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Pitch

Pitch is a versatile English term with multiple distinct meanings across scientific, technical, and everyday contexts. The term derives from Old English "pic" for a resinous substance (from Latin "pix"), while senses involving throwing or fixing come from the Old English verb "piccean" meaning to thrust or prick (related to "pick").^[1] In its original sense, pitch refers to a black or dark, viscous, tenacious substance obtained as a residue from the distillation of organic materials such as coal tar, wood tar, or petroleum, historically used for waterproofing, caulking ships, and paving.^[1] This material, also known as bitumen or asphalt in certain forms, has been employed since ancient times for construction and preservation, as seen in biblical references to coating vessels like Noah's Ark.^[2] In acoustics and music, pitch denotes the perceptual property of a sound that allows it to be ordered on a frequency-related scale from low to high, primarily determined by the fundamental frequency of the sound wave in hertz (Hz). For instance, higher pitches correspond to faster vibrations, and the international standard for concert pitch sets the note A above middle C at 440 Hz (A440), facilitating tuning across instruments like pianos and orchestras. Historical variations in pitch standards existed due to regional differences in instrument design and performance practices, with earlier levels often lower than modern ones. In sports, particularly baseball, a pitch is the act of throwing the ball from the pitcher to the batter at home plate, typically from 60 feet, 6 inches away, with the goal of inducing a swing, strike, or out.^[3] Pitches vary in type, including fastballs (reaching over 100 mph), breaking balls like curveballs that alter trajectory mid-flight, and off-speed pitches such as changeups to deceive hitters.^[4] This delivery initiates each at-bat and is governed by rules defining legal motions to prevent balks or illegal pitches.^[5] In other sports, "pitch" can also refer to the playing field, particularly in soccer (football). A sales pitch, or simply pitch in business contexts, is a concise, persuasive oral presentation or script designed to convince a potential customer to purchase a product or service by highlighting its benefits and addressing needs. Effective pitches often last one to two minutes, employ storytelling or problem-solving frameworks, and adapt to the audience, such as in elevator pitches for quick networking encounters.^[6] In architecture and engineering, roof pitch measures the steepness or incline of a roof's slope, expressed as a ratio of vertical rise to horizontal run (e.g., 6/12 means 6 inches rise per 12 inches run), influencing water drainage, structural integrity, and aesthetic style.^[7] Common pitches range from low-slope (2/12 to 4/12) for flat-like roofs to steep (9/12 or more) for gabled or mansard designs in rainy or snowy climates, where steeper angles prevent accumulation.^[7] This metric, also called slope, guides material selection and building codes.^[7] In broader engineering contexts, pitch can denote angular or rotational inclination, such as the tilt of an aircraft's nose.

Acoustics and Music

Acoustic Pitch

Acoustic pitch is the perceptual correlate of the periodicity in a sound waveform, primarily determined by its fundamental frequency, which allows humans to distinguish sounds as higher or lower in tone.^[8] In psychoacoustics, pitch is defined as the subjective attribute of auditory sensation that can be ordered on a scale extending from high to low, closely tied to the repetition rate of the sound wave.^[9] This perception arises because the auditory system extracts the dominant periodic component from the acoustic signal, enabling differentiation even in everyday sounds like speech or music.^[8] The human ear achieves pitch perception through the cochlea's basilar membrane, a flexible structure that vibrates in response to sound waves transmitted via the ossicles from the eardrum.^[10] According to the place theory, different frequencies stimulate specific regions along the membrane due to its gradient in stiffness and width: high frequencies cause maximal displacement near the base (oval window), while low frequencies peak toward the apex (helicotrema).^[11] Hair cells atop the membrane transduce these vibrations into neural signals, with auditory nerve fibers tuned to characteristic frequencies that encode pitch locationally.^[12] This frequency-to-place mapping, empirically demonstrated by Georg von Békésy through observations of traveling waves, underpins the physiological basis of pitch sensation.^[12] Early investigations into pitch sensation were pioneered by Hermann von Helmholtz in the 19th century, who conducted experiments using tuning forks and resonators to isolate tonal components and demonstrate how the inner ear analyzes complex sounds into their harmonic constituents.^[13] In his seminal 1863 work, On the Sensations of Tone as a Physiological Basis for the Theory of Music, Helmholtz proposed that pitch results from the selective resonance of basilar membrane fibers to specific frequencies, laying the groundwork for modern psychoacoustics.^[13] His resonator analogy, where glass spheres tuned to particular tones mimic hair cell selectivity, highlighted the ear's role in decomposing sounds, influencing subsequent theories of auditory processing.^[14] Psychoacoustically, pitch perception in complex tones involves the integration of harmonics—integer multiples of the fundamental frequency (f₀)—which reinforce the perceived pitch even if f₀ is absent, a phenomenon known as the missing fundamental.^[15] Low-order (resolved) harmonics provide spectral cues via place coding on the basilar membrane, while higher-order (unresolved) harmonics contribute through temporal cues from phase-locked neural firing to the waveform's periodicity.^[15] However, this can lead to pitch ambiguity, where multiple f₀ values might fit the harmonic series, particularly in stimuli with sparse or high-order harmonics, requiring higher auditory centers to resolve the dominant periodicity.^[15] Such ambiguities are more pronounced in unresolved complexes, where temporal envelope cues dominate but are less precise than spectral resolution for low pitches.^[15] Physically, the fundamental frequency f of a sound wave relates to the speed of sound v and wavelength \lambda by the equation

