semitones filter

The semitones filter calculates melodic semitone intervals for **kern spine notes. The filter can also be used to highlight steps, leaps, repetitions, and interval directions in the rendered notation.

Options

Displaying semitone intervals

The default output of the semitones filter creates a **tti (twelve-tone interval) spine after each **kern spine. This analysis is not printed in the rendered notation. To view the semitone interval analysis in the notation, add the -c option to output the analysis in **cdata spines (meaning “chord-like” data) that will be displayed above the notation.

Notice that the melodic semitone interval is shown on the first note of the interval. Try editing the musical text on the left to watch the analysis change in the graphical notation on the right.

Highlighting categories of intervals

The following options can be used to highlight groups of intervals:

Examples of various highlighting options are given below.

Highlight repeated notes

Adding the -r option will highlight notes that repeat.

Highlight upward intervals

Adding the -u option will highlight notes that create upward semitone intervals.

Highlight downward intervals

Adding the -d option will highlight notes that create downward semitone intervals.

Highlight stepwise intervals

Adding the -s option will highlight notes that create stepwise semitone intervals.

Highlight leap intervals

Adding the -l option will highlight notes that create melodic leaps.

The boundary between leaps and steps is 3 by default (the smallest leap is three semitones, or a minor third). To change the boundary between leaps and steps use the -j option (meaning “jump”) followed by the minimum leap size, such as -j4, which will define a 3 (minor third) as a step. To make the example clear, the -1, option is used below to highlight only the first note creating the intervals:

Highlight mixtures of interval groups

The up/down interval options can be paired with the step/leap intervals to highlight intervals that satisfy both requirements:

Here is an example of highlighting only upward steps:

And downward leaps:

Highlighting only one interval note

The -1 option can be used to highlight only the first note of an interval pair:

and -2 highlights only the second note of the interval:

Highlight styling

Various interval groups can be highlighted in different colors by using the --mark and --color options. Both must be specified to mark intervals with different colors.

made, and the color of the groups can be controlled independently. Here is an example of using the default markers @ and red color for the upward leaps, and then using a different marker to indicate a different color for downward leaps:

Rests

By default intervals are not calculated across rests:

By adding the -R option, rests will be ignored:

Note exclusion/inclusion

The -x option can be used to prevent an interval from being calculated based on a regular expression pattern. Here is an example where the interval after a fermata is suppressed:

Note that the interval for the fermata is x, meaning that it is excluded from the analysis. This is useful for use as a segmentation boundary for post-processing of the extracted intervals. When the string is a semi-colon (;), the quotes around the exclusion expression does not have to be in quotes, but if the filter is used on the command-line, the quotes are required.

The -X option reverse the exclusion, and only note tokens that contain the specified regular expression will be analyzed:

So this example only calculates the intervals that start on fermata notes.

VHV Examples

Here is an example using the following filters to highlight each refined interval class:

!!!filter: semitones -ul2A
!!!filter: semitones -dl2A --mark j --color hotpink
!!!filter: semitones -us2A --mark V --color dodgerblue
!!!filter: semitones -ds2A --mark Z --color blue
!!!filter: semitones -r2A --mark + --color limegreen
!!!filter: satb2gs

Try copy-and-pasting the above filter lines into VHV for the example Bach chorale used below.

The -2 option is used to highlight only the second note of the interval notes. This means that the color indicates the approach interval. You can try changing this to -1 to have the color indicate the departure interval. The -A option is used to prevent multiple duplicate output analysis spines to be generated. This is optional, since the analysis spines are not displayed in the graphical notation.

Click on the image to load the score and the highlighting filters into VHV. Then use the left/right arrow buttons at the top of the page to browse through other chorales with the highlighted intervals.

Try adding -x ';' to each semitones filter to ignore intervals after fermatas.

Try adding -j 5 so that leaps are defined as forths or larger intervals.

MIDI note numbers

Adding the -m will extract MIDI note numbers rather than semitone intervals:

Here is an example of extracting both MIDI note numbers and semitone intervals:

Notice that the MIDI note number plus the semitone interval below it gives the note number of the next note.

Dealing with chords

When chords are present in the input data, only the first note in the chord will be considered. If you do not know the ordering of notes in the chord, or you want to force the highest or lowest note in the chord to be used, use the chord filter to sort the notes in the chord before analysis.

