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{{short description|Indonesian musical rhythmic and metric used in Gamelan}}
{{for|the surgical operation|colostomy}}
{{Redirect|Lancaran|the type of ship|Lancaran (ship)}}
[[Image:Ladrang cycle.png|thumb|Ladrang form on the phrase making or colotomic instruments. p = ''kempyang'', t = ''ketuk'', ⋅ = pause, N = ''kenong'', P = ''kempul'', GONG = ''gong ageng''.<ref name="Lindsay, Jennifer 1992 p.48-49">Lindsay, Jennifer (1992). ''Javanese Gamelan'', p.48-49. {{ISBN|0-19-588582-1}}.</ref>]]

'''''Colotomy''''' is an [[Music of Indonesia|Indonesian]] description of the [[rhythm]]ic and [[meter (music)|metric]] patterns of [[gamelan]] music. It refers to the use of specific instruments to mark off nested time intervals, or the process of dividing rhythmic time into such nested cycles. In the gamelan, this is usually done by [[gong]]s of various size: the ''[[kempyang]]'', ''[[ketuk]]'', ''[[kempul]]'', ''[[kenong]]'', ''[[gong suwukan]]'', and ''[[gong ageng]]''. The fast-playing instruments, ''[[kempyang and ketuk]]'', keep a regular [[beat (music)|beat]]. The larger gongs group together these hits into larger groupings, playing once per each grouping. The largest gong, the ''[[gong ageng]]'', represents the largest time cycle and generally indicates that that section will be repeated, or the piece will move on to a new section.

The details of the rhythmic patterns depend on the '''colotomic structure''' ({{langx|jv|italic=yes|bentuk}}), also known as '''''gendhing'' structure'''. There are a number of different structures, which differ greatly in length and complexity; however, all of them have some colotomic characteristics.

In the gamelan, the instruments which articulate this structure are sometimes called the '''colotomic instruments''' (also '''interpunctuating instruments''' or '''structural instruments''', while Lindsay refers to them as "phrase-making instruments"<ref>Lindsay (1992), p.10.</ref>). The Javanese names for these instruments are onomatopoeic, with the relative resonance of the words ''gong'', ''kempul'', ''kenong'', and ''ketuk'' being comparable to that of the instruments they name.<ref>Lindsay (1992), p.14.</ref> In the system of cipher gamelan notation ([[kepatihan notation]]), the colotomic parts are notated as [[diacritical marks]] on the numbers used to show the core melody (''[[balungan]]'').

==History and usage==
The [[English language]] term was coined, presumably in [[Dutch language|Dutch]],<ref>Pickvance, Richard (2005). ''A Gamelan Manual: A Player's Guide to the Central Javanese Gamelan'', p.63. {{ISBN|9780955029509}}.</ref> from the [[Greek language|Greek]] for a unit of rhythm (''colon'') and something that divides (-''tomy''/-''tomic''),<ref>Spiller, Henry (2004). ''Gamelan: The Traditional Sounds of Indonesia, Volume 1'', p.69. {{ISBN|9781851095063}}.</ref> by the [[ethnomusicologist]] [[Jaap Kunst]].<ref>Malm, William P. (1977). ''Music Cultures of the Pacific, the Near East, and Asia'', 2nd ed. Englewood Cliffs, NJ: Prentice Hall. Page 43.</ref>

Although the term "colotomic" was derived from Indonesian music theory, it can be applied to other musical traditions as well. In particular, it has been used to describe Japanese [[gagaku]] and Thai [[piphat]].<ref>Malm, 123 and 194-195.</ref>

==Example of a colotomic structure==<!--[[Wela]] redirects directly here-->

The ''[[lancaran]]'' is a cycle of 16 beats (''keteg'') in the following order:

::'''<code>TWTN TPTN TPTN TPTG</code>'''

where T indicates the strike of the ''[[ketuk]]'', P the ''[[kempul]]'', N the ''[[kenong]]'', and G the simultaneous stroke of the ''[[gong ageng|gong]]'' and ''kenong''. The W indicates the '''''wela''''', the pause where the ''kempul'' is omitted. Thus, the ''gong'' plays once, the ''kenong'' divides that into four parts, the ''kempul'' divides each of those in two, and the ''ketuk'' divides each of those further in two. Note that except for the ''kenong'' playing on the gong, the instruments do not play when the next one plays. (Remember that the ''[[gatra (music)|gatra]]s'' of gamelan music have the strong beat (''[[seleh]]'') at the end, not at the beginning as is often considered normal for Western music. Thus the more important structural instruments coincide with the stressed beats.)

Colotomic structures occur on even larger scales in most gamelan pieces as well. For example, a typical ''lancaran'' has four gongs,{{clarify|date=May 2012|only the ''gong ageng'' is called "gong" so four what?}} at the end of which the larger ''gong ageng'' is played. Groupings of four are most common at all levels of structure, although there are numerous exceptions at larger levels.

The colotomic structure of a piece is the length of the cycle and how the interpunctuating instruments play during that cycle, but they are also [[musical form]]s which are associated with specific structural patterns on a larger scale than the colotomic cycle, and guidelines for what [[tempo|tempi]] and ''[[irama]]'' may be used.

==Colotomic structures in Javanese gamelan==

'''Colotomic structures''' or '''''Gendhing structure''''' refers to the colotomic structure of gamelan compositions in general. ''Gendhing'' (also written, as in the old orthography, '''gending''') can also be used to refer to a specific class of colotomic structures used in Javanese [[gamelan]] music.

At its simplest, ''colotomic'' may be taken to mean, "cyclicly punctuating".<ref>Downing, Sonja Lynn (2008). ''Arjuna's Angels: Girls Learning Gamelan Music in Bali'', p.304. {{ISBN|9780549702917}}.</ref> More clearly, "gongs of different sizes are used to mark off circular segments, or cycles, of musical time."<ref name="Tenzer">[[Michael Tenzer|Tenzer, Michael]] (2000). ''Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music'', p.7. {{ISBN|9780226792835}}.</ref> Though a colotomic structure may be hundreds of units long and is generally explicitly stated, it is akin to hierarchical Western [[meter (music)|meter]].<ref name="Tenzer"/>

Most ''gendhing'' in Javanese music conform to one of these structures, except for some special ceremonial pieces and experimental new compositions.

===General===
Colotomic structures from the general repertoire.

====Gendhing====
Gendhing is the longest and most complicated of the gendhing structures. It is typically played in a slow [[irama]], although it may have faster sections. Gendhing are sometimes classified by which [[elaborating instrument]] is most prominent, called ''gendhing bonang'' or ''gendhing rebab''. Gendhing never use the [[kempul]] or [[gong suwukan]].

Gendhing have two parts, a [[merong]] and a [[minggah]] (or "inggah"). Both consist of a single [[Gong ageng#Function|gongan]] lasting four [[kenong|nongan]], but the nongan can be of different lengths. Gendhing are then classified according to the number of [[kethuk]] strokes in a nongan in each section. The merong section does not use the [[kempyang]], but the minggah section does. There are two patterns for the kethuk in the merong, ''arang'' ("infrequent, sparse") and ''kerep'' ("frequent"). Both have the kethuk play only at the end of a [[gatra (music)|gatra]], but in the kerep pattern, it is at the end of all odd-numbered gatras, whereas in the arang, it is at the end of the gatras of doubled odd numbers (that is, gatras 2, 6, 10, 14, etc.). In the minggah section, the kempyang and kethuk play in the same pattern as in the [[ketawang]], but with no other [[interpunctuating instrument]]s.

