An oscillatory neural network (ONN) is an artificial neural network that uses coupled oscillators as neurons. Oscillatory neural networks are closely linked to the Kuramoto model, and are inspired by the phenomenon of neural oscillations in the brain. Oscillatory neural networks have been trained to recognize images. Complex-Valued Oscillatory network has also been shown to store and retrieve multidimensional aperiodic signals. An oscillatory autoencoder has also been demonstrated, which uses a combination of oscillators and rate-coded neurons. A neuron made of two coupled oscillators, one having a fixed and the other having a tunable natural frequency, has been shown able to run logic gates such as XOR that conventional sigmoid neurons cannot.
Learning rate
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. Too high a learning rate will make the learning jump over minima, but too low a learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. == Learning rate schedule == Initial rate can be left as system default or can be selected using a range of techniques. A learning rate schedule changes the learning rate during learning and is most often changed between epochs/iterations. This is mainly done with two parameters: decay and momentum. There are many different learning rate schedules but the most common are time-based, step-based and exponential. Decay serves to settle the learning in a nice place and avoid oscillations, a situation that may arise when too high a constant learning rate makes the learning jump back and forth over a minimum, and is controlled by a hyperparameter. Momentum is analogous to a ball rolling down a hill; we want the ball to settle at the lowest point of the hill (corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the same direction for a long time and also avoids local minima by 'rolling over' small bumps. Momentum is controlled by a hyperparameter analogous to a ball's mass which must be chosen manually—too high and the ball will roll over minima which we wish to find, too low and it will not fulfil its purpose. The formula for factoring in the momentum is more complex than for decay but is most often built in with deep learning libraries such as Keras. Time-based learning schedules alter the learning rate depending on the learning rate of the previous time iteration. Factoring in the decay the mathematical formula for the learning rate is: η n + 1 = η 0 1 + d n {\displaystyle \eta _{n+1}={\frac {\eta _{0}}{1+dn}}} where η {\displaystyle \eta } is the learning rate, η 0 {\displaystyle \eta _{0}} is the original learning rate, d {\displaystyle d} is a decay parameter and n {\displaystyle n} is the iteration step. Step-based learning schedules changes the learning rate according to some predefined steps. The decay application formula is here defined as: η n = η 0 d ⌊ 1 + n r ⌋ {\displaystyle \eta _{n}=\eta _{0}d^{\left\lfloor {\frac {1+n}{r}}\right\rfloor }} where η n {\displaystyle \eta _{n}} is the learning rate at iteration n {\displaystyle n} , η 0 {\displaystyle \eta _{0}} is the initial learning rate, d {\displaystyle d} is how much the learning rate should change at each drop (0.5 corresponds to a halving) and r {\displaystyle r} corresponds to the drop rate, or how often the rate should be dropped (10 corresponds to a drop every 10 iterations). The floor function ( ⌊ … ⌋ {\displaystyle \lfloor \dots \rfloor } ) here drops the value of its input to 0 for all values smaller than 1. Exponential learning schedules are similar to step-based, but instead of steps, a decreasing exponential function is used. The mathematical formula for factoring in the decay is: η n = η 0 e − d n {\displaystyle \eta _{n}=\eta _{0}e^{-dn}} where d {\displaystyle d} is a decay parameter. == Adaptive learning rate == The issue with learning rate schedules is that they all depend on hyperparameters that must be manually chosen for each given learning session and may vary greatly depending on the problem at hand or the model used. To combat this, there are many different types of adaptive gradient descent algorithms such as Adagrad, Adadelta, RMSprop, and Adam which are generally built into deep learning libraries such as Keras.
