The tuning of the ancient Gaelic harp: questioning and
prospections
Vincent Michaud-Laine,
(PhD) – Université de Franche-Comté – Besançon – Laboratoire ELLIADD. (CC BY-SA 01-2025)
The ancient Gaelic harp situation, as an ancient
instrument, is a far more delicate one that might appear from the start. We
know for sure that its history spans at least from the 12th century
up to the times of Edward Bunting, its main collector, in the early 19th
century, at the end of a long and probably diverse musical life. Yet, because
of the very nature of the collecting period and the collector’s system of
thoughts, these late documents require a great deal of interpretation in order
to become intelligible, let alone in order to project them prospectively
towards more ancient times. The tuning regime of Denis Hempson, as given by
Bunting in his 1840 edition, is no exception to this. Projecting such a system
to earlier times requires a lot of prudence and circumspect precautions. Yet,
the Irish terminology transmitted to, and then by Bunting, proven solid by our
previous work[1],
can give some hints, which combined to other observations could help build up
viable hypothesis towards a fuller understanding of the plausible possibilities
of the instrument in its history. This article will strive to do so, in a
prudent, and prospective manner which will aim more at re-opening a debate
thought closed with new hypothetical angles.
Hempson’s Leath Ghleas, and the implicits
At page 23 of his 1840 edition, Edward Bunting gives
the tuning regime presented as Leath Ghleas (“the two-position tuning[2]”).
It presents the tuning routine of Denis Hempson on his 30 string harps. The
tuning is often understood as a cycle of fifth of a fixed hexachord (understand
here that term here as 6 string fixed values determined by a precise typography
of mutual fifths, the Irish harpers of Bunting’s times, like so many practical
musicians, didn’t know, use, needed nor cared about Guido d’Arezzo, solmization
or mutatio) corresponding to 4 ascending fifths and one descending
fifth, and a mobile seventh, either tuned in a high position (possibly from an
ascending fifth ?), or a low position (from a descending fifth?). Yet when one
goes to precisely see what Bunting’s shows as the tuning regime, things get a
bit less clear, we propose to synthesize these steps below.
Tuning routine with the seventh degree in high
position (F sharp):
Step 1 |
The caomhluighe get tuned |
G to g[3] |
Step 2 |
The first fifth is tuned: tead an feith cheolach
(“the melodic nerve”) |
G to d |
Step 3 |
The octave above caomhluighe is tuned. |
G to g’ |
Step 4 |
The octave below the tead an feith cheolach
is tuned. |
D to D |
Step 5 |
The octave below the caomhluighe is tuned: Cronan. |
G to GG |
Step 6 |
From the tead an feith cheolach, the fifth up
in tuned. |
d to a’ |
Step 7 |
From the obtained a’ to its lower octave: Guaille
na caomhluighe (“shouldering the caomhluighe”) |
a’ to a |
Step 8 |
From guaille na caomhluighe to a fifth up: Guaille
teaid an feith cheolach.
(“Shouldering the Melodic nerve”) |
a to e |
Step 9 |
From the guaille teaid an feith cheolach to a
fifth up. |
e to b’ |
Step 10 |
From the obtained b’ to its octave lower: An dara
os cionn na caomhluighe (“the second above the lovers”) |
b’ to b |
Step 11 |
From an dara os cionn na caomluighe to a
fifth up. |
b to f
(sharp) |
Step 12 |
From the caomhluighe to a fourth up : an
treas os cionn na caomhluighe. |
G to c. |
Step 13 |
From an treas os cionn na caomluighe up to
its higher octave |
c to c’ |
Step 14 |
The rest of the harp is tuned by octave from the
tuned strings. |
|
Tuning routine with the seventh in low position (F
natural):
Step 1 |
The caomhluighe get tuned |
G to g[4] |
Step 2 |
The first fifth is tuned: tead an feith cheolach
(“the melodic nerve”) |
G to d |
Step 3 |
The octave above caomhluighe is tuned. |
G to g’ |
Step 4 |
The octave below the tead an feith cheolach
is tuned. |
D to D |
Step 5 |
The octave below the caomhluighe is tuned: Cronan. |
G to GG |
Step 6 |
From the tead an feith cheolach, the fifth up
in tuned. |
d to a’ |
Step 7 |
From the obtained a’ to its lower octave: Guaille
na caomhluighe (“shouldering the caomhluighe”) |
a’ to a |
Step 8 |
From guaille na caomhluighe to a fifth up: Guaille
teaid an feith cheolach.