f = \frac{v}{\lambda},

expressed in hertz (Hz).^[16] This arises from the basic definition of wave propagation: the speed v is the distance traveled per unit time, equivalent to one wavelength \lambda per cycle, and with frequency f as cycles per second, v = f \lambda follows directly, allowing rearrangement to solve for f.^[16] For sound in air at standard conditions, v \approx 343 m/s, so a 1-meter wavelength yields f \approx 343 Hz, illustrating how acoustic properties determine perceptual pitch.^[16] Examples highlight pitch's perceptual nuances: a pure tone, such as a 440 Hz sine wave, evokes a precise, unambiguous pitch corresponding directly to its single frequency component, stimulating a focused region on the basilar membrane.^[17] In contrast, noisy sounds like white noise, lacking periodic structure, produce no discernible pitch due to their broadband, aperiodic spectrum that diffusely excites the membrane without a dominant periodicity.^[17] Complex tones, such as those from a violin, combine a fundamental with harmonics to yield a unified pitch via harmonic templating, even under partial masking by noise, demonstrating the robustness of harmonic-based perception.^[17]

Musical Pitch

In music, pitch refers to the perceived highness or lowness of a sound, determined by its fundamental frequency, and is central to melody, harmony, and tonal organization. Musical notation systems represent pitch through symbols that allow performers to reproduce specific frequencies accurately. The Western staff notation, developed in the 11th century by Guido d'Arezzo, uses a five-line stave with clefs to indicate pitch height, where notes are placed on or between lines to denote specific pitches within an octave. ^[18] Accompanying this is the solfège system, also pioneered by Guido, which assigns syllables (do, re, mi, fa, sol, la, ti) to scale degrees for sight-singing and ear training, facilitating relative pitch recognition. ^[19] Octave equivalence is a foundational concept in these systems, treating pitches that differ by an exact octave (a frequency ratio of 2:1) as perceptually and notationally equivalent, such as middle C (C4) and the C above it (C5), allowing music to be transposed across registers without altering its intervallic structure. ^[20] Standard pitch frequencies provide a reference for tuning instruments and ensembles. The international standard designates A4 (the A above middle C) at 440 Hz, recommended by an international conference in London in 1939 to accommodate broadcasting needs and varying national standards, and formally adopted by the International Organization for Standardization (ISO) as ISO 16 in 1955. ^[21] ^[22] This standardization ensures consistency across orchestras, recordings, and instruments, though some ensembles use alternatives like A4=432 Hz for historical or aesthetic reasons. Pitch perception varies between absolute pitch (also called perfect pitch), the rare ability to identify or produce a specific pitch without a reference tone, and relative pitch, which involves recognizing intervals between notes. Absolute pitch occurs in approximately 1 in 10,000 individuals, with higher prevalence (up to 11% in some studies of trained musicians) linked to early musical exposure and genetics, though it is not essential for musical proficiency. ^[23] ^[24] Relative pitch, more common and trainable through ear-training exercises like solfège, enables musicians to discern melodic and harmonic relationships, such as identifying a major third above a tonic. ^[24] Mathematical intervals define the relationships between pitches, with tuning systems balancing harmonic purity and practicality. Just intonation uses simple integer frequency ratios for consonant intervals, such as 3:2 for a perfect fifth or 5:4 for a major third, derived from the harmonic series to produce "pure" sounds in specific keys. ^[25] In contrast, equal temperament divides the octave into 12 equal semitones, each with a frequency ratio of $2^{1/12} \approx 1.05946, allowing modulation across all keys without retuning but introducing slight dissonance in some intervals compared to just intonation. ^[26] This system, widely adopted since the 18th century, approximates just intervals closely enough for most musical contexts. Historical tunings reflect evolving musical practices and acoustics. Pythagorean tuning, attributed to the Greek philosopher Pythagoras in the 6th century BCE, constructs scales from successive perfect fifths (3:2 ratio), emphasizing mathematical harmony but leading to dissonant thirds due to accumulated "comma" discrepancies. ^[27] In the Baroque era (roughly 1600–1750), pitch standards varied regionally, often lower than modern norms to suit vocal ranges and instrument construction; a common performance reference today is A4=415 Hz, based on surviving organ pipes and treatises, though actual pitches ranged from about 390 Hz to 466 Hz. ^[28] ^[29]