Content Credentials
Content Credentials (also known as C2PA signatures) are a digital media metadata specification. They aim to provide provenance information about a piece of media (such as an image or a video) and help prove its authenticity. They are described as the equivalent of nutrition labels for digital media. One of the stated goal of this specification is to fight online disinformation. The specification is written and maintained by the Coalition for Content Provenance and Authenticity (C2PA), a group of many media and tech organizations including Adobe, Amazon, the BBC, Google, Meta, Microsoft, OpenAI and Sony. Another organization, the Content Authenticity Initiative (CAI), is responsible for promoting the standard and accelerate its adoption. The standard relies on cryptographic digital signatures. == Adoption == There are two main stakeholders who can implement Content Credentials: Producers (softwares and hardwares that produce or modify digital media) and publishers (softwares that show digital media to users). === Producers === ==== Adobe ==== Adobe is one of the first companies to implement the specification, announcing support in Photoshop in 2021. Content Credentials can be enabled and the complete history of edits is kept. ==== Google ==== Google announced support for Content Credentials on its Pixel 10 phones in August 2025. The Content Credentials are embedded on each picture taken from the Pixel Camera, and modifications done using Google Photos. Information include picture timestamp and a non-identifiable signature that proves it was taken from a Pixel 10. As for Google Photos, a list of AI and non-AI edits are kept. Google is the first company to introduce support for Content Credentials on either phones or consumer-grade devices, and also the first company to make it available for free to all users. ==== Nikon ==== Nikon announced in 2024 that their Z6 III camera would support embedding Content Credentials in its photos. However, in 2025, a vulnerability was discovered in the software of the camera that allowed to combine unauthentic images with authentic photos and still have the resulting image with a valid digital signature. Nikon revoked the certificates. ==== Media organizations ==== CBC/Radio-Canada and the BBC both have started attaching Content Credentials to media they produce or verify. ==== OpenAI ==== OpenAI embeds Content Credentials on the images and videos it generates that includes that the media was created by AI using their platforms. ==== Sony ==== In June 2025, Sony announced the release of its Camera Verify system for press photographers and news editors using C2PA digital signatures. Initially, the system will be limited to still images, high‑end cameras, and selected news agencies. Registration with Sony Creators' Cloud is also required. === Publishers === ==== LinkedIn ==== In 2024, LinkedIn started showing a "CR" icon on images that contain Content Credentials of AI-generated images. In 2025, they announced a partnership with Adobe to allow photographers to prove ownership of images using Content Credentials. ==== TikTok ==== TikTok announced in 2024 that an "AI-generated" label would be applied to videos containing Content Credentials if they were AI-generated. In 2025, they announced that users could control the amount of AI-generated content they see, using self-reported labels, Content Credentials and an invisible, proprietary AI watermark embedded in videos by their AI editor tool. ==== YouTube ==== In 2024, YouTube started showing to users a label that reads "captured with a camera" on videos that show authentic, unedited videos taken by Content Credentials-compatible cameras.
Blocking of Twitter in Nigeria
Twitter was blocked in Nigeria from 5 June 2021 to 13 January 2022. The government imposed a ban on the social network after it deleted tweets made by, and temporarily suspended, the Nigerian president Muhammadu Buhari, warning the southeastern people of Nigeria, predominantly Igbo people, of a potential repeat of the 1967 Nigerian Civil War due to the ongoing insurgency in Southeastern Nigeria. The Nigerian government claimed that the deletion of the president's tweets factored into their decision, but it was ultimately based on "a litany of problems with the social media platform in Nigeria, where misinformation and fake news spread through it have had real world violent consequences", citing the persistent use of the platform for activities that are capable of undermining Nigeria's corporate existence. In January 2022, Nigeria lifted its blocking of Twitter after the platform agreed to establish a legal entity within the country sometime in the first quarter of 2022. == Background == On 1 June 2021, Nigerian President Muhammadu Buhari posted a tweet threatening a crackdown on regional separatists "in the language they understand". The next day, Twitter deleted the tweet, claiming it was in violation of Twitter rules, but gave no further details. Nigeria's Information Minister Lai Mohammed said that Twitter's actions were part of an unfair double standard, as Twitter had not banned incitement tweets from other groups. During the Nigerian Civil War a majority of deaths resulted from the blockade of Biafra which caused the deaths of millions of civilians from starvation, a fact that was not alluded to in the tweet. The Nigerian government has long held concerns over the use of Twitter in the country. The ongoing local End SARS protest