ORI GIN AL PA PER

The Taxonomy of a Japanese Stroll Garden:An Ontological Investigation Using FormalConcept Analysis

Michael Fowler

Received: 24 January 2012 / Accepted: 28 May 2012

Springer Science+Business Media B.V. 2012

Abstract This paper introduces current acoustic theories relating to the phe-nomenology of sound as a framework for interrogating concepts relating to the

ecologies of acoustic and landscape phenomena in a Japanese stroll garden. By

applying the technique of Formal Concept Analysis, a partially ordered lattice of

garden objects and attributes is visualized as a means to investigate the relationship

between elements of the taxonomy.

Keywords Formal concept analysis Japanese garden Acoustic theory Design studies

1 Introduction

Some of the most recent research into Japanese garden design has focused on

uncovering underlying structural traits via the human process of visual perception as

a means to describe general spatial principles used by garden designers (van Tonder

2007; van Tonder and Lyons 2005; Yamaguchi et al. 2008). The impact of the

Japanese garden as a richly visual encounter has led to a substantial body of

discourse relating to the aesthetics of these spaces, which are often understood as a

nexus between nature and art (Carlson 2000) facilitated through highly controlled

manifestations in landscape form (Nitschke 1999; Keane 1996; Young et al. 2005;

Itoh 1972; Kuitert 2002). That the widely known karesansui, or dry rock gardens ofthe Muromachi era (13361573) have similarly been frequently discussed with

regards to understanding their semiotics (Casalis 1983; Berthier and Parkes 2000;

Holborn 1978; Bring and Wayembergh 1981) have placed what Schafer (1977)

M. Fowler (&)Fachgebiet Audiokommunikation, Technische Universitat Berlin, Berlin, Germany

e-mail: synthifou@gmail.com

123

Axiomathes

DOI 10.1007/s10516-012-9195-y

describes as the acoustic ecology of such spaces as an unexplored realm for Westernscience or Western metaphysics (Fowler 2010).

Within the two surviving historical Japanese garden treatises, the eleventh

century Sakuteiki (The Classic of Garden Making) and the fifth century Senzuinarabi ni yagyo no zu (Illustrations for Designing Mountain, Water and HillsideField Landscapes) there is no direct mention of gardening for acoustic effects. But

given the oral traditions of Japanese garden design and production, and its

traditionally secretive approach to the passing down of information between niwashi(master gardener) and minarai (apprentice) (Slawson 1987), the consideration ofthe acoustic qualities of a garden may have played an equally important, yet

undocumented role in the landscape design. There is just such a suggestion in

Murasaki Shikibus eleventh century Heian text Genji Monogatari (Tale of Genji),which contains a considered passage on the effects of tuning a water feature in a

Japanese garden:

The new grand Rokujo mansion was finished The hills were high and thelake was most ingeniously designed Clear spring water went singing off intothe distance, over rocks designed to enhance the music. There was a waterfall,

and the whole expanse was a wild profusion of autumn flowers and leaves

(Seidensticker 1976).

As a means to examine more closely the role of acoustic design within traditional

Japanese garden landscapes, this paper will introduce key concepts of three

prominent acoustic theorists, R. Murray Schafer, Barry Blesser and Linda-Ruth

Salter as a means to construct a taxonomy of the Japanese stroll garden Kyu

Furukawa Teien. Such an approach will allow for an examination of the connection

between designed elements of landscape and soundscape form (Schafer 1977).I further utilize the methodology of Formal Concept Analysis (FCA) (Willie 1982)

to explore the garden as a constructed ontology via the visualization of a partially

ordered lattice, which then allows for deep-level concepts and sub-concepts of the

gardens contents to be revealed for discussion.

2 Acoustic Theory: Soundscape and Aural Architecture

Theories on sound and the sounding environment as a discourse linked to

Heideggers notion of phenomenology have most prominently, and moreover only

very recently, been forwarded by the Canadian composer R. Murray Schafer. His

interdisciplinary research group founded at Simon Frasier University in Vancouver

in the late 1960s was an amalgam of researchers active in musical composition,

noise engineering, psychoacoustics and urban planning. As a means to place a

greater emphasis on the sounding environment of cities as spaces for greater design

control regarding acoustic phenomenon, Schafer introduced the notion of sound-scape as a derivation from the word landscape. Much like Heiddegers (1971)notion of place, Truax (2001) describes Schafers concept of soundscape asrepresenting the total sounding environment (or acoustic ecology) in which the

subjectivity of the listener places them within it. The soundscape is thus not merely

Axiomathes

123

emerging from the physical environment, but may also be experienced through

virtual simulations or audio recordings.

Central to the theory of soundscape is the method by which a taxonomy is

constructed that describes the constituent sounds of the acoustic space as well as a

knowledge of the auditors or the acoustic community of the environment (includingtheir cultural, social, political or aesthetic expectations). Schafer (1977) introduces

three classes of sounds, soundmarks, keynotes and sound signals whose numerousinstances compete within an environment, in effect producing particular sensory

experiences that meaningfully connect an auditor to a place.

