A Study on the Effect of Urban Form on the Street Interface Rhythm Based on Multisource Data and Waveform Classification

Abstract

Good-quality urban street space is crucial for improving walkability. Frequency and amplitude are the main spatial characteristics of the street interface rhythm, known as a “virtual–real” relation. Exploring the mechanism influencing the urban street interface rhythm can help grasp the movement trend. In this study, the correlation between frequency and urban form is explored through a Pearson correlation analysis with multisource data, and the factors influencing the urban street interface rhythm are presented. The results indicate that frequency has a moderate negative correlation with the block scale and a moderate positive correlation with the number of pedestrian access entrances (PAE-n); the PAE-n also has a strong negative correlation with the block scale. Some spatial characteristics of outstanding streets from different countries are analyzed and discussed based on waveform classification. The regularities of interface rhythm that exist within multiple streets are found: multiple gaps on the street interface exist, acting as a “beat”, which regularly integrates or separates the street interface rhythm. The frequency and amplitude of the “beat” significantly affect streets’ walkability, and the amplitude is generally low and uniform, with good visual accessibility in all directions. A “Small Block and Dense Grid” becomes a key factor in improving walkability. Basic knowledge of the street interface rhythm in urban walking space research is supplemented by this study. Furthermore, theoretical guidance and parametric evidence are provided to improve walkability and promote the continuation of the traditional context.

1. Introduction

The technological revolution has driven the advent and development of cars, giving people greater accessibility. However, this has gradually increased the urban spatial scale design, forming an automobile-oriented transport pattern. Ultimately, pedestrians are marginalized even though they are supposed to be the main actors in the street space. Streets are no longer full of life, and the traditional pedestrian-oriented pattern has been radically altered as well. Simultaneously, urban problems such as traffic congestion, air pollution, a shortage of non-renewable energy, public health, and the estrangement of human relations have become increasingly serious. Although traditional urban spatial patterns, represented by heritage-protected quarters and ancient city centers, are generally used as a blueprint for the construction of livable cities—in particular, some new urban blocks are created in an “antique-like” way—the unique charm that emanates from the walking space of real traditional urban areas seems to be difficult to reproduce. The “ancient-modern” urban walking spatial pattern is gradually becoming isolated, making these old urban areas appear to be “works of art” that have become separate from the modern urban pattern over time, causing the continuation of the traditional context to passively fall into a state of stagnation. In these circumstances, returning to “people-centered” urban life becomes a pressing issue.

Pursuing a better life has always been a long-term vision of humanity, and even more critical is the creation of a “feel better” urban spatial form, which is the fundamental goal of urban design. A convenient travel distance and the visual appeal of walking routes are crucial for shaping a fully functional walking system [1]. Tighter spacing is more effective than loose spacing in achieving street definition; one cannot forget that a major purpose of streets is to enable people to move from one place to another, i.e., not only to a location on the street but also to and from areas beyond [2]. Short street segments that can be easily crossed by walking are among the necessary conditions for urban diversity, and gaps between properties allowing for pedestrian access also play a key role in triggering turns and providing pedestrians with the possibility of free movement, which is beneficial for walking [3]. Regarding the mechanism of the interaction between “physical objects” and “psychological sensation” (i.e., the subjective perception and experience of an individual’s inner mental states, emotions, thoughts, consciousness, and feelings), humans have both positive and negative sensations. However, negative sensations do not necessarily mean an absence, reduction, or even elimination. On the contrary, these sensations may be much stronger than positive sensations [4]. In this study, “positive–negative” sensations are equivalent to the sensory stimuli provided by the differences in “real–virtual” relations in street interface forms. The “real” elements refer to buildings along the street, while the “virtual” elements refer to the “gaps” between buildings along the street (including road spaces). If the street interface is not a continuous solid street wall, this indicates that the street interface is affected by “virtual” elements. It can be seen that a “feeling good” urban space requires more than a good visual perception and walking experience; furthermore, the virtual elements of the street interface are crucial for visual perception.

In actuality, creating a walkable urban street space has become a necessary consideration, with accommodation for the factors of time and space. In particular, many researchers are trying to further stimulate and promote pedestrian transportation by improving the quality of the urban street space. The characteristics of the urban built environment are an important factor that affects various walking experiences [5,6]. Compared to spatial elements such as D/H, the physical form characteristics of the ground floor have a greater impact on street activities [7,8]. Regarding quantitative research on how the street interface and urban spaces affect walking activities, “Walkability” is the primary measurement method for whether built environments encourage residents to walk; it can be used to predict the level of physical activity and active travel [9], which are mainly related to convenience, accessibility, safety, comfort, and pleasure [10]. Convenience and accessibility are the two most fundamental psychological needs for walking, followed by safety, comfort, and pleasure [11,12]. Jan Gehl [1] provides a more direct explanation that, regardless of their walking purpose, pedestrians’ persistent pursuit of short routes far outweighs safety or other considerations. Thus, ensuring the convenience and accessibility of pedestrian access is a prerequisite for creating a walkable city. At the same time, other spatial configurations related to visual perception should be considered as well.

Recent studies suggest that the mutual feedback relation of “Man-physical objects” has become a focus of attention; this concept is generally expanded into spatial cognition and pedestrian access. From the perspective of indicators and methods, the continuity, proximity, and enclosing degree of a street interface can be characterized through the Near-Line Ratio, Built-to-Line Ratio, and Interface Density, respectively [13]. The Interface Density of good streets is generally 70% to 85% [14]. In terms of measurement with multisource data, Geographic Information Systems (GISs) and statistics are the most commonly used methods. Yue Liu [15] combined GIS and statistics to derive a method to improve the security of shared urban streets. Street interface continuity can be evaluated by the “Maximum Transection” method, which is also derived from GIS [16]. Regarding spatial cognition, Xu et al. [17] identified that the “empty” part of the street interface is the most visually attractive and that the green view helps to improve the fascination level of a street. In terms of the perception of the “empty” part, the transparency of the street interface is related to the visual extension. Streets with visual extension have a positive impact on attracting commercial stay activities [18], and a wide view of the street interface helps to improve walkability [19]. Streets with good visual extension help to enhance the healing potential of the street [20]. As seen in the studies above, much research has been conducted on the impact of virtual elements at the street interface on visual perception and walking experience. Few experiments have been carried out to discover the physical disconnection of the street interface. Chenxue Sun [21] proposed a new standpoint that the street interface is composed of both a “virtual” part (multiple gaps between buildings along the street, including road space) and a “real” part (physical entities of buildings along the street), and the “Gap” is the virtual element of the street interface indicated. Thus, the physical continuous and complete “virtual–real” relation of the horizontal dimension of street interface, which can be named the “street interface rhythm”, is related to the numbers, individual form, and spatial relation of the buildings along a street, as well as the complex interweaving relation with the road grid. Meanwhile, the waveform classification method was proposed to characterize the street interface rhythm for the first time. The extraction method of the waveform fully simulated the features in the pedestrian’s sight, and the views of famous urban planning theorists such as Kevin Lynch and psychophysical principles were used as the theoretical basis, which gave the waveform classification method the explanatory force of the “Interface Rhythm—Psychological Cognition” covariant relation. Chenxue Sun [22] proposed a quantitative method with “Frequency” and “Amplitude” as indicators to explore the impact of urban street interface rhythm on pedestrians’ psychological cognition and two main characteristics, “street interface break times” and “street interface spatial extension degree”, which were derived through immersive VR experiments and questionnaires. At the same time, psychological and psychophysical principles are the theoretical basis of the two indicators, and a systematic algorithm that can effectively reveal the covariation law of “Interface Rhythm—Psychological Cognition” is established. Other studies have shown that perceived walkability enhances a neighborhood’s social environment, while physical walkability does not [23]. Image-ability (such as the memorable quality of a place) and transparency (to what degree people can see beyond the street’s edge) significantly influence pedestrian volume in downtown streets. However, other urban design qualities, including the human scale, complexity, and enclosure, do not play a significant role in walkability [24].

Regarding pedestrian access, the better the connectivity of a walking path, the more favorable it is for pedestrian access, which is widely recognized. The road density, intersection density, block density, and connectivity node ratio are positively correlated with road connectivity [25,26], while the block length (or street spacing) has a negative correlation with road connectivity [27]. Accessibility, intersection density, and road density are the three indicators that have the greatest impact on walkability, with their impact decreasing from left to right [28]. Pedestrians tend to engage in more activities on interconnected streets [29,30], and accessibility has a much greater impact on street vitality than spatial diversity [31]. In mixed-use, medium-density environments, streets with good connectivity increase the number of pedestrians and generate higher pedestrian rates [32], and the distance between streets and the density of roadside trees are significantly correlated with pedestrian rates [33]. Walkable streets are an almost integral part of a complete network, and the best street network can provide more path choices and walking experiences; city streets that usually have the most connections to other parts of the network have the busiest traffic and commerce [34]. Pedestrians tend to choose walking paths with diversified and high-quality spatial conditions, even if these paths are not the most time-saving [35]. However, this is not entirely consistent with Jan Gehl’s earlier viewpoint that pedestrians’ persistent pursuit of short routes far outweighs safety or other factors [1]. Nevertheless, diversified paths featuring high-quality spatial conditions (visual perception) and convenience (pedestrian access) may have a certain correlation, precisely indicated by the above two viewpoints.