For an example of the gendhing structure, consider "gendhing kethuk 2 kerep minggah kethuk 4." This means that in the merong, there will be two kethuk strokes that happen on odd-numbered gatra, and in the minggah, there will be four gatras per nongan. The structure would then look like:

Merong: 
::'''<code>...T .... ...T ...N</code>'''
::'''<code>...T .... ...T ...N</code>'''
::'''<code>...T .... ...T ...N</code>'''
::'''<code>...T .... ...T ...G</code>'''

Minggah:
::'''<code>pTp. pTp. pTp. pTpN</code>'''
::'''<code>pTp. pTp. pTp. pTpN</code>'''
::'''<code>pTp. pTp. pTp. pTpN</code>'''
::'''<code>pTp. pTp. pTp. pTpG</code>'''

where "." indicates no interpunctuating instrument plays, p indicates the stroke of the [[kempyang]], T the [[ketuk]], N the [[kenong]], and G the simultaneous stroke of the [[gong ageng|gong]] and kenong. Thus, in each section, the gong plays once, the kenong divides that into four parts, and then that is divided into parts according to the given structure. Here, in each part, each nongan lasts 16 beats (''keteg''), and thus the gongan lasts 64.

That was a fairly short example; a "kethuk 4 arang" merong, for example, would look like:

::<code>'''.... ...T .... .... .... ...T .... .... .... ...T .... .... .... ...T .... ...N'''</code>
::<code>'''.... ...T .... .... .... ...T .... .... .... ...T .... .... .... ...T .... ...N'''</code>
::<code>'''.... ...T .... .... .... ...T .... .... .... ...T .... .... .... ...T .... ...N'''</code>
::<code>'''.... ...T .... .... .... ...T .... .... .... ...T .... .... .... ...T .... ...G'''</code>

and thus a nongan would last 16 gatras (64 beats), and a gongan 64 gatras (256 beats). Obviously, in a long structure like that, especially at a slow tempo, a single gongan may last many minutes.

The merong section may include a [[ngelik]], which would also have the length of a single gongan. The minggah section may also use one of the other structures, especially the [[ladrang]]. If that is the case, the piece will be noted something like "minggah ladrang". If the other section has a different name, that will be given as well.

Between the merong and inggah is a bridge section called the [[ompak]]. Typically it has the length of one nongan, and a contrasting [[balungan]] melody to the merong.

====Ketawang====
[[File:Ketawang colotomic structure.png|175px|thumb|Ketawang structure as a clock diagram.<ref>Malm, William P. (1977). ''Music Cultures of the Pacific, the Near East, and Asia'', 2nd ed., p.53. Englewood Cliffs, NJ: Prentice Hall. {{ISBN|0131823876}}.</ref><br/>T = ''kethuk'', P = ''kempul'', N = ''kenong'', Gong = ''gong ageng''.]]

The '''ketawang''' is one of the gendhing structures used in Javanese gamelan music.

Its colotomic structure is:

::'''<code>pTpW pTpN pTpP pTpG</code>'''

where p indicates the strike of the [[kempyang]],  T the [[ketuk]], P the [[kempul]], N the [[kenong]], and G the simultaneous stroke of the [[gong ageng|gong]] and kenong. The W indicates the [[wela]], the pause where the kempul is omitted. Thus, the gong plays once, the kenong divides that into two parts, the kempul (or wela) divides each of those in two, the ketuk divides each of those further in two, and finally the kempyang divides each of those in two. The [[kendhang]] usually plays in kendhang kalih style.

Ketawang usually have the specific form of an [[ompak]] that lasts one [[Gong ageng#Function|gongan]] and may be repeated several times, and a [[ngelik]] that may last three or four gongan. Some ketawang have the same ompak but different ngelik. Ketawang often begin in [[irama tanggung]] and then slow down to [[irama dadi]] or slower.

The ketawang developed in the court of Prince [[Mangkunegara IV]] (r. 1853–1881) of [[Surakarta]].

Famous ketawang: [[Puspawarna]].