Here is an example where the chords notes are mixed up, and the intervals between the single note and the chord changes in each measure due the chord-note ordering:

Sorting the chord notes from high to low, using the -d (downward) option:

Sorting the chord notes from low to high, using the -u (upward) option:

If you do not want the chord-tone notes not used in the semitone analysis to be displayed, use the -f option (meaning “first”) for the chord filter to keep only the first note of the chord. To sort notes before taking the first note, use -t to select the top (highest) note, or -b to select the bottom (lowest) note for each chord.

Command-line use

When using on the command line with no options, **tti (twelve-tone interval) spines are placed after each **kern spine from which the analysis is extracted:

humcat h://chorales/chor001.krn | semitones

**kern	**tti	**kern	**tti	**kern	**tti	**kern	**tti
*Ibass	*Ibass	*Itenor	*Itenor	*Ialto	*Ialto	*Isoprn	*Isoprn
*clefF4	*clefF4	*clefGv2	*clefGv2	*clefG2	*clefG2	*clefG2	*clefG2
*k[f#]	*k[f#]	*k[f#]	*k[f#]	*k[f#]	*k[f#]	*k[f#]	*k[f#]
*M3/4	*M3/4	*M3/4	*M3/4	*M3/4	*M3/4	*M3/4	*M3/4
4GG	12	4B	0	4d	0	4g	0
=1	=1	=1	=1	=1	=1	=1	=1
4G	-3	4B	1	4d	2	2g	7
4E	2	8cL	-1	4e	-2	.	.
.	.	8BJ	-2	.	.	.	.
4F#	1	4A	-2	4d	0	4dd	-3
=2	=2	=2	=2	=2	=2	=2	=2
4G	-5	4G	-1	2d	-3	4.b	-2
4D	2	4F#	1	.	.	.	.
.	.	.	.	.	.	8a	-2
4E	-4	4G	5	4B	5	4g	0
=3	=3	=3	=3	=3	=3	=3	=3
4C	-1	8cL	-1	8eL	-2	4.g	2
.	.	8BJ	1	8d	2	.	.
8BBL	-2	4c	2	8e	2	.	.
8AAJ	-2	.	.	8f#J	1	8a	2
4GG	7	4d	0	4g	-1	4b	-2
=4	=4	=4	=4	=4	=4	=4	=4
2D;	-7	2d;	0	2f#;	1	2a;	2
4GG	-1	4d	-5	4g	-5	4b	3
=5	=5	=5	=5	=5	=5	=5	=5
etc.

Output only analysis data

By default the output data includes all of the input data, inserting the analysis spines immediately to the right of each **kern spine. The input data can be suppressed in the output by adding the -I option, meaning “no input”:

humcat h://chorales/chor001.krn | semitones -I

**tti	**tti	**tti	**tti
*Ibass	*Itenor	*Ialto	*Isoprn
*clefF4	*clefGv2	*clefG2	*clefG2
*k[f#]	*k[f#]	*k[f#]	*k[f#]
*M3/4	*M3/4	*M3/4	*M3/4
12	0	0	0
=1	=1	=1	=1
-3	1	2	7
2	-1	-2	.
.	-2	.	.
1	-2	0	-3
=2	=2	=2	=2
-5	-1	-3	-2
2	1	.	.
.	.	.	-2
-4	5	5	0
=3	=3	=3	=3
-1	-1	-2	2
.	1	2	.
-2	2	2	.
-2	.	1	2
7	0	-1	-2
=4	=4	=4	=4
-7	0	1	2
-1	-5	-5	3
=5	=5	=5	=5
etc.

Interval histograms for Bach chorales

Using the humlib tools humcat, serialize, ridx, and sortcount, as well as the unix tool sort:

humcat -s h://chorales | semitones -I | serialize | ridx -H | sortcount | sort -nrk2

1	24
4	19
6	17
4	16
2	15
9	14
5	13
609	12
17	11
37	10
193	9
183	8
1086	7
34	6
4340	5
819	4
1038	3
15270	2
9924	1
731	r
11241	0
11157	-1
17503	-2
2065	-3
2245	-4
1589	-5
268	-6
2144	-7
116	-8
68	-9
16	-10
6	-11
461	-12
7	-14

The first column is the interval count and the second column contains the semitone interval. The largest interval is 24 (two octaves up), and the most common interval is -2 (major second).