In all of the above studies, as well as in the literature in general, the physical characteristics of the urban built environment are important factors affecting the walking experience, and the ground floor in the horizontal dimension is most closely related to pedestrian rates. Nevertheless, current research has mostly focused on the physical entity features of the street interface or on separating the road space belonging to the virtual part of the street interface to explore its impact on pedestrian activities. Therefore, few studies have focused on the continuity and complete morphological relation between the “virtual–real” physical objects of the street interface, falling short to consider overall both the physical entity (real) and the street interface (virtual), especially research on the effect of urban form on the street interface rhythm (“virtual–real” relation). Theoretical perspectives on the “virtual–real” relation of street interface in the theoretical system of urban pedestrian space are absent. Furthermore, statistics and GIS both have good forecasting effects on the trend in urban form at the macro scale but are hard to use to indicate the micro-phenomenon of pedestrian movements. In contrast, the street interface morphology measurement method based on the pedestrian perspective proposed in our previous study can characterize the micro-phenomenon function relation between physical objects and psychological cognition, but it is difficult to use to elucidate the movement law of micro-phenomenon accompanying urban form. Given the aforementioned references, the theoretical knowledge of the influence relation of urban form and street interface rhythm is lacking. Meanwhile, most quantitative analyses of the urban street interface have used only one method on either the macro or micro scale, which makes it difficult to fully reveal the underlying attributes. In addition, currently, a systematic conceptual framework that includes hypotheses is rarely used in urban street interface research, and the sample size is generally small with a simple historical background, which weakens the scientific and generalization ability of the algorithm. Therefore, this study simultaneously contributes to the theoretical perspectives of urban street interface rhythm and offers an improvement in the quantitative method of street interface characteristics.

In this study, we construct and employ a method with bi-directional interpretation capability from a “bird’s-eye view—pedestrian view”, known as the “macro—micro” dual-scale method, with the objective of revealing the effect of urban form on the street interface rhythm (Figure 1). Following this, the correlation between street interface rhythm and urban form (Sub-question 1) are explored through Pearson correlation analysis, and multiple digital samples are preprocessed using GIS and manual computation. Then, the regularity of the interface rhythm of walkable streets is revealed through waveform classification (Sub-question 2) based on the extensive collection and analysis of Euro-US and Chinese street segments. It should be noted that “statistical” analysis plays an irreplaceable role in macro-scale research on urban form, which can provide a theoretical basis for the “graph” analysis of waveform classification at the micro scale. This is the reason for choosing these two methods to explore the effect of urban form on the street interface rhythm. Current basic knowledge of street interface rhythm in the field of research on walking space in urban form might be supplemented by this study, and the theoretical guidance and parametric evidence provided will help to improve walkability and promote the continuation of traditional context as well.

2. Materials and Methods

2.1. Study Area and Multisource Data

2.1.1. Study Area

“Street segments” were the analysis unit used in this study, which consist of a series of “buildings” along the street. To improve the generalization ability of the algorithm in this study, a total of 162 samples were selected from nine cities in seven countries for the study of the first sub-question, including Jinan and Tianjin (China), Kyoto, Los Angeles, Seattle, Barcelona, London, Paris, and Milan (Figure 2). The sampled streets are widely distributed in large cities in Asia, as well as in Euro-US cities. The interface rhythm of these streets is unique in general and represents a wide range of characteristics: a long historical context of urban form; a clear and distinct urban fabric; and a spatial pattern with traditional and modern urban fabrics known as “new and old” coexist, which are representative from spatiotemporal dual dimensions.

In the study of the second sub-question, 15 Euro-US streets recognized as outstanding were selected from two books that are recognized as guidance in the urban design field (Figure A1), Great Streets and Street Design: The Secret of Building Great Towns, including Pittsburgh (USA)—Roslyn Place, Richmond (USA)—Monument Avenue, Rome (Italy)—Via dei Giubbonari and Via del Corso, Copenhagen (Denmark)—Strøget, Barcelona (Spain)—Paseo de Gracia and Ramblas, Aix-en-Provence (France)—Cours Mirabeau, Paris (France)—Avenue Montaigne, Boulevard Saint-Michel, and Avenue des Champs-Elysees, Orvieto (Italy)—Corso Cavour, Havana (Cuba)—Paseo del Prado, London (UK)—Regent Street, and Bruges (Belgium)—Steenstraat. These streets are ordinary commercial pedestrian streets only defined by buildings along the street, while streets defined by special types, such as only trees, canals, or colors, were excluded.

Next, 13 streets recognized as outstanding in China were selected to compare with the aforementioned Euro-US streets (Figure A2), including Beijing—Wangfujing Street, Shanghai—Nanjing Road, Tianjin—Heping Road and Binjiang Road, Wuhan—Hanjiang Road, Guangzhou—Beijing Road, Xiamen—Zhongshan Road, Hangzhou—Yan’an Road, Suzhou—Guanqian Street, Xi’an—East Street, Changchun—Chongqing Road, Guilin Road, and Harbin—Central Street. Some of these streets are located in concession areas with fabric characteristics similar to Western urban streets; some are traditional-style streets or historical and cultural streets with fine unspoiled fabric after experiencing the impact of rapid urbanization.

2.1.2. Data Source

Numerous road networks were downloaded from OSM (https://www.openstreetmap.org/, accessed on 21 February 2024), and city digital orthophoto maps (DOMs) and street panorama of multiple cities were obtained using Google Earth Pro. Additional field investigations were conducted in individual cities that were easily accessible (

Table 1. Data sources on the effect of urban form on the street interface rhythm.

Main Question	Sub-Question	Analysis Dimension	Data Sources
The effect of urban form on the street interface rhythm	(1) The correlation between street interface rhythm and urban form	Spatial characteristics of street interface rhythm	OSM: Road Network Google Earth Pro: DOM and Street PanoramaField Investigation
		Urban form	OSM: Road Network Google Earth Pro: DOM and Street PanoramaField Investigation
	(2) The regularity of walkable streets’ interface rhythm	Spatial characteristics of street interface rhythm	Google Earth Pro: DOM and Street Panorama Field Investigation

).

2.2. Street Interface Rhythm and Urban Form Indicators

2.2.1. Street Interface Rhythm Indicators

Established frequency and amplitude indicators [22] (Equations (1) and (2)) were applied in this study to quantify the spatial characteristics of the street interface rhythm. These are the main indicators of the street interface rhythm, with great significance in explaining the covariant relation of the “Interface Rhythm—Psychological Cognition”.

The frequency correspondingly characterizes the break times of the street interface (unit: times/ks). Its equation is as follows:

$$f=f(n^{\prime })/ks$$

(1)

where $f$ refers to the street interface’s break times in the psychological sense, and $n^{\prime }$ refers to that in the physical sense. $ks$ refers to the walk time of 1000 s. Frequency is a continuous function, which has a linear relation of 1:1 in terms of the functional relation between physical and psychological. The values range from 0 to +∞, which indicate the continuity of the street interface from better to worse.

The amplitude correspondingly characterizes the spatial extension degree of the street interface (unit: km). Its equation is as follows:

$$A=\Delta A+a_0$$

(2)

where A refers to the street interface’s spatial extension degree in the psychological sense, and $\mathsf{\Delta }A$ refers to that in the physical sense. $a_0$ refers to the width of the main street. Amplitude is a step function where the lower set represents the depth of the street interface’s lateral space, the higher set represents the distance between the road node and the main street, and the values range from 0 to 1. In the lower set, complexity and spatial depth perception go from weak to strong. In the higher set, physiological perceptions of convenience go from strong to weak.

2.2.2. Urban Form Indicators

While the direct relation between street interface rhythm and urban form is explored, the indirect effects of intermediate variables should also be investigated, which is important in fully exploring the complexity of the effect of urban form on the street interface rhythm; two urban form variables are addressed.

The block scale ($b_{\mathrm{s}}$) is mentioned first, in which urban roads do not exist in the block, so the urban road spacing can also be used to represent the block scale. The block scale negatively correlates with the urban road traffic capacity (unit: m).

The number of pedestrian access entrances (PAE-n, $p_{\mathrm{n}}$) can be utilized to characterize the number of pedestrian access entrances that can be directly crossed by walking on the main streets of adjacent blocks. PAE-n is contributed by urban roads and non-urban roads and has a positive correlation with walking accessibility (unit: times/ks).

2.3. Other Street Interface Form Indicators

The synergistic relation between the two pedestrian default attributes, visual perception and walking, can be characterized by the “visual perception–pedestrian access” spatial element synergy ratio (VP-PA Synergy). VP-PA Synergy = $p_{\mathrm{n}}/f$. An increase in the VP-PA Synergy is accompanied by an increase in the PAE-n contribution to frequency. This shows that under the condition that the VP-PA Synergy is equal to 1.00, all street interface breaks exist, acting as PAEs.

The street interface rhythm may be more conspicuously based on the physical form, which is compared to the storefront rhythm. The existing storefront rhythm indicator $W/D$ was developed by Yoshinobu Ashihara, and the storefront rhythm recurs with $W/D$ below 1.00, resulting in a stronger sense of enclosure, where W refers to the storefront width and D refers to the main street width. Based on the existing storefront rhythm indicators, the gap width ratio (GWR) $W_{\mathrm{g}}/a_0$ was proposed in this study, where $W_{\mathrm{g}}$ refers to the street gap width and $a_0$ refers to the main street width. This indicates that the GWR is under the condition of below 1.00, which means that the spatial relation along the street is more compact with a stronger sense of enclosure; on the contrary, it is more discrete with a weaker sense of enclosure. With the GWR is equal to 1.00, which means that the street space is in an intermediate range between compact and discrete and with a moderate sense of enclosure.