began on Twitter and got amplified in 2020 when it had 48 million tweets in ten days. Buhari's government floated the idea of social media regulation on different occasions prior to banning Twitter. Attempts to pass an anti-social media bill in the past have failed majorly due to massive outcry on Twitter. Days before the ban, the country's minister of information called Twitter's activities in Nigeria suspicious, citing its influence on the End SARS protests. == Aftermath == Three days after Twitter was suspended, it was reported that the move had cost the country over 6 billion naira and would also contribute to the worsening unemployment in the country. ExpressVPN reported an over 200 percent increase in web traffic and searches for VPN spiked across the country. In response, Nigeria's Minister of Justice and Attorney General of the Federation Abubakar Malami at first openly threatened to prosecute citizens who bypass the ban using a VPN but then denied saying so after a screenshot of a Twitter deactivation notification he shared on Facebook showed a VPN logo. Nigeria's cultural minister Lai Mohammed stated the ban would be lifted once Twitter submitted to locally licensing, registration and conditions. "It will be licensed by the broadcasting commission, and must agree not to allow its platform to be used by those who are promoting activities that are inimical to the corporate existence of Nigeria." In late June 2021, Twitter announced it would enter talks with the Nigerian government over the platform's suspension. The talks began in July 2021. On 15 September 2021, Mohammed said the Nigerian government will lift the ban on Twitter in a "few days." The Minister said Twitter gave a progress report of their talks with them, adding that it has been productive and quite respectful. On 1 October 2021, President Muhammadu Buhari in his Independence Day broadcast said Twitter must meet the Nigerian government's five conditions before the suspension of the social media platform will be lifted. The conditions are: Respect for national security and cohesion; registration, physical presence and representation in Nigeria; fair taxation; dispute resolution; local content. == Reactions == The ban was condemned by Amnesty International, the British, Canadian and Swedish diplomatic missions to Nigeria, as well as the United States and the European Union in a joint statement. Two domestic organizations, the Socio-Economic Rights and Accountability Project (SERAP) and the Nigerian Bar Association, indicated intent to challenge the ban in court. Twitter itself called the ban "deeply concerning". Former U.S. President Donald Trump, who was permanently suspended from Twitter following the United States Capitol attack in January, praised the ban, stating "Congratulations to the country of Nigeria, who just banned Twitter because they banned their President", and also called on other countries to ban Twitter and Facebook due to "not allowing free and open speech." == Lifting of the ban == On 12 January 2022, the Nigerian Government lifted the ban after Twitter agreed to pay an "applicable tax" and establish "a legal entity in Nigeria during the first quarter of 2022".
IP Multimedia Subsystem
The IP Multimedia Subsystem or IP Multimedia Core Network Subsystem (IMS) is a standardized architectural framework for delivering IP-based multimedia services. Historically, mobile phones have provided voice call services over a circuit-switched network, rather than over an IP-based packet-switched network. Various VoIP technologies are available on smartphones; IMS offers a standardized protocol across different vendors. IMS was originally designed by the wireless standards body 3rd Generation Partnership Project (3GPP), as a part of the vision for evolving mobile networks beyond GSM. Its original formulation (3GPP Rel-5) represented an approach for delivering Internet services over GPRS. This vision was later updated by 3GPP, 3GPP2 and ETSI TISPAN by requiring support of networks other than GPRS, such as Wireless LAN, CDMA2000 and fixed lines. IMS uses IETF protocols wherever possible, e.g., the Session Initiation Protocol (SIP). According to the 3GPP, IMS is not intended to standardize applications, but rather to aid the access of multimedia and voice applications from wireless and wireline terminals, i.e., to create a form of fixed-mobile convergence (FMC). This is done by having a horizontal control layer that isolates the access network from the service layer. From a logical architecture perspective, services need not have their own control functions, as the control layer is a common horizontal layer. However, in implementation this does not necessarily map into greater reduced cost and complexity. Alternative and overlapping technologies for access and provisioning of services across wired and wireless networks include combinations of Generic Access Network, softswitches and "naked" SIP. Since it is becoming increasingly easier to access content and contacts using mechanisms outside the control of traditional wireless/fixed operators, the interest of IMS is being challenged. Examples of global standards based on IMS are MMTel which is the basis for Voice over LTE (VoLTE), Wi-Fi Calling (VoWIFI), Video over LTE (ViLTE), SMS/MMS over WiFi and LTE, Unstructured Supplementary Service Data (USSD) over LTE, and Rich Communication Services (RCS), which is also known as joyn or Advanced Messaging, and now RCS is operator's implementation. RCS also further added Presence/EAB (enhanced address book) functionality. == History == IMS was defined by an industry forum called 3G.IP, formed in 1999. 