While an extended rationalization is beyond the scope of this article (for this, see Jan, a brief summary, in the form of the following list, may be useful. Examples 2 (i) and 2 (ii) show a musemeplex- Paraphrase , where Gluck bases the main melodic phrase of his aria (transposed for ease of comparison) on the first restatement of the Gigue by J.S.
Likeness3.3
The wide arc of the melodies is certainly similar, but they differ in some important details. Indeed – in an arguably false, anti-memetic dichotomy – he warns that “the transference of the trope Filius ecce patrem, the view that its versions are all actualizations of a matrix, must be reckoned with.
Framework3.4
However, some of the Likenesses Cope26 positions may be more usefully considered short, highly marked quotations, such is their singularity (see Figure 4). But it is certainly problematic to make such a clear distinction between a middle-level Framework and quasi-first-level commons here, given the fusion of these structural levels proposed in the second half of the passages27.
Commonality3.5
As stylistic forms, commons are the building blocks of stylistic structures, which arguably constitute most museums (Narmour 1990: 34). Rather, it appears to have arisen 'conceptually', as a result of the operation of a musical-operational/procedural meme governing the b1–(d2 implied)/d1–b voicing exchange.
Categorical Intersection3.6
However, if the chronological, geographical and cultural distance between these specimens is representative of the distribution of other copies of this museum, it is clearly ahistorical (especially its last three entries which can be considered as an independent sub-museum). If so, other copies can easily be found in different periods and places of music history.
Models of Musical Distance and Weight4.1
The EMD and Psychological Aspects of Similarity
EMD aligns well with psychological, evolutionary, and neurobiological perspectives on pattern perception and transmission/mutation, and these will now be considered in turn. From a psychological point of view, one can assume that the difference-distance between two pattern forms is proportional to the effort required in cognition to relate them. The connection between two closely related forms, whereby a low-value EMD connects them, is therefore easier to recognize than that between two more divergent forms, which will be separated by a high-value EMD.
Thus, EMD is both a measure and a predictor of perceptual-cognitive similarity and thus ease of recognition. In this context, EMD can also be considered as an index of the perceptual-cognitive salience of the replica museum: how special or wonderful the replica museum is, when recognized in comparison to the memory of its source, can be directly hypothesized to be . proportional to the EMD value, the latter is assigned to the copy form in recognition.
The EMD and Evolutionary Aspects of Similarity
The EMD and Neurobiological Aspects of Similarity
A given cortical area can support many overlapping hexagons as a result of the embedding of multiple "attractors" into the cortex. Two types of ground motion appear to be involved in the operation of the HCT, which are abstracted in Figure 9. Inter-museum ground motion is shown in Figure 10, which again represents the beginning of Bach's C major fugue, but this time presented again under HCT conditions.
These also indicate pulse duration (note length), using traditional Western rhythmic symbols. 17 is represented by arrows pointing from the S/T (spatial (clamp)/temporal (sequence/rhythm)) coordinates of the source to those of the copy. The absolute value of EMD depends on the particular parameters used in its calculation and the specific weight applied to them.
Summary of the EMD in Relation to Memetic Phenomena4.5
The total EMD value is calculated here using Temperley's Krumhansl-based weightings (see Section 5.2 for details)38. That is, keeping the same weights for all calculations allows comparison of a number of musemes, both in source and copy form, using the EMD as an index of relative mutation distance (Section 4.3). This section identifies seven muses in a passage from a Beethoven sonata and suggests potential source code indexes (i.e., corresponding, homologously related forms) for them from works by Beethoven's immediate and more distant predecessors39.
It then classifies the source and copy forms according to Cope's categories in order to understand how copy museums of different Copean types are integrated into a new idiostructural context. It then applies the EMD calculus to the museums in an attempt to measure the psychological, evolutionary, and neurobiological distance between the hypothesized source and the Beethoven copy according to the various weighting schemes outlined in Section 4.1. In addition to developing a methodology for such use of EMD (which can be refined in future research by, for example, adding other weighting schemes that represent more subtle indices of importance), the analysis will give rise to data that can be used (among other ) to assess the probability that two given patterns are homologously related, and to enter into the more ambitious project of mapping the museum pool outlined in Section 6.
