Many cultures have arrived to twelve notes per octave. Many people accept 12 tone equal temperament (12TET) as the correct tuning. Yet there is something odd about the tuning of musical instruments:
• 12 pure fifts do not stack up to 7 octaves, but overshoot it with a margin.
• 3 pure major thirds do not stack up to an octave.
• 1 pure major third plus 1 minor third do not add up to 1 pure fifth.
This oddity caused centuries of discussions among German composers and tuners, until princes Amalia Von Pruissen, herself a composer, decided the matter could no longer be discussed. This gave way for the most bleak variant of tuning known at the time: all oddities are spread out equally over the keyboard, 12TET.
Personally, I can't stand it. I made sure I completely understand the matter. This branched off into many projects.
You can easily hear the issue for yourself
Play the flageolet above the forth fret on the low E of a guitar. Then tune the G string to G# by comparing it to the flageolet at the 12th string of the G string.
Tune the rest of the guitar like most people do:
• Tune the high e to the flageolet on the 5th fret of the low E,
• the b string to the flageolet above the 7th fret,
• the D string fretted to E' to the flageolet above the 12th fret,
• and the A fretted to B to the flageolet above the 7th, or just the open E string.
Grab 022000 (the Em shape, but now it is a E) and notice how pure it sounds.
Then compare the b on the thrird fret on the g# string, to the b string. Notice how far off this sounds. That fret is in the wrong place.
Music projects that involve tuning
• My guitar is out of tune. Your's is too. I took the frets off and took a year to relearn how to play it, more or less. Fretless guitar is rediculously hard to play. Do not do this. Fretless guitar is very limited in sustain and possibilities.
• I took the frets of a second guitar. An electric one. I plan to build an electronic sustainer into it. Much harder than I thought. Therefor, it is an ongoing, slowly ongoing, current project.
• I took the frets of a bass. Freedom! Good idea.
• I always hated the pianos, until I found out it is the tuning I hate. I still avoid them if possible. Piano's are worse than guitars, because they also need stretched tunings: Octaves are wider than 2:1, but fifths can be more pure. Thirds, however, are harsh. If given the opportunity, I have pianos tuned to Lehman/Bach tuning. I tried Prelleur, Young, WerckmeisterIII, and Kirnberger. Lehman sounds way better and not too far removed from 12TET for others to complain. There is a variant of Lehman that I prefer, though, but that is too rare for it to be available in pro tuning apps and devices.
• I built an raspberry pi into my synth rack. It takes in all midi data, and cooks it. It runs a Pure Data patch, that routes each note to a different channel, and shoots pitch bend info to each channel, to tune the whole rack to Lehman/Bach tuning. (In midi, pitch bend works per channel, not per note, annoyingly.)
• I moved the frets of my saz around to experiment. It's currently in 1/4 comma meantone.
• I dialed Lehman Bach into my Proteus sound module.
• My home made midi secuencer sends pitch bend information after each note, to keep things in tune.
• I bought a 2D keyboard that offers twice as much black keys and can be tuned to 1/4 comma meantone, and Pytharorean tuning by the click of a button. On this keyboard, the As and G# are two different keys. The orientation of the keys is so that one will chose the right tone for the chord. Pythagorean tuning with the option of the right flavor of black keys, allows for gorgeous harmonies. The 2D layout led to a deeper understanding of modes and modulations. Learning to play the Striso board is an ongoing project of mine.