3G.IP developed the initial IMS architecture, which was brought to the 3rd Generation Partnership Project (3GPP), as part of their standardization work for 3G mobile phone systems in UMTS networks. It first appeared in Release 5 (evolution from 2G to 3G networks), when SIP-based multimedia was added. Support for the older GSM and GPRS networks was also provided. 3GPP2 (a different organization from 3GPP) based their CDMA2000 Multimedia Domain (MMD) on 3GPP IMS, adding support for CDMA2000. 3GPP release 6 added interworking with WLAN, inter-operability between IMS using different IP-connectivity networks, routing group identities, multiple registration and forking, presence, speech recognition and speech-enabled services (Push to talk). 3GPP release 7 added support for fixed networks by working together with TISPAN release R1.1, the function of AGCF (access gateway control function) and PES (PSTN emulation service) are introduced to the wire-line network for the sake of inheritance of services which can be provided in PSTN network. AGCF works as a bridge interconnecting the IMS networks and the Megaco/H.248 networks. Megaco/H.248 networks offers the possibility to connect terminals of the old legacy networks to the new generation of networks based on IP networks. AGCF acts a SIP User agent towards the IMS and performs the role of P-CSCF. SIP User Agent functionality is included in the AGCF, and not on the customer device but in the network itself. Also added voice call continuity between circuit switching and packet switching domain (VCC), fixed broadband connection to the IMS, interworking with non-IMS networks, policy and charging control (PCC), emergency sessions. It also added SMS over IP. 3GPP release 8 added support for LTE / SAE, multimedia session continuity, enhanced emergency sessions, SMS over SGs and IMS centralized services. 3GPP release 9 added support for IMS emergency calls over GPRS and EPS, enhancements to multimedia telephony, IMS media plane security, enhancements to services centralization and continuity. 3GPP release 10 added support for inter device transfer, enhancements to the single radio voice call continuity (SRVCC), enhancements to IMS emergency sessions. 3GPP release 11 added USSD simulation service, network-provided location information for IMS, SMS submit and delivery without MSISDN in IMS, and overload control. Some operators opposed IMS because it was seen as complex and expensive. In response, a cut-down version of IMS—enough of IMS to support voice and SMS over the LTE network—was defined and standardized in 2010 as Voice over LTE (VoLTE). == Architecture == Each of the functions in the diagram is explained below. The IP multimedia core network subsystem is a collection of different functions, linked by standardized interfaces, which grouped form one IMS administrative network. A function is not a node (hardware box): An implementer is free to combine two functions in one node, or to split a single function into two or more nodes. Each node can also be present multiple times in a single network, for dimensioning, load balancing or organizational issues. === Access network === The user can connect to IMS in various ways, most of which use the standard IP. IMS terminals (such as mobile phones, personal digital assistants (PDAs) and computers) can register directly on IMS, even when they are roaming in another network or country (the visited network). The only requirement is that they can use IP and run SIP user agents. Fixed access (e.g., digital subscriber line (DSL), cable modems, Ethernet, FTTx), mobile access (e.g. 5G NR, LTE, W-CDMA, CDMA2000, GSM, GPRS) and wireless access (e.g., WLAN, WiMAX) are all supported. Other phone systems like plain old telephone service (POTS—the old analogue telephones), H.323 and non IMS-compatible systems, are supported through gateways. === Core network === HSS – Home subscriber server: The home subscriber server (HSS), or user profile server function (UPSF), is a master user database that supports the IMS network entities that actually handle calls. It contains the subscription-related information (subscriber profiles), performs authentication and authorization of the user, and can provide information about the subscriber's location and IP information. It is similar to the GSM home location register (HLR) and Authentication centre (AuC). A subscriber location function (SLF) is needed to map user addresses when multiple HSSs are used. User identities: Various identities may be associated with IMS: IP multimedia private identity (IMPI), IP multimedia public identity (IMPU), globally routable user agent URI (GRUU), wildcarded public user identity. Both IMPI and IMPU are not phone numbers or other series of digits, but uniform resource identifier (URIs), that can be digits (a Tel URI, such as tel:+1-555-123-4567) or alphanumeric identifiers (a SIP URI, such as sip:[email protected] ). IP Multimedia Private Identity: The IP Multimedia Private Identity (IMPI) is a unique permanently allocated global identity assigned by the home network operator. It has the form of a Network Access Identifier(NAI) i.e. user.name@domain, and is used, for example, for Registration, Authorization, Administration, and Accounting purposes. Every IMS user shall have one IMPI. IP