Soundmarks are those sounds that are considered culturally significant or deemed

by an acoustic community to warrant preservation (e.g., church/temple bells, town

square clocks, foghorns), while keynote sounds are those which are continuously

operable within a site and form a background (e.g., traffic, air conditioner sounds,

muzak). Sound Signals represent foregrounded sounds within a soundscape and thus

may dynamically change and include local soundmarks, though as Truax (1999) and

Augoyard and Torgue (2005) have noted, within modern cities the increase in the

SPL (sound pressure level) of emergency warning signals is a direct consequence of

the increased noise floor level of urban spaces. Truax (2001) also argues that within

urban environments, sound signals are overwhelmingly generated through electro-

acoustic means and are contributing to the masking of historical soundmarks and

thus producing lo-fi (low fidelity) auditory environments.In contrast to Schafers focus on the taxonomy of a soundscape as a distinct and

separable entity of an environment or ecology (Carter 2003), Blesser and Salter

(2007) have built an acoustic theory more closely aligned with the architectural

phenomenology of Alberto Perez-Gomez (2001). For Blesser and Salter the auditory

experience of a sounding environment might equally be facilitated through real or

virtual means, though their notion of the aural architecture of space is contingent onthe materiality, geometry and texture of its context. Using the key terms of activeand passive aural embellishment, an environments spatial context can beconsidered not only in regards to Schafers taxonomy of sound classes, but also

the effects of landscape or architectonic forms in filtering, reflecting, diffusing and

diffracting sound waves, which consequently create particular acoustic typologies

(or identifiable behaviors). Like Schafers theory of soundscape, the notion of aural

architecture also implies listening as a subjective activity in which particular

combinations of active and passive aural embellishments sum to activate an

auditors spatial auditory awareness.

3 The Garden of Kyu Furukawa Teien

Given that most of the interest in the field of design studies of the Japanese garden

has arisen from investigations that focus purely on the visual manifestations of

landscape form (Nitschke 1999; Keane 1996; Young et al. 2005; Itoh 1972; Kuitert

2002), the case for considering the taxonomy of a Japanese garden as a spatial

phenomena in which objects or elements are sources emerging from landscape andsoundscape contexts seems feasible. In fact Blesser and Salter (2007) have used

Axiomathes

123

their theory of aural architecture to position the Japanese garden as an example of a

highly considered aural design space, though historical Japanese garden treatises are

remiss with instructions regarding design considerations of the acoustic environ-

ment (Takei and Keane 2001; Slawson 1987). But recent visits (Fowler 2010;

Fowler and Harvey 2006) to the Tokyo garden Kyu Furukawa Teien suggest Blesser

and Salters notion of a highly considered acoustic design operating within the

Japanese garden is a quality readily experienced on-site. In particular, the presence

of a shakkei no oto or auditory shakkei (borrowed sound scene) (Fowler 2013) setsthis garden apart from many of its more famous Kyoto contemporaries.

Completed in 1917 and featuring a Western-style house designed by ex-patriot

English architect Josiah Conder (18521920), the garden of Kyu Furukawa Teien in

Kita-ku, Tokyo is an excellent example of a chisen-shiki-kaiyu-teien or strollgarden. Using the slope of the surrounding Muashino highland, the garden, designed

by Ogawa Jihei (18601933), exhibits many of the common traits of Taisho

(19121926) landscaping. By typically combining the elements of previous

Japanese garden styles, Kyu Furukawa Teien uses rock features (including a

karetaki or dry waterfall) prominent in the Muromachi-era (13361573), a largepond (shinjiike) favored in Heian (7941185) garden aesthetics, and a tea house andtea garden most commonly found in Meiji (18681912) designed landscapes. As

van Tonder and Lyons (2005) have noted, the traditional focus of rocks, rock

groupings or rock formations are also abundant in Kyu Furukawa Teien, as is the

preference for odd numbering, the suggestion of numerous landscape typologies

(e.g., ravines, mountains, rivers), predilection for asymmetrical compositions,

uniform textures and natural looking features.

The landscape features of the garden (see Fig. 1) also combine what Carlson

(2000) considers the dialectic relationship they construct when elements of the

naturally appearing environment (topography, plantings, water) are juxtaposed with

artificial architectonic objects (lanterns, bridges, architecture). Indeed all the

elements of a garden, from the topography, rock placements, paths and water

features have been codified and named within the two extent treatises on garden

making (each available in modern translations): the eleventh Century Sakuteiki(Takei and Keane 2001) and fifth Century Senzui Narabi ni yagyou no zu (Slawson1987). But in the case of Kyu Furukawa Teien, a number of the landscape features

are also active aural embellishments and thus contribute to the gardens soundscape

design.

The most prominent of the landscape features that contribute to the acoustic

activation of the site is the ootaki or large waterfall and the suiro (a smallwatercourse) that empties shinjiike to the southwest. With a drop of 10 m theprojection of the sounds of falling water from the ootaki can be heard across the site.In what Schafer would identify as a soundmark, the ootaki represents thepredominate sound signal of the garden in which other sounds such as the exterior

hum of the city or the sound of wind in the trees provides a background keynote.