(“Shouldering the Melodic nerve”) |
a to e |
Step 9 |
From the guaille teaid an feith cheolach to a
fifth up. |
e to b’ |
Step 10 |
From the obtained b’ to its octave lower: An dara
os cionn na caomhluighe (“the second above the lovers”) |
b’ to b |
Step 11 |
From the caomhluighe to a fourth up : an
treas os cionn na caomhluighe. |
G to c. |
Step 12 |
From an treas os cionn na caomluighe up to
its higher octave |
c to c’ |
Step 13 |
From an treas os cionn na caomhluighe to a
fourth up : tead an leath ghleas (“the string of the two-position
tuning”) |
c to f (natural) |
Step 14 |
The rest of the harp is tuned by octave from the
tuned strings. |
|
The above tables, made from Bunting’s text, show (in
red) that at least one string is tuned by a fourth and not a fifth. It has been
argued that this was either a mistake by Bunting or a shortcut from Hempson.
Neither of these two opinions can be solidly grounded. However, if that tuning
routine is accurately transmitted by Bunting, one can no longer speak of
“Pythagorean” tuning by a cycle of pure fifths as tuning certain strings by
fourths would not be within the practice in such a system. So that would hint
towards a non-adequation of that Irish tuning system to a continental known
historical cycle of fifths-based tuning.
In any case, the leath ghleas will, by nature,
pose the question of the quality of the fifths implied. As stated before, it
has been widely accepted that this Irish tuning is to be regarded as a
“Pythagorean” tuning and that implicitly means that the fifths tuned are pure
fifths. This, however, is not strictly seconded by anything in Bunting’s
comments or text or any other historical sources and surprisingly so as it would
be quite a striking archaic trait, worthy of note and mention, in the
time-period concerned, after centuries upon centuries of temperaments,
third-centered mesotonism and rectification of fifths. So, this pure-fifth
implicit is a modern interpretation and one that is not really rooted in any other
convergent document, whether on concordances of local or historical period’s
contexts of practices or hints or clarifications within the documents. Bunting,
in fact, seems unsurprised by such a tuning system and only regrets that the
harpers collected do not seem to know about the theory behind such a routine
(understand here that they don’t know the theory in the terms known by Bunting
and which he universalizes).
The hypothesis of a pure fifths tuning, in the case of
a diatonic high resonance instrument isn’t unplausible yet we would like here
to broaden the picture so as to relay healthy doubts which could lead to other
experiments in trying to reconstruction this instrument’s possible ancient
musical colors, and in that process, highlight the fact that our
interpretations are based on what WE project now of that music of the past.
If such tuning as the leath ghleas is
implemented with pure fifths, it will produce major thirds[5]
which will be higher than pure thirds and therefore rather unstable in chords
or arpeggios. This comes down to whether the music arrangements of the harpers
(and not of Bunting) were considering the thirds as structural in the harmony.
Determining this from the expurgated and highly revised musical samples we have
from Bunting’s notes or published works is extremely complex, a tad utopic and
isn’t the subject of this article, so we will, for rhetorical reasons, consider
the two options: the thirds might, or might not be structural. If they are not,
pure fifths can be used but if they are, in terms or arpeggios, chords or arpeggio-based
or chordal constructions of melodies, then, in the tuning the fifths of a-e and
e-b need to be lowered as they would produce major thirds in the keys of G and
C which would be rather unstable.
There nevertheless is a third possibility. The thirds
might not have been structural in the Irish musical system, but the tuning
could still very well have been influenced by centuries of musical ambient
atmosphere where the thirds were structural. The harpers in Bunting times,
factually, did not compose anymore and seemed to shrink their performing
repertoire around Irish airs that they literally worshiped, and to the
exception of any other type of music. Yet, they were not cut from society, and
that society has gone through Renaissance, then Baroque and the birthing
Romantic period of musica style and musical colors, in terms of quality of
intervals. Moreover, these harpers gravitate around noble patrons who all
practiced and entertained a taste for global European art music. Strict Pythagorean fifth tuning is not
practiced anymore by such European art music practitioners in the times of
Bunting’s collecting although the equal temperament is just starting its career
and is probably, in the early days of the 19th century, only one - however
very notable and quickly gaining in popularity - among others. Yet the thirds
have definitely been structural in the music around Ireland for a couple of
centuries and this fact definitely would have forged a cultural ear.
