>$2) print “Parts overlap at line: ” NR}’

# 9. Check for exposed octaves. hint -c $1 > $TMPDIR/s1 extract -f 1 $1 | deg > $TMPDIR/s2 extract -f 2 $1 | deg > $TMPDIR/s3 extract -f 1 $1 | mint | humsed ‘s/.*[3-9].*/leap/’ > $TMPDIR/s4 extract -f 2 $1 | mint | humsed ‘s/.*[3-9].*/leap/’ > $TMPDIR/s5 assemble $TMPDIR/s1 $TMPDIR/s2 $TMPDIR/s3 $TMPDIR/s4 $TMPDIR/s5 > $TMPDIR/temp egrep -n ‘P1.*^.*^.*leap.*leap|P1.*v.*v.*leap.*leap’ $TMPDIR/temp | sed ‘s/:.*/./;s/^/Exposed octave at line: /’

# Clean-up some temporary files. rm $TMPDIR/template $TMPDIR/upper $TMPDIR/lower $TMPDIR/s[1-5] $TMPDIR/temp``


Reprise

In this chapter we have illustrated how to package complex Humdrum command scripts into shell programs. This allows us to create special-purpose commands. We learned that files can be transformed into executable scripts through the**chmod**command. We also learned how to pass parameters from the command line to the script, and how to assign and modify the contents of variables. In addition, we learned how to influence the flow of control using the**if**and**for**statements. Finally, we learned that multi-line scripts can be typed directly at the command line without creating a script file.

Shell scripts can be very brief or very long. It is possible to create scripts that carry out highly sophisticated processing such as searching for voice-leading transgressions. There are innumerable features to shell programming that have not been touched-on in this chapter. Several books are available that provide comprehensive tutorials for shell programming.

Locating Violations of the Rules of Voice-Leading

The traditional rules of voice-leading have formed a standard component of conservatory training for art musicians.

For illustration purposes, we’ll apply some of the Humdrum tools to the problem of identifying betrayals of the classic rules of voice-leading in a **kern-encoded score. Note that our purpose here is not to legislate how to compose or arrange! We’re simply using the traditional voice-leading rules as a way to introduce various pattern-searching techniques.

(1) Parts Out Of Range

RULE: “Avoid parts that are out of range.”

The Humdrum |census|_ command provides a summary of various elementary features of any Humdrum input. With the -k option, |census|_ provides a summary of a further ten features pertaining to **kern format inputs. This includes the highest and lowest notes present.

census -k

Since we are interested in the highest and lowest notes for each individual part (rather than for the whole piece), we should |extract|_ each part before processing it with census.

extract -i '*soprano'  > soprano.part
census -k soprano.part

On UNIX, a set of commands that sequentially process a given input can be joined together as a “pipeline”. A pipeline feeds the output of one process to the input of another process. This means that we can simplify the above sequence of commands into a single pipeline:

extract -i '*soprano'  | census -k

We could then repeat the pipeline for each voice present:

extract -i '*alto'  | census -k extract -i '*tenor'  | census -k extract -i '*bass'  | census -k

If we wanted to get a little fancier, we could filter the output so that only the highest and lowest pitch information is output. The UNIX grep command will let us define a string for searching; egrep permits compound strings, such as the use of the OR bar (|):

extract -i '*soprano'  | census -k | egrep 'Highest|Lowest'

(2) Augmented/Diminished Melodic Intervals

RULE: “Avoid parts that move by augmented or diminished intervals.

Implementing this is simple. We first translate our pitch- related data to the melodic interval format – **mint. This can be done using the Humdrum mint command. For example, consider the following melodic fragment from the 2nd movement of Bach’s Brandenburg Concerto No. 5:

**kern
8r
8f#
8b
16.cc#
32dd
8a#
16.b
32cc#
8dd
*-

Given this input, the mint command will produce the following output. Plus signs indicate ascending intervals, while minus signs indicate descending intervals; ‘P’ means perfect, ‘M’ means major, ‘m’ means minor, ‘A’ means augmented, and ‘d’ means diminished:

**mint
[f#]
+P4
+M2
+m2
-d4
+m2
+M2
+m2
*-

Searching for diminished or augmented intervals is as simple as using the Unix grep command, with the appropriate regular expression:

grep -n '[Ad]'

The -n option will cause grep to prepend the line number of any matching patterns, so we can refer back to the original input file.