Other signals that occur seasonally within Kyu Furukawa Teien include bird life,

aquatic animals (such as the movement of fish and turtles) as well as insects (cicadas

during summer months). The other passive landscape features of the garden act in

concert with these active aural embellishments. In particular, shinjiike and its low

Axiomathes

123

Fig

.1

Rep

rese

nta

tive

landsc

ape

elem

ents

of

the

gar

den

atK

yu

Furu

kaw

aT

eien

(see

also

Tab

le2).

To

pro

w(L

-R):

keik

oku

(rav

ine)

,is

hid

oro

(sto

ne

lan

tern

),ch

a-s

hit

u(M

eiji

tea

ho

use

),ka

reta

ki(d

ryw

ater

fall

).S

econd

Row

(L-R

):so

ri-b

ash

i(w

oo

den

arch

bri

dge)

and

myo

seki

(tu

rtle

rock

),sh

inji

ike

(po

nd

),is

hid

xoro

(sto

ne

lan

tern

),n

ori

-n

o-i

shi

(mo

un

tain

pat

h).

Th

ird

Ro

w(L

-R):

saw

ata

riac

ross

the

kare

taki

,ex

teri

or

arch

itec

tura

lco

nte

xt,

ish

iba

shi

(sto

ne

bri

dge)

,to

bi-i

shi

(ste

ppin

gst

on

ep

ath

).F

ourt

hR

ow

(L-R

):se

kito

(sto

ne

pag

oda)

,F

uru

kaw

are

sid

ence

,h

eav

ytr

eeco

ver

,o

ota

ki(w

ater

fall

)

Axiomathes

123

lying topographic aspect together with the various acoustically reflective rocks

around it, including the formation of the karetaki (dry waterfall comprised of stonesemulating the movement of water), enable the soundmark of the ootaki to penetratethe site and produce what Blesser and Salter (2007) describe as an acoustic arena(a localized area in which sounds can be heard). This arena then facilitates the

operation of the gardens shakkei no oto (Fowler 2013), in which the distant soundof falling water at the ootaki, while hidden from view at the karetaki by over 50m, isclearly heardan effective borrowing of the waterfalls soundscape to compliment

the implication of moving water that is manifest within the rock sculpture of the

karetaki.

4 Generating an Ontology Using Formal Concept Analysis

That the theories of Schafer, Blesser and Salter can be readily used in analyzing the

acoustic qualities of Kyu Furukawa Teien through naming or identifying the

function of various landscape/soundscape elements leaves the deeper question of

the structure and connections between such elements as an unaccounted one

especially in the case of the shakkei no oto. As a particularly relevant question to thediscipline of design theory, an inquiry into the garden as a synthesis between

qualities of landscape ecology that produce or enable acoustic behaviors may

provide a new discourse on the conceptual attributes and goals of the Japanese

garden designer. By positioning the Japanese garden as a design space (Woodburyand Burrow 2005) in which a networked structure of related descriptions of partial

and/or intentional designs are housed, allows for a systematic analysis of the design

artifacts using the technique of FCA (Willie 1982). With FCA, an ontology of the

garden is constructed in which a systematic investigation into its taxonomy may

reveal deeper spatial predilections regarding its design space.

As Priss (2006) notes, FCA has most widely been used in the information

sciences, Artificial Intelligence, information retrieval and software engineering as a

method for data analysis, knowledge representation and information management.

Wolff (1994) describes the fundamentals of FCA as an mathematical exploration of

incidence relations between objects and attributes. Vogt and Willie (1995) define a

formal context (see Table 1) as a collection of binary relations between a set of

objects, G (derived from the German word Gegenstande) and their correspondingattributes M (Merkmale). Given that it may be impossible to list all attributes of anygiven object, a specific formal context or closed world is assumed (Davey and

Priestley 2002). This formal context (K) is then expressed as: K G; M; I forwhich G and M are sets while I is a binary relation between G and M, i.e., I GM (Ganter et al. 2005). This fundamental tenant of FCA is understood as objectg has the attribute m, and is notated as gIm or g; m 2 I:

Table 1 is a generated formal context of objects and attributes from site visit

observations of the Japanese garden Kyu Furukawa Teien. By utilizing attributes

forwarded by Schafer (1977), Blesser and Salter (2007) together with Carlsons

(2000) contention that Japanese gardens are a dialectic construction between

natural and artificial elements, the context attempts to canvas qualities of both

Axiomathes

123

landscape and acoustic phenomena. The additional attributes of seasonal, terrestrialand architectonic similarly provide a scope for interrogating the myriad instances ofobjects within the garden. Rather than pursuing the impracticality of specifying all

instances of garden objects (e.g., every species of tree etc.) object classes are used,

of which instances (i.e., g 2 G) can be found in Table 2 and represent anexhaustive account of meaningful garden objects.

Formal concepts, cn; are derived from K through a mapping of the intention andextension of a concept: ext(cn), int(cn). The extension of a concept consists of a set

Table 1 K (Kyu Furukawa Teien)

AAE PAE Ter. Nat. Art. Sea. Arch. Sou.