Engineering and Measurement

Linear and Mechanical Pitch

In mechanical engineering, linear pitch denotes the uniform distance between repeating features in components designed for motion or fastening, such as the spacing of threads on a screw, teeth on a gear, or links in a drive system. This measurement ensures compatibility, strength, and precise operation in assemblies. For screw threads, pitch specifically refers to the axial distance, measured parallel to the screw axis, between corresponding points on adjacent threads; in single-start screws, this equals the lead, or the axial advance per full revolution.^[30] Pitch plays a critical role in applications like bolted joints, where standardized thread pitches facilitate interchangeability and load distribution. The ISO metric screw thread standard (ISO 261), for instance, defines preferred diameter-pitch combinations, such as M6x1.0, indicating a 6 mm nominal diameter with a 1 mm coarse pitch for general-purpose fastening in machinery and structures.^[31] In power transmission, timing belts employ pitch as the center-to-center distance between adjacent teeth, typically in metric sizes like 5 mm (T5 series), enabling synchronous drive without slippage in automotive and industrial equipment.^[32] Similarly, roller chain drives define pitch as the distance between the centers of adjacent roller pins, such as 12.7 mm (1/2 inch) in standard ANSI chains, which determines sprocket compatibility and load capacity in conveyor and machinery systems.^[33] Calculations for pitch vary by component but emphasize geometric consistency. For screws, the pitch represents the lead per thread in single-start designs, directly specifying the axial progression; multi-start screws multiply this by the number of starts to yield the total lead. In gears, the circular pitch p is derived from the pitch circle circumference divided by the number of teeth, given by p = \frac{\pi d}{z}, where d is the pitch diameter and z is the number of teeth; equivalently, p = \pi m, with m as the module (m = \frac{d}{z}). These relations ensure meshing accuracy in gear trains.^[34]^[35] The concept of standardized pitch originated with the Whitworth thread system, developed by British engineer Joseph Whitworth in 1841 as the first national screw thread standard in Britain, featuring a 55° thread angle and varying pitches to unify manufacturing amid the Industrial Revolution. This laid the groundwork for modern systems like ISO metric and Unified threads. Pitch units are typically millimeters in metric systems or inches in imperial ones, with coarse pitches (e.g., 1.0 mm for M6 bolts) favoring higher shear strength and faster assembly in high-load applications, while fine pitches (e.g., 0.75 mm for M6) enhance precision, vibration resistance, and tensile strength in adjustable or delicate mechanisms.^[36]^[37]^[31]

Angular and Rotational Pitch

In rotational dynamics and engineering, pitch refers to the angular rotation of an object about its lateral or transverse axis, which runs horizontally from side to side through the center of mass. This motion tilts the object's longitudinal axis up or down, such as the nose-up or nose-down orientation of an aircraft.^[38] In aviation, pitch is one of the three primary rotational degrees of freedom, alongside roll and yaw, enabling control over climb, descent, and angle of attack.^[39] Pitch control is critical in various applications, particularly in transportation and dynamics. In aircraft, elevators—hinged surfaces at the rear of the horizontal stabilizer—are deflected to generate aerodynamic moments that adjust the pitch attitude, allowing pilots to maintain stable flight or respond to disturbances.^[40] For ships navigating waves, pitch manifests as the fore-and-aft rocking motion where the bow rises and falls relative to the stern, influenced by wave encounter frequency and vessel hull form; positive pitch occurs when the bow elevates above the equilibrium level.^[41] In automotive engineering, vehicle suspension systems manage pitch during acceleration or braking, where the front dips and rear rises (or vice versa), affecting ride comfort and handling; semi-active dampers can mitigate excessive pitch to preserve stability.^[42] Pitch is measured as the angle θ, typically in degrees, representing the deviation of the object's longitudinal axis from the horizontal plane in the pitch plane. This angle directly influences aerodynamic or hydrodynamic stability; for instance, in aircraft, longitudinal static stability is quantified by the static margin, defined as the dimensionless distance between the center of gravity (CG) and the neutral point (NP), normalized by the mean aerodynamic chord \bar{c}:

h_n - h = \frac{x_{NP} - x_{CG}}{\bar{c}}

where h_n and h are the fractional distances of the NP and CG from a reference point, respectively. A positive static margin (typically 5-15% for conventional aircraft) ensures restoring moments oppose pitch disturbances, enhancing inherent stability without control inputs.^[43]^[44] Historically, the Wright brothers pioneered effective pitch control in their 1903 Flyer, the first successful powered airplane, by incorporating a movable biplane elevator forward of the wings to directly vary the angle of attack and provide nose-up or nose-down authority during flight. This innovation, tested extensively in gliders from 1900-1902, addressed stability challenges in early aeronautics and enabled controlled sustained flight on December 17, 1903.^[45] In flight dynamics, pitch is analyzed through angular rates and orientations using Euler angles, which describe the vehicle's attitude in three dimensions. The pitch angle θ is the second Euler angle, representing rotation about the lateral axis from the horizontal. The corresponding pitch rate q, measured in radians per second (rad/s), is the body-axis angular velocity about this transverse axis, contributing to the rotational kinematics alongside roll rate p and yaw rate r. The time derivative of θ incorporates q via the relation:

\dot{\theta} = q \cos \phi - r \sin \phi

where ϕ is the roll angle; this equation forms part of the standard 6-degree-of-freedom equations of motion for simulating aircraft behavior.^[46] These parameters are essential for modeling pitch response in stability analyses and autopilot design.^[47]

Pitch in Electromagnetism

In electromagnetism, pitch refers to the axial distance between consecutive turns of wire in a helical coil, such as in solenoids or antennas, which influences the magnetic field distribution and overall device performance.^[48] This parameter, often denoted as p, determines the coil's effective length and turn density, distinguishing it from purely mechanical interpretations by its role in generating and shaping electromagnetic fields.^[49] In inductor design, pitch critically affects the self-inductance of a solenoid, where the inductance L for a long solenoid approximates L \approx \mu_0 \frac{N^2 A}{l}, with \mu_0 as the permeability of free space, N the number of turns, A the cross-sectional area, and l the coil length.^[50] Since l \approx N p for uniform winding, a smaller pitch increases turn density, shortening l relative to N and thereby enhancing L, which is essential for applications requiring strong magnetic fields, such as transformers or electromagnetic actuators.^[49] Variations in pitch introduce corrections to this formula, potentially altering L by several parts per 100,000, as derived from elliptic integral analyses of winding deformations.^[49] For antennas, pitch defines the geometry of helical structures, where the pitch angle \alpha is given by \alpha = \arctan\left( \frac{p}{\pi d} \right), with d as the coil diameter.^[51] This angle, typically 12° to 14° for optimal axial-mode operation, shapes the radiation pattern by controlling the phase progression of currents along the helix, enabling circular polarization and directive beams for frequencies from VHF to microwave bands.^[52] In helical antennas, adjusting pitch modulates the axial length per turn, impacting gain and bandwidth; for instance, values around 13° maximize forward radiation along the helix axis while suppressing back lobes.^[53] Pitch variations, such as close-wound (minimal p, nearly touching turns) versus spaced or sparse-wound (larger p), tailor electromagnetic coils to specific frequency regimes. Close-wound configurations maximize inductance and are suited for low-frequency uses like power electronics, where high magnetic flux density is prioritized over inter-turn capacitance.^[54] In contrast, spaced windings reduce parasitic capacitance and self-resonance effects, making them ideal for high-frequency applications, such as RF inductors or normal-mode helical antennas operating below 500 MHz, where excessive proximity would degrade efficiency.^[54] These designs, often analyzed via distributed parameter models, ensure minimal losses in sparse configurations at elevated frequencies.^[54]

Business and Sales

Sales Pitch

A sales pitch is a concise oral or written presentation designed to persuade potential buyers to purchase a product or service by highlighting its benefits rather than merely listing features.^[55] This approach focuses on how the offering solves customer problems or improves their situation, making the value proposition clear and compelling.^[56] The origins of the sales pitch trace back to 19th-century American sales techniques, particularly in traveling medicine shows where performers used entertaining lectures to promote patent medicines as cure-alls.^[57] These shows, popular in rural areas from the late 1800s onward, combined music, comedy, and dramatic testimonials to draw crowds before the "doctor" delivered a persuasive talk emphasizing miraculous benefits.^[58] Effective sales pitches often follow the AIDA model, a framework outlining four stages: Attention, where the pitch grabs the audience's focus with a hook like a surprising fact; Interest, building curiosity through relevant details; Desire, evoking emotional want by connecting benefits to needs; and Action, prompting an immediate next step such as a purchase or call.^[59] Developed in the early 20th century but rooted in earlier advertising principles, this structure guides salespeople in creating logical, persuasive flows.^[60] Key techniques in sales pitches include storytelling to make messages relatable, handling objections by addressing concerns empathetically, and closing with a direct call to action. For instance, in door-to-door sales, a representative might start with a story about a neighbor's success using the product to build rapport, then counter price objections by reframing value over cost, and close by asking, "Shall we get this set up for you today?"^[61]^[62]^[63] In modern contexts, sales pitches have adapted to digital formats like email and video, allowing broader reach and personalization. Videos embedded in emails, for example, can increase reply rates by 26% compared to text-only messages. Successful digital pitches are typically under two minutes long, with 30-60 seconds often cited as optimal for maintaining engagement and driving conversions.^[64]^[65] These formats extend to more specialized applications, such as startup funding presentations.^[66]