====Lancaran====
The '''lancaran''' is one of the [[gendhing structure]]s used in Javanese [[gamelan]] music. It is the shortest of the gendhing structures that are not from the [[wayang]] repertoire. '''Gangsaran''' and '''bubaran''' are related structures that share the same colotomic structure.

Groupings of four are most common at all levels of this structure. The basic [[colotomic structure]] is a cycle of 16 beats (''keteg'') in the following order:

::'''<code>TWTN TPTN TPTN TPTG</code>'''

where T indicates the strike of the [[ketuk]], P the [[kempul]], N the [[kenong]], and G the simultaneous stroke of the [[gong ageng|gong]] and kenong. The W indicates the [[wela]], the pause where the kempul is omitted. Thus, the gong plays once, the kenong divides that into four parts, the kempul divides each of those in two, and the ketuk divides each of those further in two. Note that except for the kenong playing on the gong, the instruments do not play when the next one plays. The kendhang plays in kendhang kalih style. A typical lancaran has four gongs, at the end of which the larger [[gong ageng]] is played.

Lancaran are usually played fast, usually in [[irama lancar]]. Some lancaran have a separate section which can be played between repetitions of the four-gong [[ompak]], known as the [[nyekar]] or [[Balungan|lagu]]. Lancaran are often written in [[balungan nibani]].

'''Bubaran''' are played more moderately, usually in [[irama tanggung]], but are usually written in [[balungan mlaku]]. They also use a distinctive kendhang pattern. A bubaran is used as an ending piece, to be played while the audience is departing. The best-known bubaran is [[Udan Mas]].

'''Gangsaran''' is a variety of lancaran which consists of simply a repeated tone. It originates from the [[wayang]] repertoire. It can appear at the end of a composition as well.

====Ladrang====
[[File:Ladrang cycle balungan.png|thumb|Ladrang form on the balungan instruments. GONG = ''gong ageng''.<ref name="Lindsay, Jennifer 1992 p.48-49"/>]]

The '''''ladrang''''' is one of the [[gendhing structure|''gendhing'' structures]] used in [[Javanese language|Javanese]] [[gamelan]] music.

The basic [[colotomic structure]] is a cycle of 32 beats (''keteg'') in the following order:

::'''<code>pTpW pTpN pTpP pTpN pTpP pTpN pTpP pTpG</code>'''

where p indicates the strike of the ''[[kempyang]]'', T the ''[[ketuk]]'', P the ''[[kempul]]'', N the ''[[kenong]]'', and G the simultaneous stroke of the ''[[gong ageng]]'' and ''kenong''. The W indicates the ''[[wela]]'', the pause where the ''kempul'' is omitted. Thus, the gong plays once, the ''kenong'' divides that into four parts, the ''kempul'' divides each of those in two, the ''ketuk'' divides each of those in two, and the ''kempyang'' divides each of those in two.  The ''[[kendhang]]'' usually plays in ''kendhang kalih'' style.<ref name="Guide">Sorrell, Neil (1990). ''A Guide to the Gamelan'', p.68-69. London: Faber and Faber.</ref>

The ''ladrang'' is similar to the ''[[ketawang]]'' except that four (instead of two) ''[[kenong|nongan]]'' comprise a ''[[Gong ageng#Function|gongan]]''. It is also similar to the ''[[lancaran]]'', except it is twice as slow, and the ''kempyang'' plays in between each beat of the ''lancaran''.<ref name="Guide"/>

Many ''ladrang'' have two sections, an ''[[ompak]]'' and a ''[[ngelik]]'', each of which typically last one ''gongan''. ''Ladrang'' can be played in any ''[[irama]]'' except for ''lancar''.<ref name="Guide"/>

===Wayang===
In [[Java]]nese [[gamelan]] music, there are a few [[gendhing structure]]s derived from the [[wayang]] repertoire: [[Colotomy#Ayak-ayakan|Ayak-ayakan]], [[Colotomy#Sampak|Sampak]], and [[Colotomy#Srepeg|Srepeg]].