Rocks 9 9 9

Garden ornaments 9 9 9

Moving water 9 9 9 9

External sounds 9 9 9 9

Topography 9 9 9 9

Still water 9 9 9

Fauna 9 9 9 9

Habitable architecture 9 9 9

Paths 9 9 9

Flora 9 9 9 9

Earth 9 9 9

Bridges 9 9 9

AAE active aural embellishment, PAE passive aural embellishment, Ter. terrestrial, Nat. natural, Sea.seasonal, Arch. architectonic, Sou. soundscape

Table 2 Instances of g in G

G g 2 G

Rocks myoseki (named rocks), mumyoseki (unamed rocks)

Garden ornaments sekito (pagoda), ishidoro (stone lanterns)

Moving water ootaki (large waterfall), suiro (small water course)

Exterior sounds traffic, air conditioner noise, aircraft, human activity

Topography miyama-no-sakai (mountainous area), jiban (plain or flat ground),keikoku (ravine), karetaki (dry waterfall)

Still water shinjiike (pond in shape of the Chinese ideogram for heart)

Fauna koi (carp), turtles, birds, insects

Habitable architecture Furukawa residence, cha-shitu (tea house), pavillion

Paths tobi-ishi (stepping stone path), nori-no-ishi (mountain path)

Flora azaleas, conifers, maples, cowberry, honeysuckle, bamboo, plum,

cherry, moss, grasses

Earth soil, sand

Bridges ishibashi (stone bridge), soribashi (wooden arched bridge)

Axiomathes

123

of all formal objects that have all the formal attributes of the concept and vice versa

(Priss 2008). Ganter et al. (2005) use a derivation operator to account for formalconcepts of K through assigning arbitrary X G and Y M conditions thatundergo the following mappings:

X ! XI fm 2 M j gIm for all g 2 Xg;Y ! YI fg 2 G j gIm for all m 2 Yg:

But as Priss (2006) has noted, the success of a formal context within disciplines

outside of those concerned purely with the inherent mathematical qualities lies in

the careful modeling of attributes, for which the derived concepts need not spe-

cifically correspond to intuitive notions of the user. In Table 3 a detailed definition

of M is presented along with examples of G for K of Kyu Furukawa Teien. A formal

concept of K is thus defined as a pair (A, B) with A G; B M; A BI ; andB = AI. The collection of all concepts of a formal context is then denoted as BK:Ganter et al. (2005) further describes the subconcept-superconcept-relation withinBK as operable under the conditions:

A1; B1 A2; B2 : () A1 A2 () B1 B2:This property then generates a hierarchy among concepts for which higher order

superconcepts, (A2, B2), may include lower level subsets, or subconcepts,(A1, B1), which then correspondingly account for the notion of an inheritance ofattributes or class inclusion (Priss 2008).

Table 3 Definitions of M in BK with respect to GM Definition of M G

Soundscape Sound class instances (signals, soundmarks,keynotes) according to Schafers (1977)theory of soundscape

Fauna, moving water, exterior sounds

Active aural

embellishment

Blesser and Salters (2007) definition of

sound sources of an environment as agents

that provide acoustic identity to a space

Fauna, moving water, exterior sounds

Seasonal Objects or agents that are influenced by

seasonal changes

Flora, fauna, exterior sounds

Natural pertaining to the natural environment Rocks, moving water, topography,

flora, earth, fauna, still water

Artificial Objects that are produced or designed or

serve functional purposes: also ephemera

that are a function of human activity

Garden ornaments, exterior sounds,

topography, habitable architecture

paths, bridges

Terrestrial Features or land-form elements of the earth Topography, flora, moving water,

still water, paths, earth, rocks

Passive aural

embellishment

Blesser and Salters (2007) definition of the

acoustic properties (materiality) of a space

in governing the behavior of sound sources

(filtering, diffraction, reflection, absorption)

Topography, flora, still water, paths,

earth, rocks

Architectonic Pertaining to the built environment or

architectural features or fabrication

Habitable architecture, garden

ornaments, bridges

Axiomathes

123

But the notion of superconcepts and subconcepts is perhaps best revealed through

FCAs most distinct feature, the Hasse, or line diagram which is a visualization of

BK: As shown in Fig. 2, circles denote objects or attributes with labels sittingabove indicating an attribute, and below an object. At the top of the diagram is an

empty circle representing the power set, PS; and at the bottom of this diagram theempty set, . The reading rule of the line diagram states that an object g has anattribute m if and only if there is an upwards leading path from the circle named byg to the circle named m (Wolff 1994). As an example, within the KyuFurukawa Teien lattice, the concept seasonal is notated:

fcSeag ffauna, exterior sounds, florag; fSea.g Another interesting property that arises from a partially ordered lattice are

unforeseen concepts such as those ones unnamed in BKsee Fig. 2. The oneinstance of a formally named subconcept, fcArchg; architectonic, within the latticeoccurs as a subset of the extents of the superconcepts fcArtg; artificial, and fcPAEg;

Fig. 2 Line diagram of BK generated using ConExp software (Yevtushenko 2000). Abbreviations asfollows: Sou. soundscape, AAE acoustic aural embellishment, Sea. seasonal, Nat. natural, Art. artificial,Ter. terrestrial, PAE passive aural embellishment, Arch. architectonic. See Table 3 for definitions

