Now I somewhat get what they are talking about but I simply don't understand that math. I am simply too ignorant about the terms and basically everything they are talking about.

Any math wizards around here that are now laughing at my pathetic ignorance? I sure hope so because this is the only part I can't get my head around.

1: What the fuck is gradus
2: so fast asi can tell this is just about alternate tuning systems. I just skimmed. But essentially when you divide a frequency by different ratios you get different tuning systems

1: What the fuck is gradus
2: so fast asi can tell this is just about alternate tuning systems. I just skimmed. But essentially when you divide a frequency by different ratios you get different tuning systems

Yes that is what I thought as well. It is how he derives the basic intervals, 1st, 8th, 5th, 3rd etc. from the arithmetic. But I don't understand how he does it. like how do you derive the fifth from the 1st and the octave by arithmetic? half of an octave is not a 5th right? I don't know, I shouldn't even by trying. I am just hoping there is someone on this forum who has a bit of knowledge in math who can give me a short down to earth summery or point me in some direction where I am able to find out for myself.

This seems to be hinting at the 'Just intonation' tuning system. Where all intervals are whole number ratios to each other. Some people call this tuning more 'Natural' or stable, and I actually did some writing in a just system when I was in school.

Yes that is what I thought as well. It is how he derives the basic intervals, 1st, 8th, 5th, 3rd etc. from the arithmetic. But I don't understand how he does it. like how do you derive the fifth from the 1st and the octave by arithmetic? half of an octave is not a 5th right? I don't know, I shouldn't even by trying. I am just hoping there is someone on this forum who has a bit of knowledge in math who can give me a short down to earth summery or point me in some direction where I am able to find out for myself.

Look at a guitar string. Cut the string in half and you're at the 12th fret - 1 octave. Cut that distance in half and you're at the 7th fret - a fifth. Et cetera. If you were to calculate the fundamental frequency of a note and then compare that to the frequency of an interval above it, it would approximate a certain (mathematical) interval. It doesn't exactly line up perfectly though which is inconvenient for writing music or for instance tuning a piano, so there's various tuning systems that nudge the ratios slightly so it all wraps around nicely into a circle instead of a spiral. That way we can have a 12 tone system that works for any key instead of having a near infinite set of intervals that change depending on the root note of the key.

Fairly interesting if you like math and geometry and want to understand the science behind tuning systems. But if you're going to beat your head against some dense theory, your time would be better spent reading a book on jazz harmony or something else that actually has a practical use in composition. Although a light understanding of how the intervals are derived is useful in understanding why certain intervals are more important and where stability, consonance and dissonance come from. There's a reason the power chord is so ubiquitous; it's the simplest and most stable two-note chord you can play.