Multimedia Public Identity: The IP Multimedia Public Identity (IMPU) is used by any user for requesting communications to other users (e.g. this might be included on a business card). Also known as Address of Record (AOR). There can be multiple IMPU per IMPI. The IMPU can also be shared with another phone, so that both can be reached with the same identity (for example, a single phone-number for an entire family). Globally Routable User Agent URI: Globally Routable User Agent URI (GRUU) is an identity that identifies a unique combination of IMPU and UE instance. There are two types of GRUU: Public-GRUU (P-GRUU) and Temporary GRUU (T-GRUU). P-GRUU reveal the IMPU and are very long lived. T-GRUU do not reveal the IMPU and are valid until the contact is explicitly de-registered or the current registration expires Wildcarded Public User Identity: A wildcarded Public User Identity expresses a set of IMPU grouped together. The HSS subscriber database contains the IMPU, IMPI, IMSI, MSISDN, subscriber service profiles, service triggers, and other information. ==== Call Session Control Function (CSCF) ==== Several roles of SIP servers or proxies, collectively called Call Session Control Function (CSCF), are used to process SIP sign
Learning curve (machine learning)
In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. Typically, the number of training epochs or training set size is plotted on the x-axis, and the value of the loss function (and possibly some other metric such as the cross-validation score) on the y-axis. Synonyms include error curve, experience curve, improvement curve and generalization curve. More abstractly, learning curves plot the difference between learning effort and predictive performance, where "learning effort" usually means the number of training samples, and "predictive performance" means accuracy on testing samples. Learning curves have many useful purposes in ML, including: choosing model parameters during design, adjusting optimization to improve convergence, and diagnosing problems such as overfitting (or underfitting). Learning curves can also be tools for determining how much a model benefits from adding more training data, and whether the model suffers more from a variance error or a bias error. If both the validation score and the training score converge to a certain value, then the model will no longer significantly benefit from more training data. == Formal definition == When creating a function to approximate the distribution of some data, it is necessary to define a loss function L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} to measure how good the model output is (e.g., accuracy for classification tasks or mean squared error for regression). We then define an optimization process which finds model parameters θ {\displaystyle \theta } such that L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} is minimized, referred to as θ ∗ {\displaystyle \theta ^{}} . === Training curve for amount of data === If the training data is { x 1 , x 2 , … , x n } , { y 1 , y 2 , … y n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\},\{y_{1},y_{2},\dots y_{n}\}} and the validation data is { x 1 ′ , x 2 ′ , … x m ′ } , { y 1 ′ , y 2 ′ , … y m ′ } {\displaystyle \{x_{1}',x_{2}',\dots x_{m}'\},\{y_{1}',y_{2}',\dots y_{m}'\}} , a learning curve is the plot of the two curves i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ) , Y i ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}),Y_{i})} i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ′ ) , Y i ′ ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}'),Y_{i}')} where X i = { x 1 , x 2 , … x i } {\displaystyle X_{i}=\{x_{1},x_{2},\dots x_{i}\}} === Training curve for number of iterations === Many optimization algorithms are iterative, repeating the same step (such as backpropagation) until the process converges to an optimal value. Gradient descent is one such algorithm. If θ i ∗ {\displaystyle \theta _{i}^{}} is the approximation of the optimal θ {\displaystyle \theta } after i {\displaystyle i} steps, a learning curve is the plot of i ↦ L ( f θ i ∗ ( X , Y ) ( X ) , Y ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X),Y)} i ↦ L ( f θ i ∗ ( X , Y ) ( X ′ ) , Y ′ ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X'),Y')}
Harmonic
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the fundamental frequency of a periodic signal. The fundamental frequency is also called the 1st harmonic; the other harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. An n {\displaystyle \ n} th characteristic mode, for n > 1 , {\displaystyle \ n>1\ ,} will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at 1 3 L {\displaystyle \ {\tfrac {1}{3}}\ L\ } and 2 3 L , {\displaystyle \ {\tfrac {2}{3}}\ L\ ,} where L {\displaystyle \ L\ } is the length of the string. In fact, each n {\displaystyle \ n} th characteristic mode, for n {\displaystyle \ n\ } not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions 1 3 L {\displaystyle \ {\tfrac {1}{3}}\ L\ } and 2 3 L . {\displaystyle \ {\tfrac {2}{3}}\ L~.