Axiomathes

123

passive aural embellishment. By tracing the intent of the set of objects that intersectthese concepts, we find:

fcArchg habitable architecture,

garden ornaments,

bridges

8>:

9>=

>;; fArch., Art., PAEg

0

B@

1

CA:

extcArch habitable architecture,

garden ornaments,

bridges

8>:

9>=

>;

) fcArchgfcArtg; fcPAEgFrom this example, what Ganter et al. (2005) describe as the attribute

implications can be deduced under the conditions:

A ! B () AI BI with A; B MWhich in BK of Kyu Furuakwa Teien corresponds to the notion that

farchitectonicg ! fArt., PAEg (i.e., the attribute architectonic implies the attri-butes artificial and passive aural embellishment).

5 Design Praxis and Ecology

One of the more striking characteristics that emerges from BK of Kyu FurukawaTeien is the sense of a distinct partitioning between the sets of attributes {Sou.,

AAE, Sea., Nat.} and {Art., Ter., PAE, Arch.} (see Fig. 2 for key to abbreviations).

Using Yevtushenkos (2000) ConExp software for line diagram generation, the node

sizes of the attributes are varied according to object extension count (larger the

diameter the greater number of objects within the extent). The six unnamed

subconcepts within the diagram highlight its hierarchical partitioning, though

assigning an arbitrary naming convention allows a deeper interrogation into the

nature of the partitioning within BK. If assigning the three far left subconcepts asca; cb; cc; then the extents of these subconcepts and their implications are comprisedof:

extca ffauna, exterior soundsg;fcag ! fSou., AAE, Sea.g:

extcb ffauna; movingwaterg;fcbg ! fSou., AAE, Nat.g:

extcc ffauna, florag;fccg ! fSea., Nat.g:

One of the first readily understood characteristics to emerge from this sub-lattice

is of the attribute equivalence relation between Schafers notion of {Sou.} and

Blesser and Salters concept of {PAE}, which can be identified through the

subconcept-superconcept relations of ca and cb

Axiomathes

123

fcagfcSoug; fcAAEg:fcbgfcSoug; fcAAEg:

and extfcSoug extfcAAEg) fSou.g fAAEg

Further to this is the association between each of the attributes of this sub-lattice.

The union of these three subconcepts highlights a feature of the Kyu Furukawa

Teien sub-lattice that might best be described as one concerned with, or pertaining

to the Ecological (as a landscape and soundscape phenomena) given the nature ofthe objects as living or dynamic organic instances that may produce active acoustic

phenomena. By considering the instances, a and b in the extension a 2 A; andintention b 2 B; of the summed subconcepts, SE; reveals:

[E fca [ cb [ ccg;

a 2[

E () 9A 2 E; a 2 A ;b 2

[E () 9B 2 E; b 2 B ;

thus:

extfca; cb; ccg [

A2EA

flora, fauna,

moving water,

exterior sounds

8>:

9>=

>;:

intfca; cb; ccg [

B2EB Sou., AAE,

Sea., Nat.

:

That Schafer (1977) and Truax (2001) have positioned soundscape studies as a

form of ecological analysis of site despite criticism from Ingold (2009), Arkette

(2004) and Carter (2003) that their approach lacks a greater engagement with the

environment as a totality remains a point of contention, though within BK; thesuggestion that Kyu Furukawa Teiens ecological elements might be described in

terms of qualities relating to acoustic and environmental systems points toward amulti-sensory dimension of the garden. What I have interpreted here as pertaining to

the Ecological stems from the inheritance of the attributes ofS

Esoundscape,active aural embellishment, seasonal, naturalwhose corresponding objectsrepresent a distinct subgroup within BK: Similarly, the inclusion of the objectexterior sounds highlights Blesser and Salters (2007) notion that the acoustic

arena of an aural architecture may extend well beyond the visual horizon. Its

inclusion here alludes to the fact that considerations about the ecology of the garden

must regard the greater context of the site beyond its own demarcations. But by the

same token, this concept may also be applied locally within the garden when

reading it as a series of connected landscape encounters. Through the traditional

technique of miegakure, a visitors movements through the garden is carefullyorchestrated so as to both reveal and focus awareness on specific aspects, features,

or sounds within the garden at particular points. This could then account for the

previous study of shakkei no oto operating at the karetaki (Fowler 2013). Here, the

Axiomathes

123

outside sounds are captured from beyond the local visual horizon (yet still within

the greater confines of the garden) and usurped to provide an auditory signal for the

obvious denotation of moving water encoded in the karetakis sculptural rockformation.