In order to avoid the letters `A’ or `d’ found in comments or interpretations, we might consider using the Humdrum |rid|_ command:

rid -GLI  | grep -n '[Ad]'

However, this will cause the line numbers output by grep to be wrong. The line numbers will correspond to the input file with the comments and interpretations removed.

A better approach is to send the complete file to grep, and use a more circumspect regular expression to eliminate comments and interpretations within grep. egrep allows us to define more complex regular expressions:

egrep '^[^!*].*[Ad]'

The expression `^[^!*]’ means “not an exclamation mark or asterisk at the beginning of a line.” The expression `.*[Ad]’ means “zero or more instances of any character followed by either an upper-case letter `A’ or a lower-case letter `d’.

In other words, the complete regular expression matches any line that contains either an upper-case `A’ or lower-case `d’ as long as the beginning of the line does not start with an exclamation mark (i.e. Humdrum comment) or an asterisk (i.e. Humdrum interpretation).

If we want to look for augmented or diminished intervals in a particular part or voice, we would begin by using the |extract|_ command to isolate the voice of interest.

Finally, putting all of the elements together in a Unix pipeline, we get the following command for identifying augmented or diminished melodic intervals:

extract -i 'alto'  | mint | egrep -n '^[^!*].*[Ad]'

If there is no output, then there are no augmented or diminished intervals present.

(3) Consecutive Fifths or Octaves

RULE: “Avoid consecutive fifths and octaves between any two parts.

Let’s focus on identifying consecutive fifths – since the process is the same for octaves.

Either the Humdrum |patt|_ or |pattern|_ commands can be used to find patterns that span more than one line or record. For this example, we’ll use |patt|_ .

First, we need to reformat our input so the data represent harmonic intervals rather than pitches. The Humdrum |hint|_ command will change most pitch representations to the harmonic interval representation – **hint. Consider, for example, the following input:

**kern  **kern
=1      =1
4c      4e
4G      4d
=2      =2
2F      2c
*-      *-

Given the following command:

hint

The following output will be produced:

**hint
=1
M3
P5
=2
P5
*-

(Notice that, in this case, the consecutive fifths are separated by a barline.)

Second, we need to define a pattern template for the |patt|_ command. The template is a series of one or more regular expressions that are stored in a separate file. In this case the pattern is trivial: just two consecutive perfect fifth tokens. We might store the following pattern in the file “template”:

P5 > P5

(Note that if we were looking for consecutive `fifths’ that need not necessarily be `perfect,’ we could simply eliminate the letter “P” in each interval given in the template.)

Given the above output from the |hint|_ command, we could search for occurrences of the defined pattern using the following command:

> The -f option is used to identify the file (template) in which the pattern-template has been stored. The -s option tells |patt|_ of any input records that should be skipped during the search process. The -s option is followed by a regular expression – in this case the equals-sign – so that any input records containing the equals-sign (i.e. **hint barlines) are ignored.

The default output from |patt|_ identifies the location of any instances of the pattern it finds in the source document.

The appropriate pipeline is:

hint | patt -f template -s =

There are a few refinements we ought to add to this process. Currently, we are searching for parallel perfect fifths only. The consecutive fifths rule pertains to all intervals that are compound-equivalents to perfect fifths (such as perfect twelfths, etc.).

This additional criteria is easily handled. The |hint|_ command provides a -c option that causes all compound intervals to be represented by their non-compound equivalents. For example, major tenths and major seventheenths, etc. will all be represented as “M3”, and so on. Hence we would modify our pipeline:

hint -c  | patt -f template -s =

(Note that an alternative way of handling the compound-intervals question would be to define slightly more complex regular expressions in our template file, e.g.

P5|P12|P19 > P5|P12|P19

In regular expressions the vertical bar (|) denotes the logical `OR’ operation. So the above pattern says “a perfect fifth OR a perfect twelfth OR a perfect nineteenth followed by a ...”)