2.4. Statistical Analysis

The street interface rhythm is a part of the urban fabric. Under the premise that the correlation between the street interface rhythm and urban form is confirmed, it is meaningful to study the regularity of the interface rhythm of walkable streets. Therefore, the correlation should be explored first. The regularity is revealed in Section 2.5.

2.4.1. Hypotheses

To accurately predict the correlation between the street interface rhythm and urban form, a scientific and reliable systematic conceptual framework must be built. Thus, as shown in Figure 3, a conceptual framework was proposed, corresponding to the interpretation of the “Statistics” analysis of Figure 1. Several underlying theoretical relations constructed before formulating the proposed conceptual framework are listed as follows.

• The theoretical derivation of the underlying causality

First is the physical break, which is the triggering factor for the form changes in the street interface rhythm, and the most basic “quantity” characteristic of this triggering factor is described by frequency. In contrast, amplitude further describes their “degree”, so frequency is analyzed first, followed by amplitude. Accordingly, frequency should be considered the representative indicator of street interface rhythm, which has an irreplaceable prerequisite significance for studying the correlation between street interface rhythm and urban form.

Second, according to the indicator definitions in Section 2.2, as the value of PAE-n becomes higher, the street interface is broken more frequently by the PAEs, which is further related to frequency. However, in urban design, the road grid is generally planned first, and then the slow traffic system, such as side streets, is distributed. It follows that the block scale may first affect PAE-n and then frequency. Meanwhile, continuous street interfaces can be disrupted by urban roads, thus directly affecting frequency. Therefore, frequency, block scale, and PAE-n may have the attributes of dependent, independent, and intermediate variables in that order.

• The theoretical derivation of the variable attributes

The theoretical derivation of the potential properties of indicators is shown in Figure 3a. In combination with the definition of the indicators in Section 2.2.2, the block scale is only contributed by urban roads, PAE-n is contributed by urban roads and non-urban roads, and frequency is contributed by a series of interface spaces along the street (including the road space). Some potential theoretical derivations are as follows: (1) The larger the block scale, the greater the stock of building monomers, which may lead to a higher frequency. (2) The higher the PAE-n, the more times the street interface is interrupted by the roads, but for the continuity of the street interface to be unaffected, the non-road interface breaks may be reduced accordingly, which may lead to a lower frequency. (3) The larger the block scale, the sparser the urban road grid; however, for the walking accessibility to be unaffected, a higher minimum base may exist within the PAE-n, so the influence from the block scale is possibly weak. Meanwhile, the relation between the block scale and PAE-n can be roughly presented.

• Hypotheses and Analysis Steps

Some basic hypotheses and analysis steps to be constructed are shown in Figure 3b. (1) Frequency was assumed to be positively correlated and affected by the block scale; (2) frequency was assumed to be negatively correlated and affected by PAE-n; (3) PAE-n was assumed to be negatively correlated and affected by the block scale, probably with a weak correlation. Subsequently, combining the above theoretical relations and the indicator attributes mentioned in Section 2.2, the smaller the block scale, the higher the PAE-n and the lower the frequency, which means that the stronger the urban road traffic capacity, the better the walking accessibility and the continuity of the street interface.

Given the aforementioned situations, the correlation between frequency (f) and block scale ($b_{\mathrm{s}}$) was analyzed first. Then, the correlation between frequency (f) and the number of pedestrian access entrances (PAE-n, $p_{\mathrm{n}}$) was analyzed, and the correlation between block scale ($b_{\mathrm{s}}$) and the number of pedestrian access entrances (PAE-n, $p_{\mathrm{n}}$) was analyzed last. Ultimately, these correlated results were combined to obtain the complete chain of the influence relation between the three variables.

2.4.2. Research Design and Applicability Analysis

In order to verify all our hypotheses shown in Figure 3b regarding the correlation between the street interface rhythm and urban form, this study employed a Pearson correlation analysis, with IBM SPSS Statistics 26 being used as a tool to perform the calculations. It is important to note that only two variables can participate in the analysis process. Data continuity from all variables should be represented, and the approximate normal distribution characteristics should be matched by all variables, which are the prerequisites for the Pearson correlation to be adopted.

• Construction of “Two-Variable” Analysis

Given the derivation in Section 2.4.1, the correlation between the street interface rhythm and urban form was transformed into a pairwise influence relation between f, $b_{\mathrm{s}}$, and $p_{\mathrm{n}}$, where correlations between them were analyzed each time.

• Data Continuity

Frequency is the representative indicator of the street interface rhythm derived in Section 2.4.1. According to [22], frequency has an approximate continuity in the mathematical sense.

• An Approximately Normal Distribution

For the experimental conditions to be controlled, an ideal experimental environment should be created. For this reason, the three variables (f, $b_{\mathrm{s}}$, and $p_{\mathrm{n}}$) were assumed to satisfy the condition of “approximate normal distribution”.

In summary, the match between the hypotheses and Pearson correlation analysis was verified, indicating that the research design is effective and workable. Furthermore, the methodological accuracy of the Pearson correlation analysis is sufficient for this study.

2.4.3. Sample Collection

The samples were collected using a grid. The ultimate goal of this study was to apply the research results to improve the walkability of urban street spaces. Thus, taking the walking distance of a 500 m radius can be accepted by most people as the setting condition of the grid unit, which benefits the interpretation of the walking dimension of this study. Furthermore, it is not uncommon for the block scale to exceed 500 m. Thus, the 1 × 1 km horizontal orthogonal grid units were determined.

2.4.4. Measurement of Street Interface “Frequency” at the Macro Scale

As illustrated in Figure 4, numerous road networks with DOMs were imported into a Geographic Information System (GIS). In order to emphasize the “figure–ground” relation, the “building space” was transformed into a “black–white” base map. The main street center lines and auxiliary lines were plotted, with the auxiliary lines offset appropriately to the street interface on both sides, and the buildings along the street were intersected by the auxiliary lines. Then, the irrelevant intersections were eliminated, which was achieved via comparison with the street panorama. As follows, the frequency on each side of the street interface can be defined as half the intersection points, formed by auxiliary lines intersecting the contour lines of the buildings along the street, then divided by twice the length of the main street center lines.

2.4.5. Measurement of Block Scale and PAE-n

In modern planning patterns, the grade of urban road networks is very different. Frequent pedestrian–vehicle mixing is discouraged on arterial roads; however, it is permitted on secondary roads and encouraged on branch roads. In addition, purely vehicular access is not conducive to increased walkability. Therefore, only intersections of main streets with secondary trunk roads, branch roads, or side streets result in PAEs. Insignificant grade differences exist in the checkerboard roadway network; hence, all urban roads are considered main streets. In addition, temporary pedestrian side streets are not encompassed in the PAEs, such as gated communities with occasional openings and narrow gaps between adjacent buildings.

The block scale can be obtained by measuring the OSM data directly with GIS. The PAE-n can be measured according to the method in Figure 5, so the PAE-n of each side of the street interface is defined as the number of intersections formed by the center line of the main streets themselves plus the number of intersections formed by the center line of the main streets with the center line of side streets. Meanwhile, we can subtract the number of intersections formed by the center line of the arterial roads themselves, then multiply the above results by two, and finally divide by the length of the main street center line.

2.5. Waveform Classification Analysis

The regularity of the interface rhythm of walkable streets was investigated through waveform classification (Sub-question 2), which corresponds to the interpretation of the “Graph” analysis in Figure 1. The waveform classification analysis can be measured using the indicators of frequency, amplitude, VP-PA Synergy, and GWR mentioned in Section 2.2 and Section 2.3. Among the 28 outstanding streets (see Section 2.1), for a street length well below 1.00 km, there was no need to extract it as a waveform; converting it to 1.00 km based on the original street and then carrying out the calculation was acceptable. In the case of a length above 1.00 km, no pre-processing was required, and the measurements were taken directly following the corresponding steps.

2.5.1. Waveform Graph

A waveform graph is required to visualize the street interface rhythm from the psychological cognition of pedestrians; then, through waveform classification, the graph is composed of multiple waveforms from which the spatial characteristics of the interface rhythm between different streets can be visually compared and interpreted. A waveform is a continuous smooth curve, the basic element of the waveform classification.

Figure 6 illustrates a conceptual model of the street interface rhythm. Taking the side interface with the most diverse characteristics as an example, based on the existing method [21], the street interface rhythm was extracted and converted into a waveform (graph), $y^{\prime }=f (x^{\prime })$ in Figure 7, where the times and degree of fluctuations reflect the break times and spatial extension degree of the street interface in turn, which can be described through frequency and amplitude, respectively (for the definition of indicators, see Section 2.2). Moreover, the effectiveness and feasibility of waveform classification in reflecting the covariant relation of “Interface Rhythm—Psychological Cognition” were proved by earlier studies in [21], so it does not need to be re-verified.

