4 ms·

Thanks for bringing in your understanding of historical tunings. Maybe a simpler correction would be to describe the example as "a Pythagorean tuning" rather th

Thanks for bringing in your understanding of historical tunings. Maybe a simpler correction would be to describe the example as "a Pythagorean tuning" rather than "THE Pythagorean tuning", which would be (according to some) technically correct despite not being historically representative. The goal of that example isn't to provide historical background, it's to provide one of the simplest possible derivations of 12 usable tones from just intervals. I believe that that the 3 being a multiplier or a divisor is a matter of perspective: if you start from the last tone in my example, the same scale is derived from reversed fractions. Starting from the middle might be closer to what you're describing, hopefully I'm getting that right. Grounding the whole thing in the harmonic series on would certainly make sense.

pclmulqdq 2y ago
You are correct about the ratios not mattering that way, but it is jarring for someone who knows about this stuff to see 4/3 (the fourth) instead of 3/2 and to see the positioning of the wolf being the I-V relationship in the scale. I would suggest that if you want to keep it, you should be explicit that the frequency relationship on this fifth is far off, and I would suggest drawing a circle of fifths (which will be a lot more clear after seeing a fifth in the harmonic series). Instinctively, that section feels very wrong despite being (mostly) right. I would personally suggest dropping it entirely - you don't need the history. Edit: I was thinking about your existing diagram a bit more, and here is the rework I might suggest without doing anything too major: Do an up-a-fifth-down-a-fourth path through the chart, and that is easier to rationalize and understand than "mostly 4/3 with 2/3 ratios interspersed when we need to drop an octave": C * 3/2 -> G G * 2/3 -> D D * 3/2 -> A A * 2/3 -> E E * 3/2 -> B B * 2/3 -> F# There is only one break from the pattern right here with two descending perfect fourths in a row: F# * 2/3 -> C# C# * 3/2 -> G# ... You can also restart from C going down to F and Bb once you reach F# and that gives you the typical Pythagorean tuning, but then you will have to explain why that happens to readers who are unfamiliar with tuning.

pclmulqdq 2y ago

You are correct about the ratios not mattering that way, but it is jarring for someone who knows about this stuff to see 4/3 (the fourth) instead of 3/2 and to see the positioning of the wolf being the I-V relationship in the scale. I would suggest that if you want to keep it, you should be explicit that the frequency relationship on this fifth is far off, and I would suggest drawing a circle of fifths (which will be a lot more clear after seeing a fifth in the harmonic series). Instinctively, that section feels very wrong despite being (mostly) right. I would personally suggest dropping it entirely - you don't need the history. Edit: I was thinking about your existing diagram a bit more, and here is the rework I might suggest without doing anything too major: Do an up-a-fifth-down-a-fourth path through the chart, and that is easier to rationalize and understand than "mostly 4/3 with 2/3 ratios interspersed when we need to drop an octave": C * 3/2 -> G G * 2/3 -> D D * 3/2 -> A A * 2/3 -> E E * 3/2 -> B B * 2/3 -> F# There is only one break from the pattern right here with two descending perfect fourths in a row: F# * 2/3 -> C# C# * 3/2 -> G# ... You can also restart from C going down to F and Bb once you reach F# and that gives you the typical Pythagorean tuning, but then you will have to explain why that happens to readers who are unfamiliar with tuning.