Another refinement relates to the selection of voices. So far, we have presumed that the input consists of just two Humdrum spines containing separate parts. In a multi-part score, we must examine each pair of voices in turn, in order to determine whether any pair exhibit consecutive fifths or octaves.

The simplest (but more tedious) approach, is simply to execute our command pipeline for each pairing of voices. For example, in a traditional four-part harmonization:

extract -i '*soprano,*alto'  | hint -c | patt -f template -s = extract -i '*soprano,*tenor'  | hint -c | patt -f template -s = extract -i '*soprano,*bass'  | hint -c | patt -f template -s = extract -i '*alto,*tenor'  | hint -c | patt -f template -s = extract -i '*alto,*bass'  | hint -c | patt -f template -s = extract -i '*tenor,*bass'  | hint -c | patt -f template -s =

(There are shorter ways of doing these permutations that involves a little shell programming, but we’ll leave that for another time.)

(4) Doubled Leading Tone

RULE: “Avoid doubling the leading-tone.”

Pitches can be identified as “leading-tones” only when we have some idea of their key-related scale-degree. The Humdrum deg command translates pitch representations to a scale-degree representation where the numbers 1 to 7 represent tonic to leading-tone designations.

Notice that the score input must contain an explicit key indication (a special type of Humdrum tandem interpretation). For example, the key of G major is indicated through the presence of the following interpretation:

*G:

Minor keys are indicated using lower-case characters. For example, the following passage is in B minor:

**kern
*b:
8r
8f#
8b
16.cc#
32dd
8a#
16.b
32cc#
8dd
*-

The deg command can be used to transform this representation to scale degree. The passage begins on the dominant (degree `5’), ascends (^) to the tonic (`1’), ascends to the supertonic (^2), ascends to the median (^3) and then descends to the leading- tone (v7), etc.:

**deg
*b:
5
^1
^2
^3
v7
^1
^2
^3
*-

The following command will eliminate durations or other possible number representations that might conflict with scale-degree designations:

deg

Having translated the representation in this way, we need to search for any lines which contain two instances of the number `7’ – that is, two concurrent instances of the leading-tone.

Searching for the number 7’ is easily done using the standard Unix `grep (get regular expression) command:

deg | grep -n '7'

This will find and output all records that contain the number 7; the -n option means that the corresponding line number will also be output.

However, we want to find instances where two or more 7s occur on a single line. For this, we can use a slightly more complex regular expression

deg | grep -n '7.*7'

In the construction ”.*” the period (.) means any character, and the asterisk means “zero or more instances of ...” Hence, the regular expression means “the number 7 followed by zero or more instances of any character, followed by the number 7”. In short, this expression will match any record in which the number 7 occurs at least twice.

As in the case of our earlier search for augmented and diminished intervals, grep is insensitive to whether the matching character string is found in a data record, or whether it occurs in a Humdrum comment or interpretation. In order to avoid matching comments or interpretations, a further refinement to our regular expression is appropriate.

deg | egrep -n '^7.*7|^[^!*].*7.*7'

In this case, the regular expression says the following: “find any occurrence of the number 7 at the beginning of the line followed by zero or more characters followed by the number 7; or match any character at the beginning of the line – other than an exclamation mark or an asterisk – followed by zero or more characters, followed by the number 7, followed by zero or more characters, followed by another number 7.

Depending on the input, it is possible that Humdrum spines will be present that do not represent scale degree information. It is possible that these other kinds of data may also make use of the number 7 – but not to represent the leading-tone. In other words, it is possible that a matching `7’ has nothing to do with scale degrees. We can ensure that this doesn’t happen by first ensuring that only scale-degree spines are present in the input to be searched.

In order to do this, we can use the Humdrum |extract|_ command as a filter, and identify the types of interpretations we want to pass. In the following modification to our pipe, the |extract|_ command has been used to ensure that only **deg spines are present:

deg | extract -i '**deg' | egrep -n '^7.*7|^[^!*].*7.*7'

There are still some refinements that we could add to this command sequence, but as it stands it is guaranteed to find all doubled leading-tones – provided the notes begin at the same time. Consider the following hypothetical passage:

**kern  **kern
*C:     *C:
8c      8g
=1      =1
4B      8g
.       16a
.       16b
4A      4cc
*-      *-

Given the above command sequence, no doubled leading-tones would be identified in this passage. However, we might wish to implement a more stringent criterion that would seek out any instances where the leading-tone sounds at the same time in more than one voice. This occurs in the above example with the sixteenth-note B concurrent with the held quarter-note B in the other part.