Memetic Analysis and Hypothesised Source Coindexes5.1
Earth Mover’s Distance Analysis
Copy muses in Example 6 (x) are transposed to C major or C minor in Example 7 and are shown below their source code indices, similarly transposed. This equivalence not only facilitates comparison, but is also the basis of the EMD calculation which, as suggested in Section 3.2, should not consider differences in pitch due to museum transposition as evolutionarily significant. To the right of each museum in Example 7 are shown the values from which the EMD.
Museme
Museme c
As one of the most ubiquitous patterns in the late eighteenth-century style, the Museme c Commonality trill. While EMD values naturally depend on Museme segmentation and the resulting tone content, Museme d segmentation is more problematic than the other Muses discussed here due to the somewhat abstract, musical-operational/procedural nature of these samples. Museme e is probably one of the most durable of all musems in common practice.
The EMD values for Museme e are an order of magnitude much higher than those for the other museums, due to the fact that Bach's localized and short-term progression in Beethoven has been greatly expanded. The EMD values for Museme f reflect the fact that although the pitches of the source form are not changed in the copy, their rhythmic position is changed54. As with Museme c, the difference in perception between the two forms is probably not as great as the EMD values might imply: they are probably seen as members of the same allele class, and their common structural function attenuates the metric differences between them.
Summary5.2.8
Conclusion: The EMD and Population Memetics
In a somewhat speculative conclusion, I will briefly review some of the implications of the museme categories adopted from Cope, and the associated EMD calculations, to make some predictions about what they might tell us about the inhabitants of the wider museme- pool56. But if this possibility were to materialize, what might the issues discussed here enable us to hypothesize about the nature of the museme pool revealed? This difference perhaps reflects the instability of the modulation to the dominant key in Example 8(ii), and the higher tesiture that this particular implementation of the modulation entailed.
A low inter-museme EMD (section 4.4) means that the copy form is not significantly different from the source, and may still occupy the same museme allele class. In contrast, a high inter-museme EMD may indicate that the copy form is leaving the parent allele class and joining another, existing allele class, or triggering a replicative process leading to the formation of a new allele class. class (Jan [nd]). These latter forces arise from people's innate perceptual-cognitive capacities, from the inherent inertia of the museme pool, and from the verbal-conceptual memes that regulate what is considered tasteful and acceptable in music.
ENDNOTES
Cope is probably referring to 'strong' replication between composers, not self-quotation – such as Haydn's apparent quotation from the opening of his Farewell Symphony, No. text compensate for the lack of duration-based grouping cues in delineating the muses that make up these figures of speech. The same is clearly true for analog-related replicators, but in this case the proximity is accidental and not due to the action of evolutionary processes.
263, the cycle has generated a satisfying amount of musical pleasure because of the perceived logic and 'rightness' of its return to the tonic harmony. The recognition of the implications of the cycle provides another, more pleasant, form of cognitive stimulus to the 'difficult' negations (albeit minimal) that have been extensively theorized by Meyer and Narmour (Jan. especially the octave placement of pitches in the cycle) is perhaps insignificant perceptually and cognitively, but is significant for the EMD calculation due to the different (by twelve) MIDI numbers for a given pitch class presented in two contexts an octave apart.
As suggested in section 2, whether this connection is the result of a conscious decision by Beethoven to adapt Haydn's music, or whether it is the result of a subconscious echo of the past, is immaterial from the perspective of the eyes of memes. 22-262 of the C minor Fugue from Book II of Bach's Das wohltemperirte Clavier, where a complete revolution around the cycle is articulated by the particular opening rhythm of the subject. In no sense, however, are the conceptual differences between the forms of any of the museums considered here so great as to undermine their status as potential evolutionary antecedents and consequences.
On computational models of music evolution: From the origins of musical taste to the emergence of grammar. The hippocampus as a spatial map: Preliminary evidence from unit activity in the freely moving rat. The neural basis of cognitive mapping: Path integration does not require hippocampus or entorhinal cortex.
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