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Years ago, I remember seeing sheet music for Jimi Hendrix's Woodstock version of the "Star Spangled Banner". The transcription had a little introduction, in which the transcriber conceded that the guitar's distortion and various sound effects that Hendrix used made some parts of the song impossible to transcribe. I don't remember seeing any indication of this on the sheet music itself, but it made me wonder:

Is there a way to mark something as un-transcribable? Are there any conventions or musical symbols on the score sheet that indicate that something cannot be reproduced by the transcriber, or alternatively, by the reader?

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    A lot of times in swing era music you will see something like "a la Dorsey", which tells the trombonist to play in a specific style. In this case with a very distinct vibrato. While it isn't direct notation, it can tell a really good trombonist more than any number of symbols. – mkingsbu Jul 9 '15 at 18:42
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All transcribed notation is an approximation. The classic dots and stems are simply not adequate for many types of music.

But before we even talk about transcription, consider that many composers have conceived of sounds that are far beyond the status quo -- often called the avant garde, but not necessarily so. Many of these composers have then invented their own notational systems to match what they are hearing.

In light of this, I would say that a transcriber saying something is "untranscribable" simply means they have given up, or doesn't realize what is possible in the history of extended notation.

Some stuff to look at:

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    You may also want to link the question on our site about graphic notation – Dom Jul 9 '15 at 15:24
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To build on NReilingh's great answer, anything* is transcribable. Transcription is just making music so that it can be communicated visually to another musician. Most conventional music makes a trade off between detail and legibility, with things like tempo, phrasing, and articulation rendered by general, fairly ambiguous symbols.

Transcription focuses on what the composer or transcriber deems most important in the score. In most music, that's pitch and rhythm. If either of these is impossible to notate because it is obscured by effects, chances are that element isn't the most important thing for that passage. A faithful transcription can give a sketch of whatever the important elements for that segment are - the minimum a performer would need to render it accurately.

In transcriptions, I've seen "undecipherable" with a rough sketch if one or more of the elements cannot be distinguished (usually pitches). In any case, watching the performer can make it easier to see the technique used, which will make pitches and rhythms easier to render accurately.

Finally, composers can usually tell performers what is important about a piece. Even in non-western music cultures that don't have written notation systems, there is still a method of communicating important elements to other musicians. An good transcription can use this information from the composer to help others perform the piece as the composer intended.

Here I add some slightly more conventional examples, though Threnody is such a cool piece that I doubt I can even come close to such a cool example. Note the absence of meter in both pieces, rather the focus is on the way the layers interlock. This may be a surprise considering that they're both pieces for percussion:

Psappha by Xenakis
(source: vicfirth.com)

And a piece that I hope to perform one day (here pitch level, form, and syllable are important, but rhythm is less rigid):

Globokar's Toucher
(source: di-arezzo.co.uk)

* anything, but also nothing. Even the simplest monophonic folk song can never be transcribed in perfect detail, while the most complex music possible can be notated in any number of methods, depending on the level of detail desired. See Threnody for a good example.

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