This criterion can be accommodated by a further refinement to our command pipeline. The Humdrum |ditto|_ command is used to replace null data tokens by the immediately preceding data token in the same spine. Consider first, the output from the deg command for the above example:

**deg   **deg
*C:     *C:
1       5
=1      =1
v7      5
.       ^6
.       ^7
v6      ^1
*-      *-

If we now invoke the |ditto|_ command, the modified output is:

**deg   **deg
*C:     *C:
1       5
=1      =1
v7      5
v7      ^6
v7      ^7
v6      ^1
*-      *-

Notice that the two null tokens in the left-hand spine have been replaced by copies of the most recent data token. Now our grep command will find the two leading tones in the second last data record.

In summary, the complete command pipeline would be:

deg | extract -i '**deg' | ditto -s = | egrep -n '^7.*7|^[^!*].*7.*7'

This may seem somewhat complicated, but the basic structure of this pipeline is suitable for a very wide variety of pattern searches.

(5) Avoid Unisons

RULE: “Avoid the sharing of pitches by two parts.”

For this rule, let’s assume that we also want to identify unisons that are spelled enharmonically (such as F-sharp and G-flat).

First, we need to translate the two parts into some absolute pitch representation – such as frequency or semitones. This will ensure that enharmonically equivalent pitches have the same representation – and so will facilitate comparison.

The Humdrum |semits|_ command translates pitches to semitone distances where middle C is denoted as zero. For example, where two voices both play B3 at the same time, both the parts will have a **semits value of minus one (-1).

Like the deg command, the |semits|_ command provides a “-x option that eliminates from the output stream any characters that don’t pertain to semitones. Hence the following command will eliminate durations or other possible numerical representations that might conflict with semitone designations:

extract -i '*alto,*tenor'``* *`` | semits -x

Next we need to compare the two parts at each moment in order to determine whether they have the same numerical value. The Unix awk command will allow us to do some arithmetic. Awk auto- matically parses an input, so the value of the first spine is referred to as $1’, the value of the second spine is `$2’ and so on. The `awk expression 1==$2' is a test of whether the first and second spines are equivalent. The awk action `print NR' means to print the current line number (record number is `NR').

So the following command will print the line number for any input in which the semitone value is the same for both the alto and tenor voices:

extract -i '*alto,*tenor'  | semits -x | awk '{if($1==$2) print NR}'

There is a problem with this pipeline however. The awk command will match all sorts of non-numeric inputs – such as where null tokens (.) occur in both parts at the same time. Consequently, we need to be careful to avoid non-numeric inputs and comments.

The regular expression `[^0-9]’ will match any line that doesn’t consist solely of numbers. The expression `[^0-9-]’ will match any line that doesn’t consist solely of numbers or the minus sign. Since the tab character will also be present in our data records, we should also include the tab in our regular expression. The tab may be denoted in regular expressions by the lower-case letter `t’ preceded by a backslash. Hence the expression `[^0-9t-]’ will match only those lines consisting solely of numbers, the minus sign, and tabs.

The following awk script will output the line numbers for all inputs where the first and second spines contain identical numbers:

awk '{if($0~/[^0-9\t-]/)next}{if($1==$2) print NR}'

Adding this construction to our pipeline produces the following command for identifying unisons:

extract -f 1,2  | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($1==$2) print NR}'

(6) Crossed Parts

RULE: “Avoid the crossing of parts.”

Part-crossing occurs when a nominally higher voice uses a pitch that is lower than a nominally lower voice.

The relations “higher” and “lower” suggest the use of an arithmetic operator such as greater-than (>) or less-than (<). In brief, we will approach this question by translating the pitches to a numerical scale, and then use the general-purpose Unix awk command to test whether the nominally lower voice is truly lower.