À
partir du moment où l’on considère que la cognition relève d’une interaction
ayant l’émergence de valeurs pour objet et qu’elle n’est pas seulement le
résultat d’une instanciation de catégories pré-programmées dans des agents
préalablement individués, on voit aussi comment intervient la notion de culture
dans la cognition. Elle implique un nouveau partage entre l’a priori et
l’expérience, que la notion de forme symbolique rend concevable. (Lassègue,
Jean, « Formes symboliques et Emergence de valeurs » dans ARC’o04,
2005, p.55)
As soon as one considers that cognition partakes of an
interaction which had the emergence of values as object and that it isn’t just
the result of the instantiating of pre-programmed categories in agents
individued before-hand, one can see how the notion of culture influences the
cognition. It implies a new sharing between a-priori and experience that the
[cassirerian] Symbolic Form concept helps to understand. (We translate)
Bunting
comments on the harpers playing and liking airs which have D as a tonic within
their tuning; by saying he find this “more imperfect” (his own words). In the E
and B have been lowered to be more pleasant in major flavored modes, but not to
the point of making the fifths A-E and E-B totally unbearable, a positional
mode of D played in this configuration would have a second and third degree a
tad lower and without being unbearable could sound “more imperfect”.
When
all of this is now stated, the irremediable conclusion jumps to the eyes: while
we will never know what it was for sure that the Irish harpers did on their
harps, whatever method we employ, how we tune the harp now is dependent on what
representations we have and what we, as Bunting’s readers – and of other
sources - project of the music system and style we observe and interpret from
the historical documents.
And it
is pretty much always going to be like that. The fact is that music exists when
played and heard. When a style and
system of music disappear from this actualized societal sphere, the writing
down of music, direct (by people who played it within their own modality of
written notation) or indirect (collected and transmitted by people outside this
music tradition and with another written system), that remains of it are never sufficient.
Reconstructing that music is then, in a large part, more an act of imagination
rather than any rigorous applying to some manner of deductive/inductive logic.
This
mobilizing of imagination by interpretation, often clouded by the unjustified
scientific claims of the fashionable “research by practice” and its
“historically informed performances”, isn’t, de facto, necessarily
non-scientific. Repeatability and refutability are however observably not a
state of the interpretation that seem to be reachable by “research by practice”
nor the similar methodologies known to produce “historically informed
performance”. And it’s in fact not a problem at all! These two polarities of
art and science sometimes hide, in their artificial clash, a third term which,
in our view, bears promise: that of a “practice by research”. On one side the artistic
practice does not need to claim to be science, to gain legitimacy in the task
of imagining an ancient soundscape[6], as a
“historically informed performance” may be tempted to do, thus cutting itself
from a certain freedom of mind and interpretation in the name of an exact
adequation to the sources, which is simply impossible to ever reach. On the
other, science can be a support to creation in a secondary process, whereas
“research by practice” risks sometimes to cut itself from the rigorous and
competent preliminary scientific explorations which enriches the range of
possibilities. So no, it is not a contradiction to consider that one can aim at
being exact on the partial documents and the obtainable, attested, textual,
organological data, to which one may indeed access, but only after a stringent
and demanding philological and semiotic reconstruction work, and, at the same
time produce very personal musical interpretations. This “practice by research”
angle is perfectly summed up by baroque violinist Julien Chauvin when he states
in a recent interview that “The ancient instruments bring us towards a way to
play but never towards the truth” (Interview for France Musique radio, Les
grands Entretiens, 01-2024). The main important point is not to make
assertive claims that aim to close debates, and stop researching processes,
thus creating delusions and an interesting lot of useless tensions.
In
conclusion, the cultural ear, that might indeed influence the perception of
certain fifths as “pure” by the Irish harpers, with the not necessarily
conscious goal of having acceptably stable major thirds in a period’s musical
atmosphere that implicitly demands them, is quite a common and well-documented
phenomenon, and one that observably is at play today as well. Our visions and
representations of the ancient music of that Irish harp should therefore resolutely
keep an honest, practical and open-minded direction, centered on the awareness
that we are situated.