} If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the n {\displaystyle \ n} th characteristic characteristic modes, where n {\displaystyle \ n\ } is a multiple of 3, will be made relatively more prominent. In music, harmonics are used on string instruments and wind instruments as a way of producing sound on the instrument, particularly to play higher notes and, with strings, obtain notes that have a unique sound quality or "tone colour". On strings, bowed harmonics have a "glassy", pure tone. On stringed instruments, harmonics are played by touching (but not fully pressing down the string) at an exact point on the string while sounding the string (plucking, bowing, etc.); this allows the harmonic to sound, a pitch which is always higher than the fundamental frequency of the string. == Terminology == Harmonics may be called "overtones", "partials", or "upper partials", and in some music contexts, the terms "harmonic", "overtone" and "partial" are used fairly interchangeably. But more precisely, the term "harmonic" includes all pitches in a harmonic series (including the fundamental frequency) while the term "overtone" only includes pitches above the fundamental. == Characteristics == A whizzing, whistling tonal character, distinguishes all the harmonics both natural and artificial from the firmly stopped intervals; therefore their application in connection with the latter must always be carefully considered. Most acoustic instruments emit complex tones containing many individual partials (component simple tones or sinusoidal waves), but the untrained human ear typically does not perceive those partials as separate phenomena. Rather, a musical note is perceived as one sound, the quality or timbre of that sound being a result of the relative strengths of the individual partials. Many acoustic oscillators, such as the human voice or a bowed violin string, produce complex tones that are more or less periodic, and thus are composed of partials that are nearly matched to the integer multiples of fundamental frequency and therefore resemble the ideal harmonics and are called "harmonic partials" or simply "harmonics" for convenience (although it's not strictly accurate to call a partial a harmonic, the first being actual and the second being theoretical). Oscillators that produce harmonic partials behave somewhat like one-dimensional resonators, and are often long and thin, such as a guitar string or a column of air open at both ends (as with the metallic modern orchestral transverse flute). Wind instruments whose air column is open at only one end, such as trumpets and clarinets, also produce partials resembling harmonics. However they only produce partials matching the odd harmonics—at least in theory. In practical use, no real acoustic instrument behaves as perfectly as the simplified physical models predict; for example, instruments made of non-linearly elastic wood, instead of metal, or strung with gut instead of brass or steel strings, tend to have not-quite-integer partials. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials. Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as pianos, strings plucked pizzicato, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique singing bowls are known for producing multiple harmonic partials or multiphonics. Other oscillators, such as cymbals, drum heads, and most percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can. Building on of Sethares (2004), dynamic tonality introduces the notion of pseudo-harmonic partials, in which the frequency of each partial is aligned to match the pitch of a corresponding note in a pseudo-just tuning, thereby maximizing the consonance of that pseudo-harmonic timbre with notes of that pseudo-just tuning. == Partials, overtones, and harmonics == An overtone is any partial higher than the lowest partial in a compound tone. The relative strengths and frequency relationships of the component partials determine the timbre of an instrument. The similarity between the terms overtone and partial sometimes leads to their being loosely used interchangeably in a musical context, but they are counted differently, leading to some possible confusion. In the special case of instrumental timbres whose component partials closely match a harmonic series (such as with most strings and winds) rather than being inharmonic partials (such as with most pitched percussion instruments), it is also convenient to call the component partials "harmonics", but not strictly correct, because harmonics are numbered the same even when missing, while partials and overtones are only counted when present. This chart demonstrates how the three types of names (partial, overtone, and harmonic) are counted (assuming that the harmonics are present): In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder) this has the effect of making the note go up in pitch by an octave, but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found halfway down the highest string of a cello produces the same pitch as lightly fingering the node 1 / 3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics. While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example, higher "harmonics" of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than strings, brass, or woodwinds. Examples of these "other" instruments are xylophones, drums, bells, chimes, etc.; not all of their overtone frequencies make a simple whole number ratio with the fundamental frequency. (The fundamental frequency is the reciprocal of the longest time period of the collection of vibrations in some single periodic phenomenon.) == On stringed instruments == Harmonics may be singly produced [on stringed instruments] (1) by varying the point of contact with the bow, or (2) by slightly pressing the string at the nodes, or divisions of its aliquot parts ( 1 2 {\displaystyle {\tfrac {1}{2}}} , 1