But that the sub-lattice ofS

E can be viewed as a descriptor of the notion of theEcological is further alluded to when considering the intersection,

TE; between the

extent of the three subconcepts:\

E extca \ extcb \ extcc

;

a 2\

E

$ 8A 2 E; a 2 A;thus :

\

A2EA ffaunag:

The object {fauna} then is perhaps the axiomatic element of this sub-lattice of

BK, and moreover both an active acoustic phenomenon of the gardenssoundscape ecology as well as a crucial element in its landscape ecology. That it

may function as both a design element within the garden (e.g., as with those

introduced animals such as ornamental koi and turtles), as well as a representativesymbol of the natural eco-system (e.g., through migratory birds, insects) implies that

the garden is a highly dynamic multi-sensory design space. This also suggests that

the garden is bounded by the intersection between those obvious manifestations in

which the designer is wholly present and controlling the landscape form and

soundscape qualities, and those instances in which uncontrolled agents or natural

phenomena seem to freely occupy or inhabit the space.

But that the object earth is vacant fromS

E is the next point of investigation forthe secondary group of unnamed subconcepts. Naming the secondary group of

subconcepts (left-to-right), cd; c; cf; the (A, B) values and implications arecomprised of:

moving water, earth,

still water, rocks,

topography

8>:

9>=

>;;fcdg

0

B@

1

CAand : fcdg! fNat., Ter.g:

earth, still water,

rocks, flora,

paths, topography

8>:

9>=

>;;fcg

0

B@

1

CAand : fcg! fTer., PAEg:

paths, topography,

architecture,

garden ornaments

bridges

8>>>>>:

9>>>=

>>>;

;fcfg

0

BBB@

1

CCCA

and : fcfg! fArt., PAEg; also fcArchgfcfg

I consider this area of the Kyu Furukawa Teien lattice as suggestive of the notion of

Design Praxis if one considers this collection of formal objects as associated with theparameters and tools of garden design (i.e., objects that are placed within or transform

the extant landscape conditions). The objects and spatial typologies located in this

Axiomathes

123

partition of the lattice have been named, codified and well documented in the traditional

Japanese garden treatises (Slawson 1987; Takei and Keane 2001) and represent a

repertory of compositional forms and structures available to the garden designer. That

they include elements of a garden which may produce not only visual articulations of site

but also auditory behaviors points towards the notion that Japanese garden design

contains potential structures for synthesizing manifestations of landscape and sound-

scape form. Examining more closely the secondary group of subconcepts as a united

group,S

D; the extent and intent contain pertinent qualities and objects that aredistinct from

SE: Defining the conditions for finding

SD and the instances, b in the

intention b 2 B; and instances of a in the extension a 2 A; the objects andattributes of

SD are comprised of:

[D fcd [ c [ cfg;

a 2[

D () 9A 2 D; a 2 A;b 2[

D () 9B 2 D; b 2 B;

thus : extfcd; c; cfg [

A2DA

moving water, flora

earth, still water, rocks,

topography, paths,

architecture, garden ornaments,

bridges

8>>>>>>>>>>>:

9>>>>>>=

>>>>>>;

;

intfcd; c; cfg [

B2DB Nat., Art.,

Ter., PAE

:

That the superconcepts fcNatg; fcArtg; fcTerg; fcPAEg represent elements thatinform

SD reveals that the notion of the design of a Japanese garden involves a

balancing of qualities in terms of acoustic behaviors and the nexus between naturaland artificial landscapes. Though the complimentary attribute to passive auralembellishment is located within

SE (i.e., active aural embellishment), the common

object moving water acts as a pivotal element between each sub-lattice of BK.This then means that as an active aural embellishment, moving water is an object

that is both an element for landscape/soundscape design as well as a constituent of

an ecological system. But the complete extents ofS

D contains a further commonobject, flora and one shared attribute, Natural, which seems to further suggest thatthe structure of BK implicates the design space of Kyu Furukawa Teien as onethat convalesces notions of the Ecological with Design Praxis:

[

A2EA \

[

A2DA fflora, moving waterg:

[

B2EB \

[

B2DB fNatg:

where : fflorag 2 fcg ! fNat.g;and : fmoving waterg 2 fcdg ! fNat.g:

Axiomathes

123

That the lattice might be read in this fashion allows for a generalized design

theory to emerge from the formal context of Kyu Furukawa Teien. Using the

premise that the extent of attributes can be understood as a synthesis between active

notions of the Ecological interleaved with considerations about Design Praxisallows for a proposition that the garden is a highly considered entity that seeks to

balance what Carlson (2000) identifies as manifestations between the artificial and

the natural in a Japanese garden. Indeed the extent of the attributes Natural andArtificial within BK penetrate both sub-lattices as superconcepts, and thusestablish themselves as important thematic entities.

The distinctiveness of the sub-lattices yet their shared elements is further

revealed inT

D whose single element topography acts as a compliment to theobject fauna which represents the nexus of

TE

\D extcd \ extc \ extcff g;

a 2\

D

$ 8A 2 D; a 2 A;\

A2DA ftopographyg;

\

A2EA ffaunag;

\

A2DA;\

A2EA

( )