The tuning or
string disposition before Bunting’s times: a prudent prospection from the
terminology
In the times of
Bunting, the leath ghleas seems to have crystallized around a “diatonic”
(a more prudent term should perhaps be used if not invented there) scaling on a
G, with fixed values A, B#, C, D, E, the seventh F being the only re-tunable
string having two possible values F or F#. The leath ghleas, with its
mobile F and the string below Cronan being returnable, can be understood as an
archaism, seemingly only used by Hempson. The other harp gamuts we appear to
have (mostly from the correspondence between James McDonnel and Edward Bunting)
indeed all seem to solely feature a F#. This relative fixity corresponds to an
identitarian shrinkage of the harpers around the sole Irish music material. But
around the 16-17th centuries period, we know that Irish harpers
could well have delved into more global European art music. And this then
questions the tuning they might have had on wire-strung harps, instruments on
which you cannot fret strings and for which constant re-tuning would be unstable
and detrimental.
The hexachordic
hypothesis: a scordatura on b
Hexachordic theory
was somewhat of a relative standard around the 16th century.
Naturally We are pretty much aware that solmization and the rules of Mutatio
and how and when to admit ficta over the musica recta system
are first and foremost for singing/transposing purposes, within a certain type
of music, and this would apparently have in some musicologists’ objections,
nothing to do with tuning a harp. But in a taxemic vision of the musical domain
in a given culture, the type of theorical thinking which defines Music in its
boundaries, does underline a perception of intervals and their correlative
relationships. Therefore, hexachords being a typology of tones and semitones
and mutatio/ficta giving precise and limiting rules of how to switch
from one hexachord to another when building a scale, it appears to us rather
untenable to assert that this will have no incidence of how you string and tune
a harp, in terms of what fixed scalar values you’ll critically assign to each
string in a differential process according to what you need and why, and the
string disposition will then irremediably decide of the tuning strategies.
The Leath
ghleas could be redefined in this historical context as a fixed hexachord
of G per durum (means the Bs are always B# (B natural) and the three
first notes are distant from a tone, G-ut, A-ré, B-mi, and the semi-tone Mi/fa
is between B# and C). The Irish harp could then very easily be fitted with a
scordatura B moll – B dur in the middle of the gamut. From Cronan (gamma-ut),
the hexachord per durum G-ut A-ré B-mi C-fa D-sol E-la could have been
followed in the upper octaves by a scordatura with the two qualities of the B
present as separate strings, thus allowing other hexachords. Thus, above caomhluighe we could have
had g a b(moll) b(dur) c etc. as a string disposition. The status of the F string,
mobile in Bunting times, could still be seem as re-tunable, and perhaps then,
the only retunable string, thus augmenting the possibilities of the harp in two
positions adding a possible hexachordum fictum with F# when the music
would require it, or changing in a transposed way the G into a C (as the key
values are not defined in terms of heights of sound). This fundamentaly would
not change what the leath ghleas is, and although there is no firm
confirmation of such tuning in the 16-17th centuries period, it
would correspond to very well-known global harp stringing and tuning strategy
throughout Europe at this period (Bermudo, Mersenne, etc…). Such tuning would
allow a certain amount of connection to art music. From an organology perspective,
this would also be very viable, the string tension keeping within reasonable
values and no fretting nor intense retuning would need to be implemented. No
document exists that would prove this scordatura as an extant practice in
Ireland. The central question around this is whether the Irish harpers of then
connect to European art music which would require their harp to have more
capabilities. We won’t know for sure but do have hints of texts and paintings
attesting of the presence of Irish harpers at the Elizabethan court which were
playing with other court musicians, as well as early collections of lute or
harpsichord pieces which feature, alongside continental or European usual art
music (pavanes, galliards, canaries, etc.) piece from a more Irish, or Gaelic
repertoire, proving that they were not perceived as totally incompatible. Since
there is historical plausibility, then there surely is artistic legitimacy in
exploring such a tuning in conjunction or not to a European art music on the
Irish harp.
A “tetrachordic”
British way? A wild guess from the terminology
From old man Hempson’s
resources, Bunting seems to have obtained a terminology of the tuning of the
harp that looks a tad more complex than the leath ghleas itself. We
pointed out in our previous work that this terminology is difficult to assess
due to the facts of Bunting not being an Irish speaker and that he doesn’t
fully understand what this terms entails but try nonetheless to interpret them
from his own musical system which he perceives as superior and universal, and since they are not in use by anyone
anymore, their reality isn’t exactly tangible for the collected harpers either.