2.5.2. Measurement of Street Interface “Frequency” and Other Indicators at the Micro Scale

Regarding creating continuity at the street interface, the fact that these 28 streets were considered “outstanding” was inevitably related to their unique advantages, as described in Section 2.1. These streets’ DOMs were converted to the waveform classification to calculate the associated data.

2.5.3. Characterization Methods of Complex Data

Creating a better-feeling urban form, which belongs to the urban design category, has theoretical significance in this study. Given this, the meanings of frequency and amplitude can be transformed into urban design dimensions in order to ensure that the indicators are more theoretical.

As seen in Figure 7, the frequency and the higher sets of amplitude are relatively homogeneous, with the former describing the amount of road/non-road space at the street interface and the latter describing the problem of long/short scales of street segments. However, the meaning of the indicators in the lower set of amplitude is more complex, which describes two urban problems: large/small street corners and the presence/absence of open space with non-road attributes along the street. This study provides a “feature” representation to visually interpret these indicators.

From the perspective of modern urban planning patterns, the street corner scale can be interpreted in two aspects: large radius/small radius and non-build-to-line/build-to-line. Street corners with large radii and non-build-to-line/build-to-line are labeled ↑0/1, which indicates large street corners; street corners with small radii and non-build-to-line/build-to-line are labeled ↓0/1, which indicates small street corners. If mixed, they are labeled as appropriate.

The assessment was conducted based on the most dominant characteristics of each street. If open space with a non-road attribute is predominant along the street, it indicates open space with a non-road attribute along the street as “presence”, labeled with “●”. If not, it indicates open space with a non-road attribute along the street as “absence”, labeled with “○”.

Moreover, satisfying either large street corners or open space with a non-road attribute along the street as “presence”, indicating that the lower set of amplitude is high, and low otherwise.

3. Results

3.1. The Correlation between the Street Interface Rhythm and Urban Form

The following results were comprehensively represented by the R-value and p-value, which were visualized through a two-dimensional scatter plot.

3.1.1. Street Interface Frequency and Block Scale

Figure 8 illustrates the results. This figure shows that Tianjin, Barcelona, and Milan show a significant strong negative correlation with |R|-value greater than 0.700 ***, while other cities show a significant moderate negative correlation. The specific relevant data are summarized in

Table 2. The correlation indicators of the street interface frequency and block scale.

City	Frequency		Block Scale		R-Value	p-Value
	SD	AVG	SD	AVG
Jinan—China	3.93	9	164.92	415.09	−0.568 **	<0.01
Tianjin—China	5.86	12	186.04	359.91	−0.710 ***	<0.001
Kyoto	3.94	20	65.29	132.05	−0.522 *	<0.05
Los Angeles	7.95	14	110.15	194.69	−0.671 *	<0.05
Seattle	7.65	14	95.02	145.23	−0.608 *	<0.05
Barcelona	2.99	11	22.66	107.80	−0.959 ***	<0.001
London	2.44	11	14.72	104.88	−0.573 *	<0.05
Paris	1.78	9	106.23	170.05	−0.652 **	<0.01
Milan	3.23	10	68.25	174.59	−0.711 ***	<0.001
Superposition	5.72	12	156.36	214.27	−0.470 ***	<0.001

* p < 0.05, ** p < 0.01, and *** p < 0.001.

; among them, |R| ≥ 0.700 indicates a strong correlation, 0.300 < |R| < 0.700 indicates a moderate correlation, and |R| ≤ 0.300 indicates a low correlation. The p-value indicates statistical significance. The smaller the p-value, the more significant the correlation. * represents p < 0.05, indicating significance. ** represents p < 0.01, indicating very significant. *** represents p < 0.001, indicating extremely significant.

3.1.2. Street Interface Frequency and PAE-n

Figure 9 illustrates the results. This figure shows that Barcelona and Paris have a significantly strong positive correlation with |R|-values greater than 0.700 ***, while the other cities show a significantly moderate positive correlation. The specific relevant data are summarized in

Table 3. The correlation indicators of the street interface frequency and PAE-n.

City	Frequency		PAE-n		R-Value	p-Value
	SD	AVG	SD	AVG
Jinan—China	3.93	9	1.37	3	0.660 ***	<0.001
Tianjin—China	5.86	12	2.53	4	0.655 ***	<0.001
Kyoto	3.94	20	2.92	9	0.595 **	<0.01
Los Angeles	7.95	14	2.95	7	0.589 *	<0.05
Seattle	7.65	14	4.25	9	0.577 *	<0.05
Barcelona	2.99	11	3.21	12	0.812 **	<0.01
London	2.44	11	2.21	10	0.584 *	<0.05
Paris	1.78	9	2.70	7	0.800 ***	<0.001
Milan	3.23	10	2.48	7	0.618 **	<0.01
Superposition	5.72	12	3.67	7	0.474 ***	<0.001

* p < 0.05, ** p < 0.01, and *** p < 0.001.

; among them, |R| ≥ 0.700 indicates a strong correlation, 0.300 < |R| < 0.700 indicates a moderate correlation, and |R| ≤ 0.300 indicates a low correlation. The p-value indicates statistical significance. The smaller the p-value, the more significant the correlation. * represents p < 0.05, indicating significance. ** represents p < 0.01, indicating very significant. *** represents p < 0.001, indicating extremely significant.

3.1.3. PAE-n and Block Scale

Figure 10 illustrates the results. This figure shows that all the samples show a significantly strong negative correlation, and the value of |R| is greater than 0.700 **. Specific relevant data are summarized in

Table 4. The correlation indicators of the block scale and PAE-n.

City	Block Scale		PAE-n		R-Value	p-Value
	SD	AVG	SD	AVG
Jinan—China	164.92	415.09	1.37	3	−0.822 ***	<0.001
Tianjin—China	186.04	359.91	2.53	4	−0.804 ***	<0.001
Kyoto	65.29	132.05	2.92	9	−0.715 **	<0.001
Los Angeles	110.15	194.69	2.95	7	−0.920 ***	<0.001
Seattle	95.02	145.23	4.25	9	−0.918 ***	<0.001
Barcelona	22.66	107.80	3.21	12	−0.847 **	<0.01
London	14.72	104.88	2.21	10	−0.910 ***	<0.001
Paris	106.23	170.05	2.70	7	−0.902 ***	<0.001
Milan	68.25	174.59	2.48	7	−0.911 ***	<0.001
Superposition	156.36	214.27	3.67	7	−0.818 ***	<0.001

** p < 0.01, and *** p < 0.001.

; among them, |R| ≥ 0.700 indicates a strong correlation, 0.300 < |R| < 0.700 indicates a moderate correlation, and |R| ≤ 0.300 indicates a low correlation. The p-value indicates statistical significance. The smaller the p-value, the more significant the correlation. * represents p < 0.05, indicating significance. ** represents p < 0.01, indicating very significant. *** represents p < 0.001, indicating extremely significant.

3.2. Waveform Classification and Data of Outstanding Streets

3.2.1. Outstanding Euro-US Streets

Figure A3 displays the waveform classification of the street interface rhythm. In this figure, fluctuations that seem like “accents” appear in the figure, where the gentle tendency of the fluctuations is broken by intervals. These “accents” are roughly evenly spaced and appear to be fixed notes of continuous and complete street interface rhythmic movement, suggesting that the interface rhythm of outstanding streets is not disordered but rather that multiple gaps that exist act as a “beat”, whereby street interface rhythms are regularly integrated or separated. In terms of street types, residential streets have a more “metrical” or less distinct “beat”, while commercial–residential streets have a distinct “beat”. Among the commercial–residential streets, the medieval streets are more “rapid”, while the modern planning streets are more “slow”.

Table 5. The frequency, VP-PA Synergy, and other data of outstanding Euro-US streets.

Street Name	Formation Periods of City Fabric	Urban Block (m)		Original Data	Frequency (times/ks)	VP-PA Synergy
		Long Side of Block	Typical Scale
Pittsburgh—Roslyn Place ★	20th Century—Grid	85	45 × 85	4|3 (85 m)	43|32	0.75|0.67
Richmond—Monument Avenue ★	20th Century—Grid	100–220	180 × 50	-	49|28	0.16|0.29
Rome—Via dei Giubbonari	Medieval—Organic	15–100	55 × 55	3|5 (180 m)	17|28	1.00|1.00
Rome—Via del Corso	Medieval—Organic	60–85	65 × 70	-	15|15	1.00|0.93
Copenhagen—Strøget	Medieval—Organic	35–215	75 × 100	-	10|10	1.10|1.00
Barcelona—Paseo de Gracia	19th Century—Grid	110–130	125 × 140	-	7|7	1.00|1.00
Barcelona—Ramblas	Medieval—Organic	30–240	90 × 65	-	8|13	1.13|0.85
Aix-en-Provence—Cours Mirabeau	Medieval—Organic	65–105	100 × 50	5|4 (430 m)	12|9	1.00|1.00
Paris—Avenue Montaigne	19th Century—Radial Type	95–300	155 × 120	-	6|5	1.50|1.20
Paris—Boulevard Saint-Michel	19th Century—Radial Type	30–260	145 × 75	-	11|9	1.00|1.00
Paris—Avenue des Champs-Elysees	19th Century—Radial Type	65–245	130 × 145	-	7|9	1.00|1.00
Orvieto—Corso Cavour	Medieval—Organic	50–165	75 × 65	-	15|20	1.00|1.00
Havana—Paseo del Prado	19th Century—Grid	60–115	115 × 85	-	9|8	1.00|1.00
London—Regent Street	19th Century—Grid	45–75	60 × 90	-	12|11	1.00|1.00
Bruges—Steenstraat	Medieval—Organic	75–125	85 × 65	5|4 (380 m)	13|11	1.00|1.00

Note: (a) The “Typical Scale” represents the general and majority ones; therefore, the block at an extreme scale is not included. (b) Residential streets are marked with “★”; if the dense gaps between residential units are excluded, the VP-PA Synergy will be 1.00|1.00. (c) The left and right sides of the frequency “|”, respectively, indicate the A and B sides of the waveform.