Investment and Startup Pitch

In the context of entrepreneurship and venture capital, an investment or startup pitch is a concise presentation designed to persuade investors of a business's potential viability and secure funding. It typically outlines the core problem the startup addresses, the proposed solution, market opportunities, and financial projections, often delivered through a pitch deck comprising 10-20 slides to maintain brevity and focus. This format emerged prominently in Silicon Valley following the venture capital boom of the 1970s, when firms like Kleiner Perkins began formalizing processes to evaluate high-risk, high-reward tech ventures, marking the shift from informal networking to structured pitches. Key elements of an effective startup pitch include demonstrating problem-solution fit, where the presenter clearly articulates a significant market pain point and how the product or service uniquely resolves it. Investors also prioritize evidence of market size, often framed using Total Addressable Market (TAM), Serviceable Addressable Market (SAM), and Serviceable Obtainable Market (SOM) to quantify growth potential—for instance, a TAM exceeding $1 billion signals scalability. Traction metrics, such as user growth rates or revenue milestones, provide proof of concept, while the "ask" specifies the funding amount sought and its intended use, like product development or market expansion. These components are emphasized in guidelines from accelerators like Y Combinator, which advise founders to prioritize data over hype. Common formats for startup pitches vary by context and time constraints. The elevator pitch, lasting 30-60 seconds, is a verbal summary delivered in informal settings to spark interest and secure follow-up meetings, focusing on the hook, value proposition, and traction. In contrast, demo day pitches, popularized by Y Combinator since its inaugural event in 2005, are 10-minute presentations followed by Q&A, showcased to multiple investors during accelerator programs to compete for seed funding. These structured events have become a staple in the startup ecosystem, with thousands of companies pitching annually across global programs. Success in investment pitches hinges on several factors, including strong traction over mere ideas, as investors favor evidence of product-market fit. Data from the 2010s indicates venture capital acceptance rates for pitches hovered around 1%, underscoring the competitive nature where only startups with compelling narratives and metrics advance to term sheets. Best practices, drawn from analyses of funded companies, stress clarity, storytelling, and rehearsal to address investor concerns proactively, with pitch decks from successes like Airbnb highlighting visuals and minimal text for impact.

Arts, Entertainment, and Media

Pitch in Film and Television

In film and television, a pitch refers to a concise verbal or written presentation designed to sell a story idea, script, or concept to producers, executives, studios, or networks, often summarizing key elements such as plot, characters, themes, and market potential.^[67] This process serves as the initial gateway for project development, allowing creators to gauge interest before committing to full scriptwriting or production.^[68] Unlike completed screenplays, pitches emphasize the project's commercial viability and emotional hook to secure funding, attachments, or greenlights. The pitching process typically begins with a logline, a one- to two-sentence summary capturing the protagonist, conflict, and stakes to hook the listener immediately.^[69] This is often followed by a treatment, a multi-page prose document outlining the narrative arc, major scenes, character development, and tone without full dialogue.^[70] Formal pitch meetings then allow creators to verbally expand on these materials, lasting 15-30 minutes and focusing on storytelling delivery to build excitement.^[71] In Hollywood, this structured approach evolved from the post-studio era, where freelance writers gained prominence after the 1948 antitrust rulings dismantled vertical integration, shifting from in-house script development to external idea submissions.^[72] Historically, during the 1920s studio system, pitches were informal discussions in writers' rooms, as major studios like MGM and Paramount controlled talent under long-term contracts and solicited ideas without formal meetings.^[72] The transition to sound films in the late 1920s brought more literary writers, formalizing idea evaluation, though true pitch culture emerged in the 1950s with freelance models and legal protections like the Desny v. Wilder ruling, which safeguarded idea disclosure.^[72] In modern practice, platforms like Netflix, which ramped up original content in 2013 with series like House of Cards, accept pitches only through established agents or production partners, emphasizing data-driven viability over unsolicited submissions.^[73] Effective techniques include incorporating visual aids such as pitch decks or mood boards to illustrate tone, settings, and style, enhancing the narrative's appeal beyond words.^[74] Pitches often highlight character arcs—the protagonist's transformation amid conflict—to demonstrate emotional depth, while referencing comparable titles (comp titles) like "a thriller in the vein of The Bourne Identity" positions the project in the market.^[75] These elements help convey uniqueness and profitability, with creators practicing delivery to maintain energy and respond to questions dynamically.^[68] Despite these strategies, pitching faces significant challenges, including intense competition where the vast majority of ideas—estimated at over 99% for script submissions—are rejected due to market saturation and executive risk aversion.^[76] Success stories underscore the potential rewards; for instance, Peter Benchley's 1974 novel Jaws, written as a full manuscript, was acquired by Doubleday and saw its film rights purchased pre-publication by producers Richard D. Zanuck and David Brown for Universal, leading to Steven Spielberg's blockbuster adaptation.) Such breakthroughs remain rare, requiring persistence amid frequent rejections to navigate the industry's gatekeeping.