However, starting on p.24 of the 1840 edition, Bunting lists under the title
“the keys” three terms that could be the starting point of a very humble and
prudent prospection. These terms have the noun fuigheall in common and
three adjectives that qualify it: beag, mór and aon. Bunting’s
translations are not to be taken very seriously, and we will make propositions
which we hope are a bit more grounded. But before, we would like to address the
fact that, although, for a traditional old-fashioned musicology perspective,
prospecting musically on the sole basis of a terminology might appear scary,
from a semiomusicology perspective (that is to say a federation of the diverse
necessary fields of knowledge by the semiotic question, that is to say the
question of what makes sense, how it makes sense and how do we access to that
making-sense) terminologies are of the essence in the case of a form of music
that disappeared totally from the environment. Indeed, such terminologies are
taxemic in nature; a taxeme is a sub-ensemble of a domain: if there is a Gaelic
Harp domain in Gaelic culture then there is discourse tied to it and a semantic
domain. Terminology’s study allows access to this semantic domain along with
coupling it with the semantic study of the representations of the harp in the
culture’s texts. So, studying the Irish terminology is very important indeed,
but a task made difficult by the interpreter Bunting, who may cloud the
analysis by his own brand of interpretations, not always extremely neutral nor
rigorous[7].
And indeed,
Bunting’s descriptions of what these fuigheall are, do not seem to make
an awful lot of sense apart from the fact that these are tunings for the harp.
The term fuigheall,
comes from an ancient fuigell, which has different meanings. The
methodology to try and extract a meaning in our musical context when we don’t
have confirming texts in the musical field with this word used goes as such: we
try, from the attested textual usage in different contexts, to extract common
semantic values, known as semantic isotopies. The main isotopy we could see as
useful is /a constructed whole organized in parts/, for which reason we propose
“system” as a translation. The adjective adds a value to this. If beag “small”
and mór “big” give no problem, aon is a bit more difficult as
Bunting’s spelling varies and fluctuates. We, however, infer that the structure
noun + adjective should prevail as the two other terms function that way. We
therefore propose án fuigell “the splendid/perfect system”[8].
Bunting suggests
that these Fuigheall introduce a tuning of certain intervals without
being extremely clear as to what would be the difference and common grounds
between the three fuigheall.
We would like to
propose, humbly, prudently and prospectively another hypothesis.
The system
terminology is reminiscent of the interpretation, transmission and brandishing
of the Aristoxenos systems of tetrachords, transiting to occidental music via
Boeccius. These systems, in essence, were a typology of how many tetrachords,
of what type and how connected, one would use in their establishing a scale, or
ambitus on a lyra. There would, of course, be strictly no sense in trying to adequate
Aritoxenos systems to a European harp tradition, but hints can be gathered from
Mersenne’s depiction of the “gothic” harp (cithara nova and antiqua in Harmonie
Universelle, Paris, 1636) which features a string disposition seemingly
based on hexachordal theory (it has consecutive Bmoll and Bdur in the two
middle octaves) but superposed with the Greek terminology of Aristoxenos
organized in tetrachords. There also is the organization of the harp tunings in
the manuscript of Robert Ap Huw (MS. 14905, British Library, c.1613) which seems
to practice a tuning made of two joint tetrachords with inner mobile strings. Again,
we understand tetrachord here as an unity of values on four strings, where degree
one-fourth is the fixed value and the two middle degrees are mobile, that is to
say a practical reality and a way to systematize and quickly visualize the
location of fixed and mobile strings - a reality that is not necessarily tied
to any particular theorical system which the Irish, when practical musicians,
may not have known, used, needed nor cared of. But importantly so, tetrachords
are defined by which interval values are implemented to set the mobiles
strings. Aristoxenos distinguishes a diatonic tetrachord as having tones
between the first, second and third strings, a chromatic tetrachord as having
semi-tones, and an enharmonic tetrachord as having quarter of tones. Naturally,
the quarter of tones do not fit in European music but the tones and semi-tones
and their typology are indeed what is central to the setting of a harp tuning.