First we need to translate the pitch representation to some sort of numerical form. We have several options. We could translate the pitches to frequency ( **freq), or we could translate them to semitones ( **semits), or we could translate them to cents (**cents). Let’s use **semits. Once again, in this representation, middle-C is represented by the number zero, and all other pitches are represented by their semitone distance (positive or negative) with respect to this reference.

We extract the two parts of interest, and then translate them to the semitone numerical representation:

extract -i '*soprano,*alto'  | semits -x

Since part-crossing may occur when one voice is holding a note, we should use the Humdrum |ditto|_ command, as we did for the doubled leading-tone problem. Hence:

extract -i '*alto,*tenor'  | semits -x | ditto -s =

Finally, we can use the Unix awk command to do a little arithmetic. Once again, in awk, 1' and 2' refer to the first and second input fields, and the built-in variable NR' refers to the current record (line) number. The expression {if($1>$2) print NR}' is a miniature program that says: “if the first input field is numerically greater than the second field for the current line, then print the line number”:

extract -i '*alto,*tenor'  | semits -x | ditto -s = | awk '{if($1>$2) print NR}'

In short, if the left-most spine has a lower numerical value than the second spine, then tell us where that occurs.

Since the **semits representation uses the lower-case letter r’ to represent a rest, we should avoid the possibility of comparing a number (note) with a rest. We can use a variation on the same `awk script as we used when checking for unisons:

awk '{if($0~/[^0-9\t-]/)next}{if($1>$2) print NR}'

Finally, the complete pipeline for identifying crossed parts:

extract -i '*soprano,*alto'  | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($1>$2) print NR}' extract -i ‘*alto,*tenor’ | semits -x | ditto -s = | awk ‘{if($0~/[^0-9t-]/)next}{if($1>$2) print NR}’ extract -i ‘*tenor,*bass’ | semits -x | ditto -s = | awk ‘{if($0~/[^0-9t-]/)next}{if($1>$2) print NR}’

(7) Parts Separated by Greater than an Octave

RULE: “Avoid intervals greater than an octave between the soprano and alto voices. Also avoid intervals greater than an octave between the alto and tenor voices.” ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::

Finding infringements of this voice-leading rule requires just a slight modification to our method for identifying the crossing of parts.

Having transformed the pitch input to a numerical form, we simply need to check whether the difference between the two semitone values is greater than 12 semitones.

The awk portion of our command is modified so that we are informed if the nominally higher voice is more than 12 semitones away from the other voice:

extract -i '*soprano,*alto'  | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($2-$1>12) print NR}' extract -i '*alto,*tenor'  | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($2-$1>12) print NR}'

(8) Overlapped Parts

RULE: “Avoid the overlapping of parts, where the pitch in an ostensibly lower voice moves to a pitch higher than the previous pitch in an ostensibly higher voice; or where the pitch in an ostensibly higher voice moves to a pitch lower than the previous pitch in an ostensibly lower voice.” ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

The following passage illustrates a violation of the part overlapping rule:

**pitch  **pitch
C4       E4
F4       A4
E4       G4
*-       *-

(In the second sonority, the lower voice (F4) moves to a pitch higher than the previous pitch in the higher voice (E4).)

This rule is similar to the part-crossing rule, only we have to compare the current pitch in one part with the previous pitch in another part.

Rather than making a direct comparison, for the purpose of this tutorial, we will make a modification to our earlier part-crossing detector. In brief, we will extract one of the parts, shift the data tokens within that part, paste the two parts back together, and then check to determine whether the shifted part shows any “crossed parts” – using our earlier command pipeline.

