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1

Other answers do a good job of proving why no non-trivial exact solution can exist. For completeness, I'll note that there is a trivial solution, albeit not especially useful musically - one note per octave. All ratios of pitches differ by some power of two, which is always an integer and thus "just" - trivially so, as only one pitch class is allowed.


5

You can't even get an equal temperament system* in which fifths and octaves are perfect. This is simply because if you had a system of equal steps in which an octave was A steps large and a twelfth was B steps large, it would stand to reason that B octaves would be equal to A twelfths, since both would be an interval of AB steps. This can't happen though: a ...


0

Looks like you’re going for a classical guitar version of a baritone guitar, which are electric steel strings, have a longer scale length and are usually tuned a 4th or sometimes a 5th lower than a regular guitar. It seems like you can take a regular set of strings but offset them by 1 position so the 2nd string would be where the 1st goes, etc. They would ...


0

SalchiPapa Octave4Plus strings have a range of 6 Octaves from C-1 to C5. They make 12 String Guitar String Sets (1A & 1B) that have Octaves on the bottom 5 pairs & a unison pair of High E Strings due to their successful High B String. Now w/ really thin strings, you need to lubricate the Nut so that they slide in smoothly, & you should eliminate ...


15

The other answers approach this from dividing the octave and showing that equal divisions must be irrational. Another way of looking at this is to consider whether we can compose an octave by successive multiplications with a rational number. The result is of course the same: we can't. Start with the Fundamental Theorem of Arithmetic: every integer ...


1

Octave4Plus has made 12 String Guitar String Sets (1A & 1B) that have Octaves on the bottom 5 pairs & unison on the top one cause they've successfully made a High B4 String. What's significant about these string sets is that there are instructions on how to install them. With strings this thin we want to eliminate as many contact points as we can ...


38

By definition this is not possible. Just intonation ratios are rational numbers, N/M where N, M are integers. Equal temperament is based on defining the smallest ratio as the n-th root of 2, 2^(1/n). For 12TET n = 12. What you are basically asking is if an irrational number can be made to exactly match a ratio of integers. This will never be possible....


13

As I understand the question, this is pure mathematics: No it is impossible. No matter, how many divisions you have, say n, the step width will always be nth root of two and therefore an irrational number. The just relations are rational numbers, so there will always be approximations, but the more you choose, i. e. the higher n is, the closer you will be ...


0

Not only can you "extract standard tuning chords" from your chords but you can play the exact same ones! I think there may be different uses of the term chord. There is the "shape" which will be different in different tunings and then there is the order of the notes which is the same. There isn't much that cannot be played in standard tuning but the hand ...


0

You play the same chords and notes in any tuning. You just finger them differently. Some licks that rely on open strings in the alternative tuning may not translate well. The reason for the alternative tuning was doubtless to facilitate such licks. But the SONG will transfer.


1

Every chord needs to use notes from that chord. In standard tuning, chord shapes are what they are due to that tuning. In the alternative tuning you quote, every chord shape will be different from those in standard tuning. The shapes will be different and sometimes that will mean the voicings will also be different. However, the intervals between the top ...


0

What I do with students, to help them understand chords on standard guitars, is to make a list of notes needed, for example, E major is E G♯ and B. Then try to find a set of those notes on frets close to each other. Not always easy, or doable, but it produces some chord shapes, most of which are the ones found in many chord charts. I suggest you do ...


1

I think the accepted answer is simply incorrect. It ignores the fact that any one of us can write a song that is impossible to play on the guitar in any tuning. For example just include notes out of range, etc. All the open string chords can be played in a movable chord format. In such formats the index finger acts as a capo. Most players will be ...


4

Your question is really two separate questions so I will answer them individually. Question 1) Is it possible to play any song on guitar without using a capo? The answer is yes (assuming both guitars are in standard tuning). A capo makes it possible to use the same chord shapes to play a song in a different key or use a different chord set to play a ...


2

It depends what you mean. If you mean play a recognisable version of the song, it's almost certainly possible without a capo or a particular tuning. If you mean getting it sounding the same without a capo or a particular tuning, then in many cases it may be difficult or impossible - the use of the capo or tuning may allow fingerings, chord voicings, and ...


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