Prospectively one
could wonder if these terms, a mere memory transmitted, could refer to such a
tetrachordic system, which would create scordature, playing with joint or
disjoint tetrachords along with mobile strings, thus offering the Irish harp a
certain amount of possibilities of ficta, in the attested context of the Irish
harp, sometimes playing European art music (for instance in the 16-17th
centuries). The hexachordic system could still be used, as a theorical system based
on assigned values of intervals for building scalar ensembles but a string
tetrachordic system (units of four strings in which there are mobile and
immobile strings, along with a superposition of such unity where there
sometimes is a common string (joint tetrachord) or not (disjoint tetrachord)
thus helping in locating half steps in the scale), could then be superposed (because its
disposition of tones and semi-tones would not be so incompatible with the
hexachordal system), partaking of a string-situation and practical logic and
instead of intervals and values of tone and semi-tone, this superposed system
establishes where the strings are which are fixed, and which are returnable.
The system would help tune and locate and play a complex scordatura in an
immediate and quick way that a complex solmization calculation would not allow.
Then the classification in three “systems” the small, the big and the perfect, could
suggest that various complexities of tetrachordal scordatura could have been
set. For instance and for instance only, the small system could have been based
on a joint tetrachord much like what seems to be Robert ap Huw manuscript’s
system. The big system could have had a disjoint tetrachordic system where a
semi-tone passage would produce a ficta possibility and the perfect
system would have a semi-tone tetrachord superposed to two joints thus getting
the steps between the recta, at least on two octaves, and one cannot then not
think of the harmonic board of the Cloyne harp, which seems to have had two
rows of strings, permitting precisely such a disposition without the tension
repartition problems that setting this series of half steps would cause to a
single row harmonic curve. These are not positive assertions but merely a
hinting that understanding a complexity is possible, if not suggested from a
terminology that Bunting cannot have invented.
Conclusion
We do not pretend
to make claims here, repeatedly, nor to be able to pierce the past’s veil by
mere conjectures around the terminology or such. But such a terminological
study rather shows, along with other documented clues, that the Irish tuning
and string disposition systems might have been far more elaborate and complex
in earlier periods than what was practiced in Bunting times, a time of decay
and shrinkage around the sole Irish music, and “identity”, somehow not unlike
what sometimes feels like the modern doxa around the instrument. It’s also
clear that the special case of the one-row-of-strings harps forced their
players to create strategies for dealing with musical systems that were not
easily implemented on such an instrument. This opens a new realm of
speculation, which is that of the practical physical relationship of such
musicians on such instruments. In other terms, the musical research on such
instrument would benefit from shifting from a “pure-form” idealized
mathematised theorical vision of music, to that, practical, of the physical
musician, with his various gestures on a physical instrument which has
characteristics and limitations, with which one needs to deal constantly, in
relationship to the intended music.
The Irish harp, in
this perspective, would appear not to be so centrally, uniquely, exclusively,
discriminatively and separately Irish, but partake of global European popular
and art-music strategies as well as harpistic common grounds, with, of course,
local and very notable Irish particularities. In short, the old Irish harp is
much in the image of medieval Ireland: cosmopolitan, European, erudite and
connected.
Bibliography:
Allaire Gaston, The Theory of Hexachords. Solmization and
the Modal System. A Practical Approach, “Musicological Studies and
Documents” no 24, American Institute of Musicology, 1972.
Alvarez-Pereyre Frank et Simha
Arom “Ethnomusicology and the Emic/Etic issue”, in The World of Music 35, no. 1, 1993,
p. 7–33.
Basso Fossali Perluigi, Il
Dominio dell’arte. Semiotica e Teorie estetiche, Rome, Meltemi, 2002.
Basso Fossali Perluigi, Vers une
écologie sémiotique de la culture, Limoges, Lambert-Lucas, 2017.
Bigo,
Louis, et al., “Computation and visualization of musical structures in
chord-based simplicial complexes.” in International Conference on
Mathematics and Computation in Music. Berlin, Heidelberg, Springer Berlin
Heidelberg, 2013.
Born Georgina, “For a Relational Musicology. Music and
Interdisciplinarity. Beyond the Practice Turn”, in Journal of the
Royal Musical Association, vol. 135, no 2, 2010,
p. 205-243.
Bosquet Jean, « Sons musicaux,
intervalles et tempéraments », in Bulletins de l’Académie royale de
Belgique, vol. 60, 1974, p. 1205–1247.
Boulez Pierre, Penser la musique aujourd’hui, Paris,
Gonthier, 1963.
Boulez Pierre, Jalons (pour une décennie), Paris,
Bourgeois, 1989.
Bouquet Simon et Rastier
François (dir.), Introduction aux sciences de la culture, Paris, PUF,
2002.