2 extcNat

The situation of the objects {fauna} 2 SE and ftopographyg2 SD; andtheir shared attribute Natural, alludes to the distinct yet interleaved nature of KyuFurukawa Teiens design space. That the nexus between landscape design and

landscape ecology (Naveh and Lieberman 1984; Turner 1989; Zonneveld 1990) has

only recently been extended through considerations on acoustic phenomena (Truax

and Barrett 2011) has been a point of inquiry central to this investigation. What is

evident then at least within this cursory study of B K) is the that objects that relateto the landscape eco-system and soundscape eco-system are located within the

ext(S

E), and their implications point towards the attributes {Sou., AAE, Sea.,Nat.}. In terms of garden design, the lattice indicates that those objects that

contribute to its geospatial attributes, ext(S

D), are variously acoustic {Sou., AAE,PAE}, architectonic {Arch.} or a landscape feature {Art., Ter., Nat.}. That the

object earth is contained in the partitionS

D rather than withinS

E is a functionof the objects intent, which includes: {Nat., Ter., PAE}. If earth had been

designated seasonal, it would of been located differently, and though it shares theattribute {Nat.} 2 SE; this characteristic perhaps highlights what (Priss 2008)identifies as the utilitarian nature of FCA to visualize the assertions at the point that

the lattice was made in terms of the definitions of M in K:

6 Conclusion

As a method for the examination of the taxonomy of Kyu Furukawa Teien, FCA has

allowed for a deeper level of investigation regarding the gardens design space. In

reading the formal ontology of Kyu Furukawa Teien as an amalgam between the

Axiomathes

123

Ecological and Design Praxis creates what I believe is a new form of analysisrelevant for design theorists. That design theory (particularly within architecture)

has commonly focussed around analysis using philosophical modes of inquiry (Hays

2000, 2010; Kipnis 2005), semiotics (Broadbent 1994; Leon 2008; Dreyer 2003) or

shape grammar Mitchell (1990) points to the diversity and complexity of the field of

inquiry. What has been generally lacking in the discourse though is an investigation

into the application of phenomenological acoustic theories, or how such theories

might be systematically appropriated to varied design contexts or extent modes of

inquiry. Perhaps an advantage of FCA for design theory, and one revealed in the

formal context of Kyu Furuakwa Teien, is the systematic nature of the construction,

reading and interpretation of the lattice whose principles are based on mathematical

relationships, yet are a function of the observed world. That a design might be

understood in terms of its underlying visual and auditory attributes, which then areused in the construction of formal concepts is a powerful property of FCA.

Similarly, the notion that an object within an ontology can be described as an

element of a larger collection (a garden, building or design), and whose relationship

within this collection can be accounted for in a very specific non-technical way

enables a high degree of malleability in the communication and dissemination of the

structure to other designers and design theorists. In this sense, FCA may be a

valuable utility that not only describes designs, but aids in their construction.

In the most general terms, this study into Kyu Furukawa Teien has also revealed

that though the documentation of Japanese garden design techniques concerning

acoustic qualities are historically scant, there are inherent instances within the

garden, which due to their attribute qualities, synthesize to create particular

landscape/soundscape encounters. The significance of the intersection between the

sub-lattices of BK, through the attribute Natural and objects {flora, movingwater} perhaps encapsulates the deeper purpose of a Japanese garden to emulate the

natural environment (Nitschke 1999; Young et al. 2005). But for the garden

designer, the manipulation and integration of moving water and flora have particular

acoustic consequences that may richly inform the resulting design space. By

delicately balancing the impact between landscape form and soundscape stimuli, the

notion that a garden is a multi-sensory environment contained within a landscape

ecology presents the garden designer with a spatial framework to operate within.

This is perhaps most readily revealed in Kyu Furukawa Teien in the use of shakkeino oto, where the intersection between the Natural, Ecological and the artificial(Design Praxis) produces a particularly considered landscape/soundscape encounterthat at once emulates the serene topography of a natural environment, as well as the

controlled hand of the intervening garden designer.

Acknowledgments This research is supported by the Alexander von Humboldt Stiftung.

References

Arkette S (2004) Sounds like city. Theory Cult Soc 21(1):159168

Augoyard JF, Torgue H (2005) Sonic experience: a guide to everyday sounds. (trans: McCarthy A,

Parquette D). McGill-Queens University Press, Montreal

Axiomathes

123

Berthier F, Parkes G (2000) Reading Zen in the rocks: the Japanese dry landscape garden. University of

Chicago Press, Chicago

Blesser B, Salter RL (2007) Spaces speak are you listening? Experiencing aural architecture. MIT Press,

Cambridge

Bring M, Wayembergh J (1981) Japanese gardens: design and meaning. McGraw-Hill, New York

Broadbent J (1994) Recent developments in architectural semiotics. Semiotica 101(1/2):73101

Carlson A (2000) Aesthetics and the environments, the appreciation of nature, art and architecture.

