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The specific use case I'm interested in involves build a database of audio samples for a musical algorithm (e.g., detection of genre or mood) with the intention of later distribution of the database.

Is there a short enough sample length (1 second, 1/10 second, 1/100 of second?) where the distribution of the audio clip isn't infringement? From this answer it looks like the key issue here substantial similarity, but I'm not sure exactly how it plays into this question. Another issue that might play into this is fair use, but I don't see the work as transformative in any way.

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Is there a short enough sample length (1 second, 1/10 second, 1/100 of second?) where the distribution of the audio clip isn't infringement?

There is no arbitrary rule.

Audio samples (and opposed to the underlying compositions which audio samples are a performance of) are held to the most strict standards of infringement (particularly when it comes to establishing a prima facie case of infringement prior to considering whether the fair use defense applies) of pretty much any kind of work protected by copyright. Even short samples will generally be infringing.

The leading case is Heim v. Universal Pictures Co. 154 F.2d 480 (2nd Cir. 1946) in which one of the intermediate U.S. Courts of Appeals held that infringement could be proven if "a single brief phrase, contained in both pieces, was so idiosyncratic in its treatment as to preclude coincidence," and is not instead a copy of an indistinguishable snippet of music that is in the public domain.

The lower threshold is probably that the sample needs to be long enough for a human listener to discern that it is a sample of some particular recognizable copyrighted work, if the listener is familiar with the original work.

The speed of the sample and the distinctiveness of the sampled material would influence this determination.

A single generic middle C on an ordinary piano held for a whole note at an allegro pace might not qualify as an infringement. A very distinctive three note sequence with a very distinctive vocal or sound quality in a fast tempo piece might be only a fraction of a second long and still be infringing.

The specific use case I'm interested in involves build a database of audio samples for a musical algorithm (e.g., detection of genre or mood) with the intention of later distribution of the database.

The hard and close question, in my mind, is not the size of the individual audio samples, but whether the form in which the samples are used is sufficient to constitute an infringement of one of the specific sticks in the bundles of rights that come with a copyright (e.g. reproduction, distribution, performance, derivate works) that is protected by a copyright. In other words, is an audio clip that is buried as part of training set data for an app that only an IT professional can access with a device other than the one upon which it would be typically used really distribution of a copy, or a performance, or a derivative work.

The implication of this description of the proposed activity is that a user of the software can't actually listen to any of the audio samples, which simply constitute a training data set for a machine learning process.

While copyright is broader than simply a right to prevent someone from commercially appropriating the value imparted by the creative innovations of the original work (e.g. copyright can be used to prohibit a charitable or free distribution of a copyrighted work), copyright law is also interpreted in light of its purposes. And, the primary purpose of copyright law is to prevent the commercial or non-commercial appropriation of the original work without permission from the author (or a mandatory license to perform one's own cover version of an original musical composition for a fee set by an administrative agency), and is interpreted in that light.

The value of this software to its users doesn't seem to meaningfully implicate this interest since the user doesn't benefit from any one particular individual work, so it isn't obvious to me that audio samples used in this manner are infringing.

The safer course of action, however, would be to do the machine learning process from the audio samples before distributing that software, and to include only the sound processing model that flows from that machine learning process, rather than the training set data of audio clips themselves, in the distributed product. To allow users to understand the training set and its influence on the end machine learning product, the software could be distributed with a bibliography citing to all of the works from which audio clips were taken that were used in the training data with pinpoint citations to the portions of the cited works from which audio clips were used.

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substantial similarity is the test used when the plaintiff claims that a work is infringing because it is an imitation of the source work, or is based on the source work, but the defendant claims either that the allegedly infringi8ng work was merely inspired by the source work, or was independently conceived.

When actual copying is admitted or proved (as would be thew case when the defendant has been sampling) the role of "substantial similarity" is much reduced. The concept of fair use is often key to such suits in US courts.

Note that there is no requirement for a work to be "transformative" for it to be a fair use. Note also that as used in a fair use analysis, a use is "transformative" not because it has a different fomr ("is transformed") from the original, but because it has a different purpose from the original. A classic example is that a song lyric is intended to accompany the music, to entertain, and to provoke a particular emotional response when it is used in the original song. But if it is quoted in a text on song-writing as an example of hoe tom sue meter and rhyme to make a point, that is a "transformative" use because it is for a very different purpose than the original use, evne though its form is not changed in any way.

In the example i9n the question, a music sample used to train or form the basis of an algorithm is a very different use than a sample used as part of a song or musical composition, and so thism use might well be transformative. In fact, fromm teh dewscription it seems to me that there would mbe an excellant case for fair use. The part of any one work uses is short relativ to the whoe source work; the use is transformative; the new work cannot serve as a substitute for the sourve work; the new work does not seem to harm any market for the source work. But fair use decisions often depend on the detailed facts, so this kind of rough analysis cannot be depended on.

Also, "fair use" is a very specifically US doctrine. It would have no effect on a copyright suit brought under the laws of some other country. Other countries have different exceptions to copyright which serve some o0f the same general purposes as the fair use concept, but doe so in significantly different ways. Some countries have a concept of -fair dealing**, some have specific exceptions for research commentary, news reporting, and/or personal use. I really cannot say whether the use describes would fit one or more of these. (India, for example, has almost 30 different specific exceptions in its copyright law.)

Under US law there is no specific minimum length of sample that may constitute infringement, or that is permitted under a claim of fair use. The answer by ohwilleke is quite accurate on that point.

Note also that if a trained algorithm or neural network were distributes, that did not directly include the samples, but only parameters derived from them, that would be significantly less likely to be treated as infringement, in my view.

I could not find any reported case based on this kind of sample-derived algorithm. A person planning development of this sort might be wise to consult a lawyer with copyright expertise.

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