,

Table 6. The GWR and other data of outstanding Euro-US streets.

Street Name	Formation Periods of City Fabric	${\mathit{a}}_0$ (m)	${\mathit{W}}_{\mathbf{g}}$ (m)	GWR
Pittsburgh—Roslyn Place ★	20th Century—Grid	20	1.5–5	<0.30
Richmond—Monument Avenue ★	20th Century—Grid	50	1–35	<0.70
Rome—Via dei Giubbonari	Medieval—Organic	5	1.2–5	≤1.00
Rome—Via del Corso	Medieval—Organic	10	5–9	<0.90
Copenhagen—Strøget	Medieval—Organic	12	4–9	<0.75
Barcelona—Paseo de Gracia	19th Century—Grid	60	20–50	<0.83
Barcelona—Ramblas	Medieval—Organic	35	5–12	<0.34
Aix-en-Provence—Cours Mirabeau	Medieval—Organic	40	5.5	<0.14
Paris—Avenue Montaigne	19th Century—Radial Type	35	9–20	<0.57
Paris—Boulevard Saint-Michel	19th Century—Radial Type	32	10–32	≤1.00
Paris—Avenue des Champs-Elysees	19th Century—Radial Type	70	10–45	<0.64
Orvieto—Corso Cavour	Medieval—Organic	5	1–4.5	<0.90
Havana—Paseo del Prado	19th Century—Grid	40	8–16	<0.40
London—Regent Street	19th Century—Grid	30	3–20	<0.67
Bruges—Steenstraat	Medieval—Organic	12	2.5–8	<0.67

Note: (a) The average distance between most buildings on the street interface is denoted as “$a_0$ ”. (b) The “Gap’s Width” represents the general and majority ones; therefore, large urban places that exist in a certain sense, such as squares and parks, are not used within the calculation. (c) Residential streets are marked with “★”.

and

Table 7. The amplitude of outstanding Euro-US streets.

Sort Order	Street Name	Formation Period of City Fabric	Amplitude (m)
			Lower Set/Higher Set
1	Orvieto—Corso Cavour	Medieval	↓1, ○/70 (65)
2	Rome—Via del Corso	Medieval	↓1, ○/80 (70)
3	Richmond—Monument Avenue	19~20th Century	↓1, ○/88 (50)
4	Aix-en-Provence—Cours Mirabeau	Medieval	↓1, ○/90 (50)
5	Barcelona—Ramblas	Medieval	↓1, ○/100 (65)
6	Paris—Boulevard Saint-Michel	19~20th Century	↓1, ○/107 (75)
7	Copenhagen—Strøget	Medieval	↓1, ○/112 (100)
8	London—Regent Street	19~20th Century	↓1, ○/120 (90)
9	Havana—Paseo del Prado	19~20th Century	↓1, ○/125 (85)
10	Barcelona—Paseo de Gracia	19~20th Century	↓1, ○/190 (140)
11	Paris—Avenue Montaigne	19~20th Century	↓1, ○/290 (255)
12	Paris—Avenue des Champs-Elysees	19~20th Century	↓1, ○/330 (260)
——	Rome—Via dei Giubbonari	Medieval	-
——	Bruges—Steenstraat	Medieval	-
——	Pittsburgh—Roslyn Place	19~20th Century	-

Note: (a) The data in “( )” represent the depth of a typical block scale. (b) Considering the habit of reading, the amplitude is calculated in units of “m”, and the amplitude data are multiplied by “10⁻³” to convert to “km”, and the range can be controlled within (0,1]. (c) In this study, the diagonal 45° corner of Barcelona—Paseo de Gracia is considered a small radius/build-to-line (↓1).

display the relevant data. Table 5 lists the frequency, VP-PA Synergy, and block scale. Intuitively, the frequency of residential streets is significantly higher, from 28 to 49 times/ks, than commercial–residential streets, from 5 to 28 times/ks, which is probably why the former is more “metrical”. Regarding the formation period, the medieval streets have a typical scale concentrated below 100 m, which is significantly lower than the modern streets concentrated below 180 m. Moreover, among the commercial–residential streets, the frequency of medieval streets is higher, from 10 to 28 times/ks, than that of modern planned streets, from 5 to 9 times/ks, indicating that with the space–time evolution, the block scale gradually increased and the frequency became lower, which verified the reliability of the research findings in Section 3.1.1. Meanwhile, both 100 m and 180 m are lower scales, which indicates that the “small block” property has never been broken. In addition, 13 of the 15 Euro-US streets had VP-PA Synergy no lower than 1.00, which suggests the interface breaks act as PAEs in most streets.

Table 6 lists the $\hspace{0.17em}{W}_{\mathrm{g}}$, $a_0$, and $W_{\mathrm{g}}/a_0$. In terms of street types, the interval of $a_0$ is similar in residential streets and commercial–residential streets. Still, the former has $W_{\mathrm{g}}/a_0$ below 0.70, which is lower than most of the latter, from 0.70 to 1.00, indicating that the spatial relation of residential streets is more compact. Regarding the period of formation, most medieval streets have $W_{\mathrm{g}}/a_0$ below 1.00. In contrast, most modern streets have $W_{\mathrm{g}}/a_0$ close to 1.00, indicating that with the space–time evolution, the spatial relations along the street became more discrete and gave a weaker sense of enclosure with the increasing block scale. Among the 15 Euro-US streets, all of them have $W_{\mathrm{g}}/a_0$ below 1.00, indicating that most of the streets are more compact.

The amplitude is summarized in Table 7, which displays all streets with the characteristics of ↓1 and ○. It shows that the higher set of amplitude is lower in all streets. In terms of the formation period, medieval streets have a higher set of amplitude from 70 to 112 m. In comparison, the higher set of amplitude of modern planned streets from 80 to 330 m, concentrated at 88 to 190 m, but remains at a low level, which indicates that the length of street segments is slowly increasing with the evolution of space–time. The “short street segment” property has never been broken. Sorting the higher set of amplitude from low to high, it can be found that the block scale is randomly sorted, indicating that the grade difference in Euro-US urban roads is not significant, thus revealing the law that the block scale is independent of the higher set of amplitude.

3.2.2. Outstanding Streets in China

Figure A4 displays the waveform classifications of the street interface rhythm in China. As shown in the figure, multiple gaps acting as “beats” are generally found in streets in China, where the interface rhythm is regularly integrated or separated, with a pattern similar to that of Euro-US streets. Regarding street types, the interface rhythm of the Chinese local plan pattern is more “metrical” with unapparent beats, while the concessionary streets have apparent beats. In terms of the different periods of formation of the Chinese local planning pattern, the interface rhythm of ancient and modern streets is quite similar. Comparing the Euro-US and Chinese waveform classifications, the former has apparent beats. At the same time, the latter is more “metrical” with unapparent beats, indicating that the homogeneity of the spatial distribution of the “virtual-real” elements of the street interface is the key aspect of the Western planning pattern but not of the local Chinese planning pattern.

Table 8. The frequency, VP-PA Synergy, and other data of outstanding streets in China.

Street Name	Formation Periods of City Fabric	Urban Block (m)		Original Data	Frequency (times/ks)	VP-PA Synergy
		Long Side of Block	Typical Scale
Beijing—Wangfujing Street ★	Yuan Dynasty	250–800	330 × 550	-	9|7	0.89|0.86
Shanghai—Nanjing Road	French Concession—O.R.C.	50–200	110 × 85	-	11|10	0.82|0.90
Tianjin—Heping Road	Japanese and French Concessions—O.R.C.	75–400	100 × 95	-	7|11	1.00|1.00
Tianjin—Binjiang Road	French Concession—O.R.C.	85–250	100 × 100	-	9|9	1.00|1.00
Wuhan—Hanjiang Road	British Concession–Qing Dynasty	100–150	100 × 115	-	9|6	0.89|1.00
Guangzhou—Beijing Road	Western Han Dynasty	105–230	115 × 220	-	14|6	0.71|1.00
Xiamen—Zhongshan Road	O.R.C.	70–220	100 × 55	-	8|9	1.00|1.00
Hangzhou—yan’an Road	O.R.C.	60–120	120 × 75	-	6|8	1.17|1.00
Suzhou—Guanqian Street ★	Qing Dynasty	355–400	355 × 735	8|7 (780 m)	12|10	0.83|0.80
Xi’an—East Street ★	Sui and Tang Dynasties	600–830	625 × 515	-	5|8	1.00|0.63
Changchun—Chongqing Road	O.R.C.	90–250	190 × 180	-	10|9	1.00|1.00
Changchun—Guilin Road	O.R.C.	65–160	160 × 70	-	13|10	0.77|1.00
Harbin—Central Street	Qing Dynasty	50–200	60 × 200	-	14|9	1.00|1.00

Note: If a street marked with “★” is divided into side streets, the long sides of the block are on Beijing—Wangfujing Street, Xi’an—East Street, and Suzhou—Guanqian Street, which are from 110 to 260 m, 150 to 245 m, and 60 to 170 m, respectively, with the typical scale mostly within 200 m. Other streets are delineated by urban branch roads, so side streets that further divide the block do not exist.