Pitch in Music and Performance

In music and performance, pitch serves as a foundational element for achieving cohesion and expressiveness in live settings, where vocalists and instrumentalists must align their tones precisely to create harmonious ensembles. This involves not only individual accuracy but also collective synchronization, as discrepancies can disrupt the overall sound, particularly in unamplified acoustic environments like theaters or concert halls. Performers rely on pitch to convey emotional nuance, with subtle variations enhancing dramatic effect in genres such as opera and jazz improvisation.^[77] Techniques for maintaining pitch accuracy are essential for performers, beginning with ear training exercises that develop the ability to recognize and replicate tones, such as interval identification and melodic dictation, which build internal pitch reference over time. In ensembles, pitch matching involves singers or players listening to a lead tone—often from an oboe or concertmaster—and adjusting their instruments or voices accordingly, a process honed through call-and-response drills and group warm-ups to foster intuitive synchronization. For vocalists, this includes resonance tuning, where performers modify vowel shapes to stabilize pitch under varying acoustic conditions.^[77]^[78]^[79] In opera, performers often adjust pitch slightly higher—up to A=442 Hz or more—for better projection in large halls, as the brighter timbre cuts through orchestral accompaniment and enhances acoustic resonance without electronic aid. Similarly, in live electronic music, pitch correction tools like Auto-Tune, introduced by Antares Audio Technologies in 1997, enable real-time adjustments during performances, allowing artists to maintain intonation amid improvisational sets or vocal strains. DJs employ pitch shifting effects to harmonically blend tracks, transposing keys without altering tempo for seamless transitions in live mixes, a technique central to genres like house and techno.^[79]^[80]^[81]

Sports and Recreation

Pitch as a Throw or Delivery

In baseball, a pitch refers to the act of delivering the ball from the pitcher's mound toward the batter at home plate during a live ball situation, with the pitcher required to have possession of the ball and contact with the pitcher's plate.^[82] The primary objective is to throw the ball through the strike zone—an imaginary rectangular area over home plate extending from the midpoint between the batter's shoulders and the top of their uniform pants down to just below the kneecap—for it to be called a strike if the batter does not swing.^[83] Common pitch types include the fastball, designed for maximum velocity and straight trajectory with backspin; other variations like curveballs or sliders introduce movement through altered grips and wrist snaps. For instance, the four-seam fastball holds the MLB record speed of 105.8 mph, achieved by reliever Aroldis Chapman on September 24, 2010, during a game against the San Diego Padres at Petco Park.^[84] Pitching techniques emphasize precise grip, arm action, and release to control speed and movement. For a standard fastball, the pitcher grips the ball with the index and middle fingers placed across the wide-set seams (about ½ to 1 inch apart), thumb underneath for support, promoting a clean release off the fingertips to generate backspin and minimize side deviation.^[85] Release occurs as the arm reaches full extension near hip height, with the fingers pulling downward through the ball for velocity, typically measured by radar guns that became standard in Major League Baseball starting in the mid-1970s to provide real-time speed readings from behind home plate.^[86] Historically, professional baseball pitching emerged in the late 1860s, with the Cincinnati Red Stockings becoming the first openly salaried team in 1869, featuring pitchers like Asa Brainard who delivered underhand or overhand styles in their undefeated season.^[87] In cricket, a pitch denotes the bowler's delivery of the ball toward the batsman and the defended wicket, propelled with a run-up and arm action to challenge the batter's timing and placement.^[88] Deliveries vary widely, including swing bowling—where the ball curves laterally in flight due to the seam's orientation disrupting airflow, creating conventional swing (seam angled toward slips for outswing or leg side for inswing) or reverse swing under worn-ball conditions—and spin bowling, which imparts rotation to cause sharp deviation after pitching, such as off-spin (turning from off to leg side) or leg-spin (turning from leg to off side).^[89] Representative spin variations include the googly (a leg-spinner disguised to turn oppositely) and doosra (an off-spinner mimicking a straight delivery), executed by wrist or finger flicks at release.^[90] Cricket bowling techniques focus on seam position, wrist angle, and release point for deception. For swing, the bowler grips the ball with index and middle fingers along the seam, thumb opposite, and releases with the seam upright or tilted to exploit air pressure differences, achieving speeds up to 100 mph in international play.^[91] Rules prohibit illegal deliveries, such as a no-ball called when any part of the bowler's front foot lands wholly or partially beyond the popping crease during the delivery stride, awarding the batting side a free hit and run penalty.^[92] Radar guns, introduced in cricket during the late 1990s, are used for speed tracking during matches and training.^[93] Historically, cricket transitioned from underarm to overarm bowling in the 1860s; roundarm had become dominant by then, but bowlers like Edgar Willsher were no-balled for raising the arm above shoulder height until overarm was legalized in 1864, revolutionizing pace and variety.^[88]^[86]