The following command pipe will shift the data tokens in a spine down one record. (The last data record will disappear.)

context -n 2 -p 1 -d XXX  | humsed 's/XXX.*//'

In this tutorial, we won’t discuss how this works, since the |context|_ and humsed commands will be covered in a future tutorial. For now, we can note that shifting (say) the alto part can be done by extracting the appropriate voice, and then using the shift command sequence shown above:

extract -i '**alto'  | context -n 2 -p 1 -d XXX | humsed 's/XXX.*//' > alto.shf

If we want to compare, say, the soprano and alto voices, we need to extract both parts, and shift one of them:

extract -i '*soprano'  > soprano extract -i '*alto'  | context -n 2 -p 1 -d XXX | humsed 's/XXX.*//' > alto.shf

Next, we need to assemble the shifted and unshifted parts back into a single score:

assemble alto.shf soprano > tempfile

Then we test this intermediate file for instances of “part-crossing” – using our earlier command pipeline:

semits -x tempfile | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($1>$2) print NR}'

Avoiding the temporary file altogether:

assemble alto.shf soprano | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($1>$2) print NR}'

Note that this procedure has determined whether any of the notes in the soprano voice are lower than the previous note in the alto voice. We also need to check whether any of the notes in the alto voice are higher than the previous note in the soprano voice. To do this, we simply repeat the process, shifting the other voice:

extract -i '*soprano'  | context -n 2 -p 1 -d XXX | humsed 's/XXX.*//' > soprano.shf extract -i '*alto'  > alto assemble alto soprano.shf | semits -x | ditto -s = | awk '{if($0~/[^0-9\t-]/)next}{if($1>$2) print NR}'

This processing needs to be applied for each pair of successive voices – soprano/alto, alto/tenor, tenor/bass.

(9) Exposed Octaves

RULE: “When approaching an octave by similar motion, ensure that at least one of the parts moves by step.” ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::

Violations of the exposed octaves rules must meet three conditions. First, the two voices must be separated by an octave (or two octaves, or a unison, etc.). (This suggests that we use the |hint|_ command with the -c option in order to reduce compound intervals to their non-compound equivalents.) Second, the voices must be moving in the same direction. (The **deg representation may be suitable here, since it distinguishes notes according to whether they are approached from below (“^”) or above (“v”).) Third, both voices must be moving by leap (e.g. more than two semitones).

To address this problem, let’s plan to create five different spines. The first spine will encode harmonic interval size so that all compound equivalents to a unison are represented by the string “P1”.

The second spine will indicate whether the lower voice is ascending or descending (“^” or “v”). Similarly, the third spine will indicate whether the upper voices is ascending or descending.

The fourth spine will indicate whether the melodic motion for the lower voice is by leap (“leap”), and the fifth spine will indicate whether the melodic motion for the upper voice is by leap.

Examples of violations of the exposed octaves rule will appear as one of the following two situations:

``(**hint **updown **updown **size **size) > P1 ^ ^ leap leap > P1 v v leap leap

Any other situation means that the exposed octaves rule has not been violated.

In other words, our final test can be expressed using the following egrep command:

egrep -n 'P1.*^.*^.*leap.*leap|P1.*v.*v.*leap.*leap'

Now all we need to do is generate our five spines and assemble them in the proper order.

The first spine is easily generated using the |hint|_ command. Remember that the -c option means that all intervals an octave or greater will be represented by the within-octave equivalent.

extract -i '*alto,*tenor'  | hint -c > spine1

The second and third spines can be generated using the Humdrum deg command:

extract -i '*alto'  | deg > spine2 extract -i '*tenor'  | deg > spine3

The fourth and fifth spines require a little more work. First, we calculate the melodic intervals for each voice using the Humdrum mint command.

extract -i '*alto'  | mint ...

Secondly, we need to change all data tokens indicating intervals greater than a diatonic second (3 or more semitones) into the data token consisting of the (arbitrary) character string “leap”. This can be done using the humsed stream editor.

`` ... humsed ‘s/.*[3-9].*/leap/’ > spine4 [spine5 for the other voice]``

Putting it all together, the following command sequence will let us identify any instances of exposed octaves between two arbitrary voices:

extract -i '*alto,*tenor'  | hint -c > spine1 extract -i '*alto'  | deg > spine2 extract -i '*tenor'  | deg > spine3 extract -i '*alto'  | mint | humsed 's/.*[3-9].*/leap/' > spine4 extract -i '*tenor'  | mint | humsed 's/.*[3-9].*/leap/' > spine5 assemble spine1 spine2 spine3 spine4 spine5 > tempfile egrep -n 'P1.*^.*^.*leap.*leap|P1.*v.*v.*leap.*leap' tempfile