Bruhn, Siglind, The Musical
Order of the World: Kepler, Hesse, Hindemith, Pendragon Press, 2005.
Burns,
Edward M., “Intervals, scales, and tuning.” in The psychology of music.
Academic
Press, 1999. p. 215-264.
Calame Claude, « Interprétation et Traduction
des cultures. Les Catégories de la pensée et du discours
anthropologiques. » in L’Homme, vol. 163, p. 51-78.
Cassirer Ernst., Philosophie des formes symboliques,
vol. 1, 2 and 3, Paris, Editions de Minuit, coll. « la
phénoménologie de la connaissance », 1972.
Cassirer Ernst, Langage et Mythe. À propos
des noms des dieux, Paris, Editions de Minuit, 1973.
Cassirer Ernst, Logiques des sciences de la
culture, Cerf, Paris, 1991.
Caporaletti Vincenzo,
« Une Musicologie audiotactile », trad. de Laurent Cugny, in Revue
d’études du Jazz et des Musiques Audiotactiles, Cahier en français,
nº 1, CRIJMA – IReMus – Sorbonne Université, Avril 2018, p. 1-17.
Cohn,
Richard, “Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz
Representations”, in Journal of Music Theory vol. 41, no 1,
p. 1-66.
Colas-Blaise Marion, Synesthésies
sonore. Du son au(x) sens, Paris, Édition Classiques Garnier, 2018.
Giavitto, Jean-Louis, « Formalisme, Exactitude,
Rigueur », in Rigueur - Mathématiques, musique, philosophie, Paul T. et
Schmidt M. (dir.), Paris, Spartacus IDH, 2021.
Giavitto, Jean-Louis, « A topological approach of musical
relationships » in Mathemusical Conversations : Mathematics and
Computation in Music Performance and Composition, World Press, 2016.
Guerrini Jean-Claude, Les Valeurs dans
l’argumentation. L’Héritage de Chaïm Perelman, Paris, Classiques Garnier,
2019.
Greimas Algirdas Julien, Sémantique
structurale. Recherche et Méthode, Paris, Larousse, 1966.
Greimas Algirdas Julien, Du Sens.
Essais sémiotiques, Paris, Le Seuil, 1970
Guillaume Astrid, « L’Interthéoricité.
Sémiotique de la transférogenèse. Plasticité, élasticité, hybridité des
théories », in Revue PLASTIR, Plasticités, Sciences et Arts, n°37,
12/2014. http://plasticites-sciences-arts.org/PLASTIR/Guillaume%20P37.pdf
[consulté en août 2023]
Guillaume Astrid, « Pour une
sémiotique diachronique des cultures. Le « Moyen-Âge »
aujourd’hui », in Textes, documents, œuvre. Perspectives sémiotiques,
Driss Ablali, Sémir Badir et Dominique Ducard (dir.), Cerisy-la-Salle- juillet
2012, Rennes, PUR, 2014, p. 381-406.
Guillaume Astrid et Kurts-Wöste
Lia (dir.), Faire sens, faire science,
ISTE, Londres, 2020.
Imberty Michel,
« Langage, musique et cognition. Quelques remarques sur l’évolution
nécessaire des problématiques psychologiques des vingt dernières années »,
in Circuit. Musiques contemporaines, vol. 13, no 2,
2003, p. 93-110.
Kurts-Wöste Lia, Missire Régis, « Sens,
signifiances, significativités. Distinctions conceptuelles pour l'intégration
d'une sémantique interprétative des textes dans une sémiotique des
cultures », Numéro spécial « Perspectives présentes et futures de
la sémantique interprétative », in Acta Semiotica et Lingvistica, vol. 27, n 2,
année 46.
Kurts-Wöste Lia
(dir.), Mondes. Productivité, enjeux et risques de la notion pour les
sciences de la culture aujourd’hui, Bordeaux, PUB, 2023.
Ladrière, Jean,
« objectivité et réalité en mathématique » in Revue philosophique
de Louvain, 84, 1966
Lassègue Jean,
« La Genèse des concepts mathématiques, entre cognition et sciences de la
culture. », in Revue de Synthèse, vol. 124, no. 5,
2004, p. 224–236.
Lassègue Jean, « Formes symboliques et Émergence
de valeurs. Pour une cognition culturalisée. », in Revue d’Intelligence
Artificielle, vol. 19, no1-2, p. 45–55, 2005.