,

Table 9. The GWR and other data on outstanding streets in China.

Street Name	Formation Periods of City Fabric	${\mathit{a}}_0$ (m)	${\mathit{W}}_{\mathbf{g}}$ (m)	GWR
Beijing—Wangfujing Street ★	Yuan Dynasty	40	7–40	≤1.00
Shanghai—Nanjing Road	French Concession—O.R.C.	30	5–30	≤1.00
Tianjin—HepingRoad	Japanese and French Concessions—O.R.C.	22	10–20	<0.91
Tianjin—Binjiang Road	French Concession—O.R.C.	28	12–28	≤1.00
Wuhan—Hanjiang Road	British Concession—Qing Dynasty	25	5–30	<1.20
Guangzhou—Beijing Road	Western Han Dynasty	28	10–30	<1.07
Xiamen—Zhongshan Road	O.R.C.	25	8–25	≤1.00
Hangzhou—yan’an Road	O.R.C.	50	10–58	<1.16
Suzhou—Guanqian Street ★	Qing Dynasty	15	8–15	≤1.00
Xi’an—East Street ★	Sui and Tang Dynasties	60	5–60	≤1.00
Changchun—Chongqing Road	O.R.C.	20	8–20	≤1.00
Changchun—Guilin Road	O.R.C.	20	8–20	≤1.00
Harbin—Central Street	Qing Dynasty	20	20	≤1.00

Note: (a) We can take the average distance between most buildings on the street interface as “$a_0$ ”. (b) The “Gap’s Width” represents the general and majority ones; therefore, large urban places that exist in a certain sense, such as squares and parks, are not within the calculation. (c) Sites under construction are not included.

and

Table 10. The amplitude of outstanding streets in China.

Sort Order	Street Name	Formation Periods of City Fabric	Amplitude (m)
			Lower Set/Higher Set
1	Xiamen—Zhongshan Road	O.R.C.	↓1, ○/80 (55)
2	Changchun—Guilin Road	O.R.C.	↓1, ○/90 (70)
3	Shanghai—Nanjing Road	French Concession—O.R.C.	↓1, ○/115 (85)
4	Tianjin—HepingRoad	Japanese and French Concessions—O.R.C.	↓1, ○/117 (95)
5	Hangzhou—yan’an Road	O.R.C.	↓1, ↓0, ○/125 (75)
6	Tianjin—Binjiang Road	French Concession—O.R.C.	↓1, ○/128 (100)
7	Wuhan—Hanjiang Road	British Concession—Qing Dynasty	↓1, ↓0, ○/140 (115)
8	Suzhou—Guanqian Street	Qing Dynasty	↓1, ↓0, ○/185 (170)
9	Changchun—Chongqing Road	O.R.C.	↓1, ○/200 (180)
10	Beijing—Wangfujing Street	Yuan Dynasty	↑0, ↓1, ↓0, ○/235 (195)
11	Guangzhou—Beijing Road	Western Han Dynasty	↓1, ↓0, ○/248 (220)
12	Xi’an—East Street	Sui and Tang Dynasties	↑0, ↓1, ↓0, ○/290 (250)
13	Harbin—Central Street	Qing Dynasty	↓1, ○/390 (370)

Note: (a) The data in “( )” represent the depth of a typical block scale. (b) Considering the habit of reading, the amplitude is calculated in units of “m” and converted to the standard unit of “km” by multiplying by “10⁻³”, so the range can be controlled within (0,1].

display the relevant data. Table 8 lists the frequency, VP-PA Synergy, and block scale. In terms of street types, concession streets have a frequency from 6 to 11 times/ks, while the typical scale is from 85 to 115 m, which is significantly lower than the Chinese local planning pattern with 5 to 15 times/ks and 55 to 735 m, indicating that the frequency dispersion is lower in the Western planning pattern. Regarding the formation period of the Chinese local planning pattern, the typical block scale in the Republic of China era (hereinafter, the modern scale) concentrated below 190 m, which is much higher than the Yuan to Qing Dynasty (hereinafter, the ancient scale) with the typical block scale concentrated below 735 m. This indicates that with the space–time evolution, there is a large to small trend in the urban block, indicating that either a “large block” or “small block” can achieve outstanding streets. Taking the side streets as the condition for dividing the blocks, the majority of blocks are under 260 m on the long side, which means the side streets play an important role in dividing large blocks into smaller ones. A total of 10 of the 13 streets in China had VP-PA Synergy over 1.00 on at least one side, indicating that most street interface breaks act as PAE, which is similar to the situation in Euro-US.

Table 9 lists the $\hspace{0.17em}{W}_{\mathrm{g}}$, $a_0$, and $W_{\mathrm{g}}/a_0$ values. In terms of street types, the concessionary streets have $a_0$ from 22 to 30 m and $\hspace{0.17em}{W}_{\mathrm{g}}$ from 5 to 30 m, which have a smaller range than the Chinese local planning pattern of 15 to 60 m and 5 to 60 m, again revealing that the Western planning pattern has a more stable spatial scale. Regarding the formation period of the Chinese local planning pattern, the modern scale has $a_0$ from 20 to 50 m and $\hspace{0.17em}{W}_{\mathrm{g}}$ from 8 to 58 m, which includes a range contained in the ancient scales of 15 to 60 m and 5 to 60 m, suggesting that the ancient and modern street scales are intertwined. Among the 13 streets in China, only one has $W_{\mathrm{g}}/a_0$ below 1.00. Compared with Euro-US streets, the latter is dominated by $W_{\mathrm{g}}/a_0$ below 1.00, which is significantly lower than the former, with $W_{\mathrm{g}}/a_0$ equal to 1.00, indicating that the spatial relation along the Euro-US streets is more compact, with a stronger sense of enclosure under the condition that $a_0$ is equal.

The amplitude summarized in Table 10 shows that the lower set of amplitude has a mixed characteristic of ↑0, ↓1, ↓0, and ○, with the latter three dominating, indicating that the higher set of amplitude of all streets is low. In terms of street types, concession streets have a higher set of amplitude from 115 to 140 m. In comparison, the Chinese local planning pattern from 80 to 390 m, concentrated at 80 to 290 m, shows that “short street segments” are common characteristics. It is important to note that this also shows that the Western planning pattern has not led to differences in this problem. In terms of the formation period of the Chinese local planning pattern, ancient streets have a higher amplitude from 185 to 390 m. In comparison, the modern streets gradually decrease from 80 to 200 m, which indicates that with the space–time evolution, the quality of the “short street segment” gradually becomes significant. Sorting the higher set of amplitude from low to high, the block scale also exhibits a strict sorting feature from low to high, indicating that the gradation of Chinese urban roads is significant, thus presenting the law that the block scale depends on the higher set of amplitude, which is completely opposite to that of Euro-US urban roads.

4. Discussion

4.1. The Factors Influencing the Urban Street Interface Rhythm

The present study investigated a large sample of streets and the correlation between the street interface rhythm and urban form was revealed, while the potential influence of the intermediate variable of the PAE-n was added to the chain of direct causality between the block scale and street interface “Frequency”. Figure 8, Figure 9 and Figure 10 and Table 2, Table 3 and Table 4 show the correlation between frequency and the block scale, frequency and the PAE-n, as well as the PAE-n and the block scale. Regardless of whether data from individual cities were randomly selected from widely distributed large Chinese and Euro-US cities or even when overlaying the data from each big city, the association remains robust, which indicates that our theoretical derivation of causality is supported by the results. Next, the direction of the correlation was analyzed in depth. The underlying factors were attempted to be explaineeed through discussion, and whether the hypothesis is supported by the results remains to be tested.

In Figure 8 and Table 2, Barcelona (R = −0.959 **) exhibits a nearly 1:1 linear relation between the street interface “Frequency” and the block scale, which is related to its highly homogeneous city fabric. The large block area in Tianjin (R = −0.710 **) is composed of high-rise, multi-story, and large-volume low-rise buildings, while the small block area is mainly composed of small-volume low-rise buildings; the setback distance and building spacing between high-rise and multi-story buildings are generally greater than those between low-rise buildings. In addition, large-volume low-rise buildings occupy a larger area, resulting in most of Tianjin’s streets being non-build-to-line and fewer individual buildings along the street. This ultimately leads to a lower frequency. Except for Barcelona, others have |R|-values from 0.522 to 0.711, which is related to street interface breaks resulting from non-build-to-line, the gaps between buildings, pocket parks, side streets (non-urban roads), etc.

In Figure 9 and Table 3, Barcelona presents the highest correlation (R = 0.812 **) between the street interface “Frequency” and PAE-n, which is related to the fact that most of the street interface breaks act as a PAE, and all of these PAEs may be provided by urban roads or by a few side roads. Seattle presents the weakest correlation (R = 0.577 *), which is related to the fact that most street interface breaks do not act as PAEs, e.g., interface breaks resulting from non-build-to-line, gaps between buildings, pocket parks, etc.