Pitch as a Playing Field

In association football, commonly known as soccer, the pitch refers to the rectangular field of play marked out for the game. According to FIFA standards, which have been in place since the organization's founding in 1904 and formalized through the International Football Association Board (IFAB), an international match pitch measures between 100 and 110 meters in length and 64 to 75 meters in width, with the recommended dimensions being 105 meters long by 68 meters wide to optimize play.^[94] These specifications ensure uniformity for professional and international competitions, though general matches allow a broader range of 90 to 120 meters in length and 45 to 90 meters in width under IFAB Laws of the Game.^[95] The first documented soccer pitch adhering to early standardized dimensions was at Kennington Oval in London, where the inaugural FA Cup final took place on March 16, 1872, between Wanderers FC and Royal Engineers, marking a pivotal moment in the sport's development.^[96] Key markings on a soccer pitch include the center circle, which has a radius of 9.15 meters (10 yards) drawn around the midpoint of the halfway line, ensuring opponents remain at least this distance during kick-offs.^[97] The penalty area, often called the 18-yard box, extends 16.5 meters from each goalpost into the field and spans 40.32 meters across, creating a rectangular zone where goalkeepers can handle the ball and fouls result in penalty kicks from the 11-meter mark.^[95] These lines, all of equal width not exceeding 12 centimeters, define areas like the goal area (5.5 meters by 18.32 meters) and corner arcs (1-meter radius), facilitating fair play and strategic positioning. In cricket, the pitch specifically refers to the rectangular central area of the field of play, measuring 22 yards (20.12 m) in length and 10 feet (3.05 m) in width, on which the wickets are situated and along which the ball is bowled.^[98] Pitches in other field sports share similar rectangular layouts but with distinct dimensions. In rugby union, governed by World Rugby, the field of play measures 94 to 100 meters in length by 68 to 70 meters in width, excluding in-goal areas that add 6 to 22 meters at each end.^[99] Field hockey pitches, standardized by the International Hockey Federation (FIH), are 91.4 meters long by 55 meters wide, with synthetic turf preferred for its consistent ball speed and reduced maintenance.^[100] Traditionally, soccer pitches use natural grass for its natural traction and aesthetic, but artificial turf has gained prevalence in multi-use venues due to durability in varying weather. Post-1966 FIFA World Cup, where heavy rain exposed drainage flaws at venues like Wembley, innovations such as undersoil heating and improved subsurface drainage systems—using perforated pipes and gravel layers—became standard to prevent waterlogging and maintain playable conditions year-round.^[101] In non-professional play, such as amateur or youth leagues under The Football Association (FA) regulations, pitch sizes often vary within the minimum and maximum limits to accommodate facilities, with smaller dimensions like 90 meters by 45 meters common for grassroots games to suit player development and space constraints.^[95]

Botany

Pitch as Plant Resin

Pitch, in the context of plant resins, refers to a viscous, black or dark brown substance derived from conifers, particularly species in the genus Pinus. It is a natural oleoresin exuded by trees to seal wounds and deter pests, consisting primarily of a mixture of terpenes (volatile hydrocarbons) and rosin acids (non-volatile diterpenoid compounds). This resin hardens upon exposure to air, forming a sticky, impermeable barrier that contributes to the tree's defense mechanisms. In botanical terms, pitch specifically denotes resins from coniferous sources, distinguishing it from other plant exudates like storax from non-conifers.^[102] The production of pitch involves collecting the oleoresin sap from conifer trunks via tapping methods, such as incisions or the traditional "cup and gutter" system, followed by distillation to separate components. Distillation of pine sap yields volatile turpentine oil and a solid residue known as rosin, while further processing through destructive distillation of pine wood or tar produces pine tar pitch, a darker, more viscous form. These processes exploit the resin's thermoplastic properties, resulting in a material that is adhesive, waterproof, and resistant to decay, with a softening point typically ranging from 80–100°C. The chemical composition is dominated by resin acids, including abietic acid (up to 45% in some forms), along with isomers like palustric and pimaric acids.^[102]^[103] Historically, pitch has been valued for its waterproofing and adhesive qualities. Ancient Romans produced pitch on an industrial scale in mountainous regions like the Pyrenees, using kilns to distill pine resin for caulking ships and sealing vessels, supporting their expansive maritime economy. Native American communities utilized pine pitch to create torches by combining it with wood or fibers, providing a reliable light source in pre-colonial times. By the 19th century, the naval stores industry in the southeastern United States scaled up production through systematic tapping and distillation of longleaf pine sap, supplying pitch for shipbuilding, rope preservation, and other maritime needs amid growing global trade demands.^[104]^[105] In modern applications, pitch and its derivatives continue to serve as key ingredients in adhesives, sealants, and insulation materials due to their binding strength and moisture resistance. Refined forms like rosin are incorporated into products such as printing inks, chewing gum, and protective coatings, while pine tar pitch finds use in roofing and electrical insulation. These uses leverage the material's natural durability, though sustainable harvesting practices are now emphasized to prevent overexploitation of conifer resources.^[102]^[103]

