User:Oak Blood Three
I am a professional electrical engineer and amateur musician.
I first started to see the cracks in equal temperament as a highschooler when tuning a guitar to pure fourths and a third. At the time, I didn't know the source of the error in the pitch of the high E, or that it was called the Syntonic comma. I thought maybe the intonation was off on my guitar.
I first learned in earnest about tuning theory as a university student. The pianos in the rehearsal rooms at my university were badly out of tune. I got tuning tools and learned how to tune by ear. (I also learned a bit about "well" temperaments.)
I'm mostly interested in just intonations (and things approximating them, and alterations of them to accommodate inharmonicity), but not exclusively.
In fact, here are some Well temperaments I devised and the spreadsheet used to calculate them.
They are two related tunings from a family of 12-tone "almost-equal" temperaments, where fifths squeeze and stretch sinusoidally as you go around the circle.
The first variation is symmetrical about D, with the narrowest fifths (696.05¢) at G–D and D-A and the widest fifths (703.95¢) at C♯–G♯ and G♯–D♯. The amount of stretch is selected to make the major third from C–E just (5/4). This leaves the major third at F♯–A♯ very wide at 407.82¢ or 5.87¢ wider than Pythagorean.
! Cosine D Well C-E Just.scl ! Kloba's Cosine Well D-Centered 12 ! 89.21 193.16 297.11 386.31 501.06 586.31 697.11 793.16 889.21 1000.00 1085.26 2/1
The second variation is also symmetrical about D, with the amount of stretch selected to make the major third from F♯–A♯ Pythagorean (81/64). The narrowest fifths are 697.74¢ (at G–D and D-A) and the widest fifths are 702.26¢ (at C♯–G♯ and G♯–D♯). This leaves the major third from C–E a little wide at 392.18¢ or 5.87¢ wider than just.
! Cosine D Well F#-A# Pyth.scl ! Kloba's Cosine Well D-Centered 12 ! 93.83 196.09 298.35 392.18 500.60 592.18 698.35 796.09 893.83 1000.00 1091.58 2/1