====Ayak-ayakan====
The '''ayak-ayakan''' is one structure.

The colotomic structure is:

::<code>...P ...P</code>
::<code>TNTN TNTN</code>

with both lines played together, and T indicating a stroke of the [[kethuk]], P the [[kempul]], and N the [[kenong]]. The kenong and kempul always play the [[seleh]]. In [[slendro]] [[pathet|manyura]], the [[gong suwukan]] is used instead of the kempul.

[[Gong ageng#Function|Gongans]] are of varying length, according to the [[pathet]]. The ending ([[suwuk]]) can occur at different points in the cycle, given the cue from the [[kendhang]] or [[kepyak]].

It usually begins in [[irama lancar]], and then slows down to tanggung, dados, or rangkep.

The ayak-ayakan is often used to accompany the entrance of puppets, or the transition between [[pathet]]s.

====Sampak====
'''Sampak''' is another structure. A sampak often follows a [[Colotomy#Srepeg|srepeg]]. It is the fastest of the wayang structures.

The colotomic structure is:

::<code>NNNNNNNN NNNNNNNN</code>
::<code>TPTPTPTP TPTPTPTP</code>

with both lines played together, and T indicating a stroke of the [[kethuk]], P the [[kempul]], and N the [[kenong]]. The kenong and kempul always play the [[seleh]]. It does not use the [[kempyang]].

[[Gong ageng#Function|Gongans]] are of varying length, usually two, three, or four [[gatra (music)|gatra]]s, based on a signal from the [[kendhang]]. The ending ([[suwuk]]) can occur at any point in the cycle, given the cue from the [[kendhang]] or [[kepyak]], and consists of a gatra played after the [[gong ageng|gong]]. The melodic shape of a sampak is distinctive, as the gatras are repeated notes in the [[pathet]]. It is played in [[irama lancar]].

=====Example=====

Sampak [[pélog]] barang:

:<code>2222 3333 7777</code>
:<code>7777 2222 6666</code>
:<code>6666 3333 2222</code>
:[[Suwuk]]: <code>xx22</code>

This sampak has three gongan. The signal to end can come at any gong, where the player plays the next two notes as normal, and then 22 (as indicated by <code>xx22</code>).

====Srepeg====
'''Srepeg''' is another colotomic structure:

::<code>...P...P ...P...P</code>
::<code>TNTNTNTN TNTNTNTN</code>

with both lines played together, and T indicating a stroke of the [[kethuk]], P the [[kempul]], and N the [[kenong]]. The kenong and kempul always play the [[seleh]].

[[Gong ageng#Function|Gongans]] are of varying length, according to the [[pathet]]. The ending ([[suwuk]]) can occur at any point in the cycle, given the cue from the [[kendhang]] or [[kepyak]]. The melodic shape of a srepeg is distinctive, as it consists mostly of the [[seleh]] alternating with a [[neighbor tone]].

It is usually fast and played in [[irama lancar]].

==See also==
{{Portal|Music|Indonesia}}
* [[Gamelan]]
* [[Cycle (music)]]
* [[Division (music)]]
* [[Irama]]
* [[Music of Indonesia]]
* [[Music of Java]]

==Notes==
{{reflist}}

==Further reading==
* Neil Sorrell. ''A Guide to the Gamelan''. London: Faber and Faber, 1990. Page 67–73.

==External links==
* [[Michael Tenzer]]. Excerpt from ''[https://web.archive.org/web/20080619055505/http://www.utsc.utoronto.ca/~sanger/MWP/05.tenzer.html#anchor785473 Balinese music]'' describing colotomic structures in Balinese music {{subscription required}}

{{Gamelan}}
{{Rhythm and meter}}

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[[Category:Gamelan theory]]
[[Category:Rhythm and meter]]
[[Category:Musical form]]