The following example creates a webpage containing an interactive plot of the semitone histogram for the Bach chorales:

humcat -s h://chorales | semitones -I | serialize | ridx -H \
     | sortcount -v --sort number -x semitones \
     -T "Bach chorale melodic semitones"  > output.html

Move the mouse over each bar to see the count for each interval.

Exclude intervals after fermatas

To avoid counting intervals after notes with fermatas:

humcat -s h://chorales | semitones -Ix ';' | serialize \
     | ridx -H | sortcount | sort -nrk2

2	17
274	12
4	11
13	10
77	9
75	8
784	7
23	6
3625	5
414	4
603	3
14715	2
9436	1
9363	0
9	r
10935	-1
17130	-2
1786	-3
2003	-4
1418	-5
249	-6
2029	-7
99	-8
55	-9
11	-10
2	-11
432	-12
6	-14

Counting only intervals between fermatas and the following notes/rests:

humcat -s h://chorales | semitones -IX ';' | serialize \
     | ridx -H | sortcount | sort -nrk2

1	24
9	19
2	18
13	17
14	16
10	15
27	14
14	13
380	12
30	11
71	10
151	9
163	8
404	7
77	6
827	5
489	4
541	3
656	2
561	1
752	r
2035	0
272	-1
459	-2
348	-3
291	-4
208	-5
38	-6
143	-7
28	-8
30	-9
10	-10
4	-11
30	-12
2	-14

humcat -s h://chorales | semitones -IX ';' | serialize \
     | ridx -H | sortcount -v --sort number -x semitones \
     -T "Intervals after fermatas" > output.html

Repeated notes are most common after fermatas.

Interval sequences in Bach chorales

Here is an example of how to identify the most common 5-interval sequences in the Bach choral repertory:

humcat -s h://chorales | semitones -I | ridx -M \
   | serialize | context -n 5 | ridx -H | sortcount | head -n 20

311	2 1 -1 -2 -2
271	-2 -2 -1 -2 2
262	2 2 1 -1 -2
246	2 1 2 -2 -1
243	1 2 -2 -1 -2
233	-2 -1 -2 2 1
227	-2 -2 -1 -2 -2
212	2 2 -2 -2 -1
203	-1 -2 -2 2 2
185	2 -2 -2 -1 -2
184	-1 -2 2 1 2
175	1 2 2 -2 -2
162	-2 -2 2 2 1
159	-2 2 1 -1 -2
150	-2 -1 -2 -2 2
147	-2 -1 1 -1 -2
147	-2 -2 -1 1 2
145	2 2 1 2 -2
144	2 1 -1 -2 2
137	-1 -2 2 1 -1

The 20 most common 5-interval sequences are all step-wise with no repeated notes, rests, or leaps.

Counting highlighted intervals

Add the -n option to count intervals that are highlighted. This will add a line at the bottom of the data with the interval count followed by the options used to select steps, leaps, upward, downward, etc.

For example, given the input data:

**kern
*M4/4
=1
4c
4d
4e
4f
=
4c
4e
4g
4cc
=
4cc
4b
4a
4g
=
4cc
4g
4e
4c
=
*-

The command/filter:

semitones -uln

will count the number of upwards leaps:

**kern	**tti
*M4/4	*M4/4
=1	=1
4c	2
4d	2
4e	1
4f	-5
=	=
@4c	4
@@4e	3
@@4g	5
@4cc	0
=	=
4cc	-1
4b	-2
4a	-2
@4g	5
=	=
@4cc	-5
4g	-3
4e	-4
4c	.
=	=
*-	*-
!!!RDF**kern: @ = marked note
!!semitone_count: 4 UP LEAP

The line

!!semitone_count: 4 UP LEAP

means that there were four upward leaps in the example.

The -M option can be used to not mark any notes in the **kern spines, and -A can be used to not output the analysis spines. These options will cause only the semitone_count line to be added to the input data:

semitones -ulnMA

**kern
*M4/4
=1
4c
4d
4e
4f
=
4c
4e
4g
4cc
=
4cc
4b
4a
4g
=
4cc
4g
4e
4c
=
*-
!!semitone_count: 4 UP LEAP

If you only want the interval count, then use the command:

semitones -uln input.krn | awk 'END {print $2}'

which in this case will return 4.