Pitch in Plant Species

Pitch pine (Pinus rigida), a coniferous species native to eastern North America, is renowned for its high resin content, which yields a viscous pitch used historically in colonial America for waterproofing ship masts and producing tar and turpentine. This tree thrives in sandy, fire-prone soils from Maine to Georgia, where its resinous wood provided essential materials for naval stores during the era of wooden sailing vessels, supporting industries that exported pitch to Europe.^[106]^[107]^[108] Other conifer species contribute to pitch production, such as the Asian sweetgum (Liquidambar orientalis), which yields storax, a balsamic resin chemically similar to but distinct from coniferous pitch; historical overharvesting in regions like Turkey led to scarcity by the 19th century, prompting exploration of alternatives like Liquidambar styraciflua for comparable resin yields, though not true pitch.^[109]^[110] In plant ecology, pitch production serves as a key defense mechanism against herbivores, with resin acting as a physical barrier that deters feeding and a chemical repellent that disrupts insect digestion. This adaptation is prominent in coniferous species distributed across boreal forests, where trees like Scots pine (Pinus sylvestris) in northern Europe and jack pine (Pinus banksiana) in North America exude pitch to protect against bark beetles and other pests.^[111]^[112]^[113] Modern cultivation emphasizes sustainable harvesting practices, particularly in Scandinavia, where Scots pine resin is tapped through non-invasive methods to produce eco-pitch for industrial and medicinal uses. In Sweden and Finland, initiatives promote controlled incisions on mature trees, allowing regeneration and minimizing ecological impact, as part of broader European efforts to revive resin economies.^[114]^[115]

References

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### Summary of Definitions for "Pitch" (Merriam-Webster)
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Pitch, a sticky, resinous substance, is mentioned in the Bible primarily in the context of construction and waterproofing.
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2-28-2 A live ball delivered to the batter is a pitch. The term implies a legally delivered ball unless otherwise stated. When a pitcher commits a balk and ...
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A sales pitch presents your offerings in concise terms. Here are the best sales pitch examples to learn which types of sales pitches to use.Storytelling: The foundation of... · How to create engaging sales...
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Both pitch and slope indicate the incline of a roof, expressed as a proportion of the vertical to the horizontal. This article describes both roof slope and ...
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Pitch is the perceptual correlate of waveform periodicity, or repetition rate. The faster a waveform repeats, the higher its perceived pitch.
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In short, m = d /z becomes the formula for the module. The diagram below shows the circular pitch graphically. outside diameter. 相关链接 - 节距.
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Spur Gear design formula for geometry, pitch, tooth clearance and critical functional data. ... Circular Pitch. p = ( π D )/ N p = π / P. Center Distance, C ...
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All of the variations of helix length and pitch shown in Figure 6 had a constant ground plane (GP) size, 118 mm, or 0.94λ diameter at the center frequency.
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None
Summary of each segment:
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@seo-title | MLB.com
**Summary of MLB Definition of a Pitch:**
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[101]
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None
### Summary of Rosin and Pitch from Pine (Extracted from https://www.ams.usda.gov/sites/default/files/media/waxes%20report%20rosin%202014.pdf)
[104]
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[PDF] Tree of the Year: Liquidambar Eric Hsu and Susyn Andrews
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A Viscoelastic Deadly Fluid in Carnivorous Pitcher Plants | PLOS One
We show that the digestive fluid of Nepenthes rafflesiana is highly viscoelastic and that this physical property is crucial for the retention of insects in its ...
[112]
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The digestive glands of carnivorous plants secrete mucilage, pitcher fluids, acids, and proteins, including digestive enzymes.Digestive And Absorptive... · Mucilage Production And... · Concluding Remarks
[113]
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Dec 15, 2010 · In Nepenthes and Cephalotus, the fluid is secreted by the trap; the other genera collect rain water. The fluid is usually acidic, rich in O2 and ...
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The amount, viscosity, and chemical composition of oleoresin can influence tree suitability for herbivores such as bark beetles (Mason 1971; Berryman 1972; ...
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[PDF] Boreal forests
Boreal forests are one of the largest biomes, located mostly between 50°N and 65°N, dominated by coniferous trees, and mainly found in Canada, Nordic countries ...
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Extractives of Tree Biomass of Scots Pine (Pinus sylvestris L.) for ...
There is some evidence suggesting that Scandinavian Scots pine varieties have the highest total resin acid content in wood compared to other macro-regions in ...