Routledge, London

Carter P (2003) Auditing acoustic ecology. Soundscape J Acoust Ecol 4(2):1213

Casalis M (1983) The semiotics of the visible in Japanese rock gardens. Semiotica 44(34):349362

Davey BA, Priestley HA (2002) Introduction to lattices and order. Cambridge University Press,

Cambridge

Dreyer C (2003) The crisis of representation in contemporary architecture. Semiotica 143:163183

Fowler M, Harvey L (2006) Teimu (the garden of dreams): aural and aesthetic atrributes of Japanese

gardens as models for spatial environments. In: Imada I, Hiramatsu K, Torigoe K (eds) The west

meets the east in acoustic ecology. Hirosaki University, Hirosaki, pp 147165

Fowler M (2010) Mapping sound-space: the Japanese garden as auditory model architectural research

quarterly 14(1):6370

Fowler M (2013) Hearing a shakkei: the semiotics of the audible in a Japanese stroll garden Semiotica

(accepted for publication)

Ganter B, Stumme G, Wille R (2005) Formal concept analysis: foundations and applications. Springer,

Berlin

Hays MK (2000) Architecture theory since 1968. MIT Press, Cambridge

Hays MK (2010) Architectures desire: reading the late avant-garde (writing architecture). MIT Press,

Cambridge

Heiddeger M (1971) Building, dwelling, thinking. (trans: Hostadter A, translator, Poetry, Language,

Thought). New York, Harper Colophon Books

Holborn M (1978) The ocean in the sand. Gordon Fraser, London

Ingold T (2009) Against soundscape. In: Carlyle A (eds) Autumn leaves: sound and the environment in

artist practice., Double-Entendre, Parid, pp 1013

Itoh T (1972) The Japanese garden: an approach to nature. Yale University Press, New Haven

Keane MP (1996) Japanese garden design. Charles E. Tuttle Co. Inc, Tokyo

Kipnis J (2005) On criticism. Harvard Design Magazine, Fall, pp 96104

Kuitert W (2002) Themes in the history of Japanese garden art. University of Hawaii Press, Honolulu

Leon AM (2008) The boudoir in the expanded field. log 11:6382

Mitchell WJ (1990) The logic of architecture: design, computation, and cognition. MIT Press, Cambridge

Naveh Z, Lieberman AS (1984) Landscape ecology: theory and application. Springer, New York

Nitschke G (1999) Japanese gardens, right angle and natural form. Taschen, Kon

Perez-Gomez A (2001) The revelation of order: perspective and architectural represetnation. In:

Rattenbury K (ed) This is not architecture: media constructions. Routledge, New York, pp 325

Priss U (2008) Facet-like structure in computer science. Axiomathes 18:243255

Priss U (2006) Formal concept analysis in information science. In: Cronin B (ed) Annual review of

information science and technology, vol 40. pp 521543

Schafer RM (1977) The soundscape: our sonic environment and the tuning of the world. Destiny Books,

Rochester

Seidensticker EG (trans) (1976) The tale of Genji, vol. 1. Charles E. Tuttle Co, Tokyo

Slawson DA (1987) Secret teachings in the art of Japanese gardens: design principles, aesthetic values.

Kodansha, Tokyo

Takei J, Keane MP (2001) Sakuteiki, visions of the Japanese garden. Tuttle Publishing, Tokyo

Truax B (2001) Acoustic communication. Ablex Publishing, Westport

Truax B (1999) AThe Handbook for Acoustic Ecology. Cambridge Street Publishing, Burnaby

Truax B, Barrett GW (2011) Soundscape in a context of acoustic and landscape ecology. Landsc Ecol

26:12011207

Turner MG (1989) Landscape ecology: the effects of patterns on progress. Annu Rev Ecol Syst

20:171197

van Tonder G, Lyons MJ (2005) Visual perception in Japanese rock garden designs. Axiomathes

15:353371

Axiomathes

123

van Tonder G (2007) Recivery of visual structure in illustrated Japanese gardens. Pattern Recogn Lett

28:728739

Vogt F, Willie R (1995) TOSCANAa graphical tool for analyzing and exploring data. In: Tamassia R,

Tollis IG (eds) Lecture notes in computer sciences 894, Springer, Heidelberg, pp 225233

Willie R (1982) Restructuring lattice theory: an approach based on hierachies of concepts. In: Rival I (ed)

Ordered sets. Reidel, Dordrecht, pp 429438

Woodbury RF, Burrow AL (2005) Whither design space?. AIEDAM, Special Issue on Des Spaces

20(2):6382

Wolff KE (1994) A first course in formal concept analysis: how to understand line diagrams. In:

Faulbaum F (ed) SoftStat93 advances in statistical software, vol 4. pp 429438

Yamaguchi K, Nakajima I, Kawasaki M (2008) The application of the surrounding landform to the

landscape design in Japanese gardens. WSEAS Trans Environ Dev 8(4):655665

Yevtushenko SA (2000) Systems of data analysis Concept Explorer. In: Proceedings of the 7th national

conference on Artificial Intelligence KII-2000. Russia, pp 127134

Young D, Young M, Yew T (2005) The art of the Japanese garden. Tuttle Publishing, Tokyo

Zonneveld IS (1990) Scope and concepts of landscape ecology as an emerging science. In: Zonneveld IS,

Forman RTT (eds) Changing landscape: an ecological perspective., Springer, New York, pp 320

Axiomathes

123

The Taxonomy of a Japanese Stroll Garden: An Ontological Investigation Using Formal Concept AnalysisAbstractIntroductionAcoustic Theory: Soundscape and Aural ArchitectureThe Garden of Kyu Furukawa TeienGenerating an Ontology Using Formal Concept AnalysisDesign Praxis and EcologyConclusionAcknowledgmentsReferences