It is not possible to learn a language such as English using only the alphabet but a guitarist can learn guitar knowing only the numeric guitar tuning. The fact that the guitar tuning is necessary and sufficient to learn guitar suggests a machine could learn to play guitar using only numbers.

While guitar can be learn using only the guitar tuning and nothing else the mathematics of guitar are by no means trivial. There are at present no machines that can write intelligent tablature.

Computer programs exist that can write tablature notation in a purely algebraic manner using a given music input interpreted for any guitar tuning, key, intonation, but not in an intelligent way that requires learning to play guitar like a human. Tablature is manifold because the same music input can be played in a very large number of different ways on guitar which raises the question of whether or not a computer can learn to play guitar using the only the guitar tuning and without direct instruction specific to the tuning algorithm.

In theory learning to write tablature should be possible using only the guitar tuning algorithm. Rules for tuning guitar are specified by a set of intervals between guitar strings, which can be represented by a kind of tuning serial number, such as the popular 5 5 5 4 5 tuning typically intonated as E A D G B E.

Tablature notation is remarkably useful for learning guitar without learning music first. Tabs can be used to learn how to understand, write, read, and play guitar using only the guitar tuning without requiring any additional intelligence. Learning guitar music from tablature does not require learning to read and write music first; at the same time learning to read and write music does not lead to learning to write tablature.

No matter how well music is learned the guitar music remains yet to be learned. In fact tablature is independent of pitch and nothing about pitch values tells how the tablature goes.

It seems likely that a computer can write tablature in an intelligence way by direct instructed by a guitarist who has already learned to play guitar, or given examples in tablature of how a human plays guitar. But the question here is can a computer use the elemental form of the tuning as numeric intervals to understand how tablature is written using general principles for the guitar but not specific to the tuning. Writing tabs and playing guitar are almost the same thing, but the question here is can a machine write tablature like a human without being able to play guitar like a human?

It is mathematically feasible in theory for a computer to model the guitar mathematical as a finite state machine defined by a simple mathematic tuning relation between pitch values and fret position numbers depicted on string lines in tablature. The guitar tuning is the initial state of the guitar by which all subsequent states on guitar are known. Tablature is a subset of all the possible states of system on the guitar which constitutes a language structure known as a two-valued language. (See Tarski, Logic, Semantics, Mathematics 1956.) This means that tablature is semi-algebraic and not purely algebraic in structure: Problems in tablature cannot be solved by algebra alone. But of course we know an algorithm such as a tuning must be always be a combination of logic and algebra. The problem is how the machine learns the special tuning logic that can only be tested (interrogated) by playing the guitar.

A remarkable feature of guitar tunings is the high probability of occurrence associated with a small number of guitar tunings that have been cherished and conserved for centuries. The vast majority of guitar tunings are useless, judging by popular use.

The observation that most tunings are useless but some very special tunings are highly original and expressive languages. These mathematically golden tunings have substantial cultural, educational, and economic value. Mathematically most guitar tunings have zero likelihood of use, which shows that guitar music intelligence converges with a high degree of specificity on certain favored tuning structures. This immediately leads to the conclusion that it is not necessary or even useful to learn every tuning.

The high probability of some guitar tunings reduces the question of whether a machine can learn guitar like a human to the smaller problem of whether or not a computers can find those golden tunings that humans are likely to use by searching over every possible tuning.

The nature of this problem, regarding what makes tunings consonant or dissonant, can only be understood by learning how to write tablature notation. Tablature, like any foreign language, makes absolutely no sense without very substantial special learning. Mastering one guitar tuning takes years, and knowledge on one confers no knowledge of another tuning. The smallest incremental change in tuning requires substantial relearning.

A computer that could accelerate guitar learning would be useful in the guitar learning and publishing industry.

There is a danger that learning guitar will take too long if there is no way to know how to write tabs correctly. What takes so long about guitar learning is not the algebraic calculation of locating a pitch value on guitar, which computers easily do, but the internal tuning logic specific to the tuning which is complex and not easily learned. It is the combination of logic and algebra that makes it possible for tablature writing to be a highly sophisticated and complex while also intuitively understood with special learning. It is well-known that semi-algebraic structures and among the most useful and aesthetically pleasing mathematic structure.

Obviously tunings are marvelous mathematic objects, so it is astonishing tunings are not recognized in the mathematic or music literature as distinct from music intelligence.

Can a computer use a generic set of instructions that are the same for all guitars to find which guitar tunings humans want to use to play music?

An equivalent question is whether or not a computer can find the best-possible tablature notation for music in a recording or a traditional music score transcribing guitar music.