In Figure 10 and Table 4, Kyoto presents the weakest correlation (R = −0.715 **), which means that the PAEs in Kyoto are not entirely dependent on urban roads. This is related to the fact that the block units are covered with side streets, especially in the large block area that still maintains a certain proportion of side streets. The |R|-values of the other cities from 0.804 to 0.920, which is strongly related to the dominance of urban roads on PAEs. The average value of the typical block scale in the seven Euro-US cities is below 200 m, which has the characteristics of a small block; Tianjin and Jinan have values of 360 m and 415 m in that order, characteristic of a large block, with both exceeding the great value of 300 m recommended by Yoshinobu Ashihara [36] as a pleasant and relaxing walking distance. Given the superposition in Figure 10, in the super-block scale from 600 to 800 m, PAE-n has a lower minimum base close to 2 times/ks. According to the indicators’ definition (see Section 2.2.2), most street segment lengths from 300 to 400 m, exceeding the suitable walking distance recommended by Ashihara. In combination, the small block with narrow road spacing supports PAE-n being dominated by urban roads. However, the large block with greater road spacing urgently needs to enhance PAE-n using side streets, i.e., non-urban roads, for the basic need of walkability to be guaranteed. However, the analysis showed that the large blocks are not being provided with sufficient rationing from PAE-n. China has experienced a transition from a “planned economy” to a “market economy”, and since then, the value of land parcels has skyrocketed. Land use is measured in terms of revenue as a primary factor, leading to the dual problem of insufficient initially planned branch roads and the evolution of original feeder roads into residential roads. Even more detrimental, the larger the block scale, the larger the enclosed residential area, accompanied by increased building spacing and public green space spacing, further exacerbating the decrease in PAE-n. In short, the above derivations reflect an unfavorable situation in which PAE is highly dependent on urban road rationing.

Combined with the attributes of the indicators (see Section 2.2), the results from Section 3.1 intuitively show that the smaller the block scale, the higher the PAE-n and frequency, which means the urban road traffic capacity becomes stronger and the walking accessibility could be better. However, it is prudent to be alert to the risk that the continuity of the street interface worsens, which challenges part of the hypotheses proposed in Section 2.4.1. Could a good urban road traffic capacity and walking accessibility be combined with good continuity? Is there some nested relation between visual perception and pedestrian access elements, which results in a street interface continuity that does not correspond exactly to frequency? Further analysis was required (addressed in Section 4.3).

4.2. “Beat” Regularly Integrates or Separates the Walkable Street Interface

A comparison of the “Rhythm and Beat” relation between urban form and the musical realm was provided by established studies: “Rhythm is the product of the grouping of elements to create, for example, emphasis, interval, accent and/or direction. Strict rhythms can be monotonous, and contrast and variety are essential in providing interest” [37]. Kevin Lynch also found that good urban form should exist based on a certain pattern: “Like any good framework, such a structure gives the individual a possibility of choice and a starting-point for the acquisition of further information. Here what would be imaged would be the developing pattern of elements, rather than the elements themselves—just as we remember melodies, not notes” [38]. Allan B. Jacobs states more directly that “beats” play a crucial role in creating outstanding streets: “There is another factor important to street definition: the spacing of buildings along a street. Buildings can be far enough apart so that, looking directly across a street or walking along one, it is normal to see beyond buildings to rear yards or to buildings on the next street. Again, the numbers and proportions are not clear and it is difficult to know for certain whether it is building spacing or one of the many other variables along a street—building height, setbacks, architectural quality, trees and shrubs and fences, for example—that are what define or fail to define a street. Visual complexity is what is required, but it must not be so complex as to become chaotic or disorienting” [2].

The fact that the “rhythm–beat” relation is deeply embedded in highly complex urban forms provides a qualitative conclusion for the aforementioned generalizations. Fortunately, it becomes a strong quantitative result in the present study: there are “beats” in walkable streets that regularly integrate or separate the street interface rhythm.

4.2.1. “Beat” Provides Pedestrian Access between Adjacent Blocks

Comparing waveform classifications (Figure A3 and Figure A4) with Google Earth DOMs (Figure A1 and Figure A2), all of the “beats” act as pedestrian accesses that can be found, which means every intersection between a “beat” and a main street acts as a PAE. Then, we can compare the “beats” of outstanding Euro-US and Chinese streets; the former is entirely comprises urban roads, while the latter comprises urban branch roads or some side streets. A significant phenomenon was revealed by this result: none of the “beats” are merely interface breaks in the physical dimension. Meanwhile, the “beat” divides or defines each block in a relatively homogeneous manner and links adjacent block units through pedestrian accesses.

4.2.2. “Beat” Plays a Synergistic Role of “VP-PA” Spatial Elements

Outstanding Euro-US streets have VP-PA Synergy above 1.00, associated with multi-directional road intersections. Overall, outstanding Euro-US and Chinese streets are dominated by VP-PA Synergy equal to 1.00, which is related to most street interface breaks acting as PAEs. As a result, “beat” is the only part of the interface break for streets with VP-PA Synergy equal to 1.00, making it an attribute of pedestrian access. Thus, “beat” plays a synergistic role in the spatial elements of visual perception and pedestrian access, which can be inferred.

4.3. “Small Block and Dense Grid” Becomes a Key Factor for Improving Walkability

4.3.1. “Small Block and Dense Grid” Is the Necessary Condition

Comparing the waveform classifications related to Beijing—Wangfujing Street; Suzhou—Guanqian Street; and Xi’an—East Street shown in Figure A4 and Table 9, side streets with “beat” properties acting as urban branch roads can be found, allowing streets in large blocks to have good walkability, where the continuity and convenience of pedestrian access to adjacent blocks are ensured.

As shown, changing a block from large to small is not the only way to improve walkability. However, the relation between “Man” and “Car” is one of the urgent urban problems to be reconciled. “Man–Car Coexistence” is the ultimate ideal of urban design. Both adopting small blocks initially in the planning process or applying “beats” to increase road density in the existing state of a large block could work well. Considering that the former has the advantage of minimum impedance, the spatial structure of a “Small Block and Dense Grid” is a necessary condition that can be considered for improving walkability. Accordingly, applying “beats” to increase road density will help solve the key problem of how to more reasonably encrypt and organize a slow traffic grid to improve walkability without increasing the density of urban roads.

4.3.2. A Small Block Is Conducive to Improving the Continuity of Street Interface

Good continuity is the default characteristic of outstanding streets. Verifying why the outstanding streets with the general law of “The smaller the Block Scale, the higher the PAE-n and Frequency” have good continuity is a retention question in the last paragraph of Section 4.1. This refers to the definition of VP-PA Synergy (see Section 2.3) using 162 samples introduced in Section 2.1 as examples to analyze their synergy. Figure 11 illustrates that the contribution of PAEs to frequency decreases as the block scale increases, indicating that the large block is more susceptible to the urban problem of redundant space along the street.

In summary, the smaller the block scale, the lower the frequency resulting from redundant spaces along the street. This may be why small blocks have a higher frequency of street interface than large blocks, while small blocks have better continuity than large blocks. So far, the retention question in the last paragraph of Section 4.1 has been explained and illustrated that reducing the amount of redundant space along the street that exists in the large blocks can effectively reduce the risk of the continuity becoming worse; a small block is conducive to improve the continuity of street interface as well. It is well-validated that good urban road traffic capacity and walking accessibility can be combined with good continuity.

4.4. Necessary Conditions for Designing a Walkable Street

4.4.1. “Beat” Reaching 5 times/ks Is a Necessary Condition for Improving Walkability

In the waveform classifications (Figure A3 and Figure A4), “beats” refer to regularly distributed breaks of street interface encapsulated by frequency, so beats are special cases of frequency.

Table 11. Statistics of the interface rhythm “beat” of outstanding Euro-US streets.

Sort Order	Street Name	Formation Periods of City Fabric	Beat (times/ks)
1	Orvieto—Corso Cavour	Medieval	15–16
2	Rome—Via del Corso	Medieval	15
3	London—Regent Street	19~20th Century	12
4	Copenhagen—Strøget	Medieval	10
5	Aix-en-Provence—Cours Mirabeau	Medieval	9–12
6	Barcelona—Ramblas	Medieval	7–9
7	Paris—Boulevard Saint-Michel	19~20th Century	≈9
8	Havana—Paseo del Prado	19~20th Century	8
9	Barcelona—Paseo de Gracia	19~20th Century	7
10	Paris—Avenue des Champs-Elysees	19~20th Century	6–7
11	Richmond—Monument Avenue	19~20th Century	6
12	Paris—Avenue Montaigne	19~20th Century	≈6
——	Rome—Via dei Giubbonari	Medieval	-
——	Bruges—Steenstraat	Medieval	-
——	Pittsburgh—Roslyn Place	19~20th Century	-

illustrates the summary results of counting the “beats” of outstanding Euro-US streets (Figure A3). In this table, medieval streets have a “beat” from 7 to 16 times/ks, while modern planned streets have a “beat” of 6 to 12 times/ks. Regarding waveform classifications, the interface rhythm of medieval streets is significantly “rapid”, while that of modern planned streets is “slow”, which could be related to the fact that the former has more “beats”. In the Middle Ages, there was no long-distance transportation such as cars; instead, there were only short-distance accesses on foot and in horse-drawn carriages. Thus, more “beats” were needed to shorten the access distances. Therefore, in contemporary times, modern planned streets are more representative, with “beats” concentrated at 6 to 12 times/ks of outstanding Euro-US streets.