Lassegue Jean, Cassirer. Du Transcendantal au
sémiotique, Paris, Vrin, 2016.
Mazzola Guerino, The Topos of
Music. Geometric Logic of Concepts. Theory and
Performance, Dordrecht, Springer, 2002.
Missire Régis, « Perception sémantique et
Perception sémiotique », in Texto ! Textes et Cultures, vol. XVIII
no 2, 2013. http://www.revue-texto.net/index.php/http:/www.revue-texto.net/Archives/docannexe/file/docannexe/file/Parutions/Archives/Parutions/Semiotiques/index.php?id=3228,
[consulté en août 2023].
Michaud-Laine, Vincent, Sémiomusicologie de la harpe
Gaélique ancienne, Paris, Classiques Garnier, 2024
Michaud-Laine, Vincent, et Giavitto,
Jean-Louis, notice « intervalle » dans Atlas des Sciences de la
Culture, Paris, Classiques Garnier, à paraître.
Molino Jean, « Fait musical
et Sémiologie de la musique », dans Musique en jeu,
no 17, p. 37-62, 1975.
Moutat Audrey, Du sensible à l’intelligible.
Pour une sémiotique de la perception, Limoges, Lambert-Lucas, 2015.
Rastier François, « De l’essence double du
langage » et le renouveau du Saussurisme, Paris, Lambert-Lucas, 2016.
Rossing, Thomas D. (dir.). The science of string instruments. New York,
Springer, 2010.
Schlenker, Philippe, “Outline of music semantics” in Music Perception: An
Interdisciplinary Journal, 2017, vol. 35, no. 1, p. 3-37.
Simondon Gilbert, L’Individuation à la lumière des
notions de forme et d’information, Grenoble, Millon, 2013.
Van Vliet Muriel, La Forme selon Ernst Cassirer. De la morphologie au structuralisme, Rennes,
PUR, 2013.
Van Vliet Muriel, « Art et Langage chez Ernst
Cassirer. Morphologie et/ou Structuralisme ? » in Images Re-vues,
Hors-série 5, janvier 2014.
Van Vliet Muriel, « Phénoménologie de la perception et
Anthropologie de l’homme en mouvement. L’Incorporation du sens de Cassirer à
Ingold » in Anthropologie et sociétés, vol. 40, no 3,
p. 2-17.
[1] Cf. Michaud-Laine,
Vincent, La sémiomusicologie de la harpe gaélique ancienne, Paris,
Classiques Garnier, 2024, chap. « terminologie
textuelle ».
[2] ibid. for all the translations and choices made one can refer to these
previously cited works.
[3] We adopt the lettering
system devised by Ann Heyman which we find more didactic for this presentation,
thus the caomhluighe are labelled G for the lowest, and g for the
highest, and double lettering will be implemented for the low octave, thus
Cronan is written GG.
[4] We adopt the lettering
system devised by Ann Heyman which we find more didactic for this presentation,
thus the caomhluighe are labelled G for the lowest, and g for the
highest, and double lettering will be implemented for the low octave, thus
Cronan is written GG.
[5] We do not consider
speaking of major thirds in the context of a music collected in the first half
of the 19th century, anachronistic, at the contrary of referring the
same music to more ancient musical system without sound evidence that they’d be
related. The purpose of the labelling ‘major’ is to be understood.
[6] A lovely and so clear expression borrowed from Ann Heymann.
[7] We would like here to
insist that no reproaches nor bitterness should logically be harbored against
Bunting without whom we wouldn’t have anything at all and who was a man of his
times, and a fine one, too.
[8] In our previous word, La
sémiologie de la harpe gaélique ancienne, Paris, Classiques Garnier, 2024,
we had dismissed the entire series as it appeared to us that such tuning were
not practiced by the harpers and Bunting seemed to have obtained them out of
intense obsessive questioning about tunings and measures in his desperate and
doomed to failure attempt to link the Irish harp to the Music of the Robert ap
Huw manuscript. Our interpretative filter was dictated by our goal to evaluate
the authenticity of the terminology and its usage in the harp practices. This
is a good example on how goals can shift how one looks at documents. Our now
exposed interpretation of aon ->án is, of course, one among others,
we do keep refutable but offer this interpretative line to try and show that
many other alleys in terms of what tunings would have been possible and viable,
are possible.