Consider a simple mathematic problem in tuning space: Suppose we are given the tablature for the “Happy Birthday” theme written in the 75345 tuning (such as Open D Minor Tuning intonated as DADFAD), but we have only the tablature and do not know which guitar tuning is correct. Without the tuning, tablature is undefined and seems to be nonsense.

The unknown guitar tuning used to write the “Happy Birthday” theme can be discovered by a procedure in which the tablature is played on guitar in every possible tuning. This is a form of tablature interrogation.

It turns out that interrogation does not require searching over every possible tuning that exists but instead converges on the correct tuning quickly. For instance, if the unknown tablature is played in a tuning with just one bad string, such as DADGAD (7 5 5 2 5), the “Happy Birthday” theme could be recognizable in the DADGAD tuning in spite of the bad notes resulting when notes fall on the incorrectly-tuned G string. Since the bad notes on the fourth string are always 2 frets off the mark, interrogating the tab with DADGAD tuning would lead directly to recognizing the correct DADFAD tuning.

In effect, the correct tuning cryptologically is the algorithm that unlocks the melodic message embedded in the tab. The tab embeds the music according to the tuning algorithm and then the tuning algorithm witness the music at specific pitch according to the guitar intonation level. It seems to the observer the music on intonation does not depend in any way on the guitar tuning but in fact an image of the guitar tuning is also embedded in the pitch values observed on intonation. Given an adequate sample it must be mathematically possible to recover the guitar tuning from the music observed on intonation.

The ability to recognize the tuning defies affine theory in which the lost and cannot be recovered. But if the tuning cannot be recovered in a recording then there is no way to learn the guitar. In a projective tuning space, however, the tuning once lost can be recovered because of language-structure specificity.

There is a way to learn guitar mathematically because just as a search for the correct tuning used to write a tab converges on the guitar tuning without having to interrogate every possible tuning, so it is that a search for the best-possible way to write tablature converges on the best tuning and key for any given music. In fact, I assert that a search for the best guitar tuning for any given music must converge quickly (no more than 6-steps, on for each string) on the best tuning.

It does not appear that there is a way to recognize the best-possible tablature or best tuning a priori, but comparing any two tabs usually shows which tab is better. This consistency in ranking tabs means a human, and likely a computer, can rank any collection of tablature written for the same music input, listing tabs in order as better or worse. Collections of tablature sequences must form a well-ordered set with a first and a last tab, and a place for every tab in between.

An interesting problem with tabs is the traditional method of learning music by using a series of increasingly more difficult music mastered by repetition suggests the guitarist learns by making tabs more difficult but there is no reason to make tablature for the same music more difficult to play than necessary. The guitarist in general wants to play music in the easiest way possible, especially for up-tempo music, not the most difficult way.

I have mastered writing tablature in many guitar tunings. It seems to me that it is not possible to write tablature for guitar using any arbitrary criteria (such as the fret span and number of fingers used for fretting notes, without taking the guitar in hand to actually see and understand how tablature is correctly used in the specific tuning space. What is clear to me is that tablature is highly specific in grammatical structure and consistent in a logical, reproducible way. Once problems in tablature are solved in any context, they do not require solving repeatedly. It may seem that every guitarist plays guitar in a different way but in fact guitarist all use the same tuning and keys.

Guitar is difficult to learn because the manifold nature of tablature makes it difficult to know which tabs are best used for learning. Trial-and-error searching for solutions to guitar logic problems creates a possibility that time and effort is wasted learning to play tabs without realizing until later the tabs are not correctly written. If all tabs for the same music in theory sound the same then tablature written in the wrong tuning, even when correct for the tuning, is a form of missense (right pitch, wrong fret number) far too abstract to penetrate by any simple method. But fret numbers in tablature always seems like nonsense to the tuning-naive, which is why tabs have always been the poor, misunderstood intellectual relation of traditional music theory.

What is so strange about guitar music is that the way that tablature is written depends only on the tuning and not in any way on the music that is heard when the tablature is intonated. It seems to the observer that all guitar tunings sound the same, which is not true as demonstrated by the convergence of tunings on a small number of numeric algorithms.

So I think that computers cannot learn guitar from the tuning like a human, but can only use a sort of tablature dictionary with a table of solutions for every tablature problem dictated by a guitarist who has already mastered the usage of tuning numbers like 7 5 4 3 4 and 5 7 5 4 3.

So I don’t think machines can learn guitar.

Guitar is a stunning example of how paradigms in common use are not understood. The perception that numbers in tabs are nonsense seem to suggest that our grip on artificial intelligence is not what it’s cracked up to be. If guitar music, a popular idiom, is not understood in mathematics, music, and computer science after three centuries of use, then what else do they not know?