In order to compare the above aspects, the “beats” of the outstanding streets in China were counted (Figure A4), and

Table 12. Statistics of interface rhythm “beat” of outstanding streets in China.

Sort Order	Street Name	Formation Periods of City Fabric	Beat (times/ks)
1	Changchun—Guilin Road	O.R.C.	≈10
2	Shanghai—Nanjing Road	French Concession—O.R.C.	9–10
3	Harbin—Central Street	Qing Dynasty	9–13
4	Tianjin—Binjiang Road	French Concession—O.R.C.	9
5	Suzhou—Guanqian Street	Qing Dynasty	≈9
6	Changchun—Chongqing Road	O.R.C.	8–10
7	Tianjin—HepingRoad	Japanese and French Concessions—O.R.C.	7–10
8	Xiamen—Zhongshan Road	O.R.C.	7–9
9	Hangzhou—yan’an Road	O.R.C.	≈7
10	Guangzhou—Beijing Road	Western Han Dynasty	6–9
11	Beijing—Wangfujing Street	Yuan Dynasty	6–8
12	Wuhan—Hanjiang Road	British Concession—Qing Dynasty	6–8
13	Xi’an—East Street	Sui and Tang Dynasties	5

illustrates the summary results. The streets formed in the modern scale have “beats” ranging from 7 to 10 times/ks, which included the 5 to 13 times/ks of the streets formed in the ancient scale, which shows that the ancient and modern scales are intertwined. China has experienced rapid urbanization, and urban streets have been widely influenced by modern planning pattern, resulting in the beats in different periods being intertwined. Overall, the overlaying data are more representative of the contemporary scale, showing beats concentrated at 5 to 13 times/ks in outstanding streets in China. By overlaying the beats of Euro-US and Chinese streets, “beats” of 5 to 13 times/ks in outstanding streets can be found.

The block scale can be characterized by the spacing of “beats”. These “beats” have a distribution characteristic of 5 times/ks, which means that approximately six blocks per kilometer are integrated or divided, with a block scale of about 200 m or a spacing of 200 m for side streets with the attribute of an urban branch road. Correspondingly, 13 beats correspond to 14 blocks, and the width is approximately 80 m. Considering possible changes in plot scales, ensuring a bottom line without an upper limit can be considered a scientific approach. Therefore, the “beat” reaching 5 times/ks is a necessary condition for improving walkability. As shown in Table 2 and Table 4, the $b_{\mathrm{s}}$ of Tianjin and Jinan is about 360 m and 415 m, respectively, which is relatively large. This could be one of the reasons why it is difficult to design walkable streets in new urban areas in China.

4.4.2. W_g/a₀ < 1.00 Is the Icing on the Cake for Improving Walkability

Comparing Table 6 and Table 9, outstanding Euro-US and Chinese streets generally have the $W_{\mathrm{g}}/a_0$ does not exceed 1.00. Among them, China has $W_{\mathrm{g}}/a_0$ equal to 1.00, with a moderate sense of enclosure, while the Euro-US value is well below 1.00, with a stronger sense of enclosure. This is related to the non-significant road grade of the former. It is worth mentioning that the intensive use of urban land can benefit extensively from a compact street space, so the spatial relation along the street interface where $W_{\mathrm{g}}/a_0$ is below 1.00 is the icing on the cake for improving walkability.

4.4.3. Low “Amplitude” and Good Visual Accessibility Are General Characteristics

The results in Section 3.2 show that the lower set of the amplitude of walkable streets is “low”, and the higher set is “low” as well. Therefore, the amplitude of walkable streets is generally low. Comparing the waveform classifications (Figure A1 and Figure A2) with Google Earth DOMs, the amplitude of “beats” is related to block depth, and the meaning of this is consistent with the higher set of amplitude.

Figure 12 and Figure 13 illustrate the summary of waveform classifications. According to Figure 12 and Table 7, the coverage of outstanding Euro-US streets is concentrated below 190 m, while China is concentrated below 290 m, as illustrated in Figure 13 and Table 10. By overlaying data from Euro-US and Chinese streets, the concentration of walkable streets is below 290 m. According to the definition of amplitude mentioned in Section 2.2, the distance between road nodes and the main streets is negatively correlated with the physiological perception of accessibility, which essentially reflects visual accessibility; thus, uniform and good visual accessibility is generally found in walkable streets.

Furthermore, according to Table 5 and Table 8, some of these outstanding streets were formed thousands of years ago, while some are only a hundred years old. It is worth noting that the regularity of the interface rhythm of walkable streets is formed by the convergence of these street characteristics. Overall, some good measures that can facilitate the integration of “ancient–modern” urban walking space patterns naturally emerged from the results.

4.5. Limitations and Prospects

Several limitations exist in this study regarding the construction of the quantitative indicator system and the systematic conceptual framework. First, all effects of urban form on the street interface rhythm cannot be revealed completely and with no omission, on the condition that only the frequency and amplitude indicators were examined in this study. According to the street interface rhythm research performed by Chenxue Sun [21], there are four characteristics of street interface rhythm, namely, the street interface break times, street interface spatial extension degree, street interface spatial tiling relation, and street interface spatial distribution relation. The established indicators, frequency and amplitude, were introduced in this study (see Section 2.2) and describe the most important characteristics of the street interface rhythm of the first two of the abovementioned characteristics, respectively. However, the latter two can be effectively perceived and described independently by pedestrians [22]. Thus, it is meaningful to study the relation of influence between the street interface spatial tiling relation, street interface spatial distribution relation, and urban form. Subsequently, the quantitative indicator system of the study on the effect of urban form on the street interface rhythm can be supplemented as needed.

Second, generally, a systematic conceptual framework including hypotheses is quite prevalent in studying basic subjects. The above scientific research path was adopted in this study. At the same time, a Pearson correlation analysis was used to explore the correlation between the street interface rhythm and urban form, which reflects the fact that the irrelevant influencing factors are excluded to a large extent, and the underlying core laws are easily revealed. However, the city is a complex mega-system, introducing the default property that nonlinearity is almost inevitable in the influence relation between the street interface rhythm and urban form. Although the Pearson correlation analysis has the obvious advantage of quickly predicting correlations, the results are limited to linearity. For example, the results from Seattle and the superposition in Figure 10 clearly exhibit nonlinearity, a phenomenon that could not be revealed through the Pearson correlation analysis within the conceptual framework of this paper. Moreover, the waveform classification has the advantage of providing a convenient graphical reference for urban designers, which is also based on some ideal conditions, including the simplification of main road bends, side street diagonal intersections, and intersection diagonal angles. Thus, the accuracy should be improved, as reflected in the above analysis. Subsequently, the quantitative indicator system of the street interface rhythm will be supplemented, and the conceptual framework will be optimized. The nonlinear and complex relation between the urban form and street interface rhythm will be further explored as well.

5. Conclusions

This study is the first exploratory analysis of the effect of urban form on the street interface rhythm. The correlation between the street interface rhythm and urban form was empirically explored through a Pearson correlation analysis with multisource data, which were based on 162 samples from nine Euro-US and Chinese cities. At the same time, the influencing factors and processes were discussed in depth and explained quantitatively. The results indicate that the street interface “Frequency” has a moderate negative correlation with the block scale and a moderate positive correlation with the PAE-n. Furthermore, the PAE-n has a strong negative correlation with the block scale.

The regularity of the interface rhythm of walkable streets was empirically revealed through waveform classification, which was conducted using data from the 28 outstanding streets selected from large cities worldwide. The following conclusions can be drawn: (1) Multiple gaps on the street interface act as the “beat”, which regularly integrate or separate the street interface rhythm and provide pedestrian access between adjacent blocks. (2) The frequency and amplitude of the “beat” significantly affect street walkability; the amplitude of the “beat” is concentrated below 290 m, which is generally low and uniform and has good visual accessibility in all directions. (3) A “Small Block and Dense Grid” is a key factor for improving walkability; a small block is conducive to improving the continuity of the street interface. (4) A “Beat” reaching 5 times/ks is a necessary condition for designing a walkable street, while $W_{\mathrm{g}}/a_0$ < 1.00 is the icing on the cake.

This study supplements current basic knowledge of the street interface rhythm in research on walking space in urban form. At the same time, theoretical guidance and parametric evidence are provided to improve walkability and promote the continuation of the traditional context. Using a systematic conceptual framework including hypotheses and based on multisource data, the scientific and generalization ability of the algorithm regarding the urban street interface is significantly improved. The “macro—micro” dual-scale method combined with Pearson correlation and waveform classification was conducted in this study for the first time, which has a great ability in explaining the complex spatial relation of the urban street interface at both the macro and micro scales. This constitutes an effective way for city planners and policymakers to plan walkable streets. The results can be widely used in the following aspects: (1) activating redundant spaces and promoting land diversity in modern urban patterns; (2) allowing “protection and utilization” to promote the integration of the “ancient–modern” urban walking spatial patterns while replacing the previous approach with “protection”; and (3) building regional characteristic commercial streets with good interface rhythm is proposed to attract more pedestrians to stay in old urban areas and their surroundings. At the same time, the traditional context will be continued by practicing urban vitality as expected.