Brilliant. I watched all three and he really makes it easy to follow - he explains the key points so you don't have to do all that math, but it really neat to see what's going on behind the scenes.
Thank you for this series. I'd be lying if I said you didn't lose me even once, but I learned a great deal, and on second watch a lot of things fell into place.
Very well done! Applause is in order. Thank you for this cool resource. I often like to teach this stuff, and you’ve made something I’ll be sharing with interested students and other curious friends.
I've been looking around on the internet and I finally understand scale construction now. Thanks for these videos! I still don't understand chords though. Why would some combinations of notes sound good while others sound discordant?
It's "lon." The more powerful slide rules back in the day included "lon" scales, which were based on base 'e' logarithms. The Keuffel & Esser 68-1100 "Deci-Lon" is an example of that. It even has "Lon" in the name. In the large manual for the slide rule, the word's "natural" and "log" were never uttered back to back...not once. Instead, it defined the lon as the "natural or Napierian Logarithm." This is because, in practice, it was quite common for some to just call them lons, for short. So it's not a made up word...merely an alternative way to refer to the log base 'e'.
Either works. As most calculators do not have a Log2 button, but do have a Ln button, he seems to have chosen to solve his equations using Ln, using the change-of-base formula Log2(x) = Ln(x)/Ln2.
He did say that you could use these expanded fractions to create other scales by privileging something other than the perfect fifth. It’s not really practical to explore all of them in a video...
@@somasundaramsankaranarayan4592 19-TET is a meantone temperament with a flat 5th but a virtually perfect minor third. Here is a piece I wrote in 19-TET: ruclips.net/video/L8zkQp4egp0/видео.html
What an incredible summary of this complicated topic. It was truly riveting the whole way through. I hope you make more videos like this!
Excellent presentation - The most useful one I've come across so far regarding tuning and microtonal sounds. I will be sharing this :-)
I'm so happy there are other people out there who love math who also love music! 🙏
Music is math! Perhaps math is music?
These series is the best ever explanation of mathematics behind scales and temperaments I found on internet
That was an incredible series! Thank you so much for this!
Brilliant. I watched all three and he really makes it easy to follow - he explains the key points so you don't have to do all that math, but it really neat to see what's going on behind the scenes.
Thank you for this series. I'd be lying if I said you didn't lose me even once, but I learned a great deal, and on second watch a lot of things fell into place.
Thank you so much for such a wonderful presentation. Truly appreciated it!
This series of video is amazing!!!
Exhausting but interesting.
Very well done! Applause is in order. Thank you for this cool resource. I often like to teach this stuff, and you’ve made something I’ll be sharing with interested students and other curious friends.
Thanks for the series. Nice job!
Great explanation. Learnt a lot by watching this 3 part series.
All Great stuff!! Just need time to digest it all!
Great summary!
I love how maths keep telling us that it ultimately has no link with music, but we still stubbornly came up with a system that is relatively good.
I went to your channel to try learn music but ended up learning Einstein💀
I always thought 12 was used because that’s the number with most factors up until that point.
I've been looking around on the internet and I finally understand scale construction now. Thanks for these videos! I still don't understand chords though. Why would some combinations of notes sound good while others sound discordant?
Great videos. But since each note on a piano, for example, can but tuned individually. Why not make them all perfect?
Drop some names on those many-octaves composers, because the works would be beyond the range of human hearing.
I've never heard anyone call log "lawn."
It's "lon." The more powerful slide rules back in the day included "lon" scales, which were based on base 'e' logarithms. The Keuffel & Esser 68-1100 "Deci-Lon" is an example of that. It even has "Lon" in the name. In the large manual for the slide rule, the word's "natural" and "log" were never uttered back to back...not once. Instead, it defined the lon as the "natural or Napierian Logarithm." This is because, in practice, it was quite common for some to just call them lons, for short. So it's not a made up word...merely an alternative way to refer to the log base 'e'.
2:02 it’s better to take log base 2
Could you make a video explaining the 833 cents scale?
These are great! under 100 views? not for long!
What wikipedia page did you find the table of comparisons between tunings?
2^(2/1200). That's my 2 cents.
That deserves more recognition! 😄
nice work
I guess what you really mean is Log2(x), or the base 2 log, rather of Ln, which is the base of e or 2.718?
Either works. As most calculators do not have a Log2 button, but do have a Ln button, he seems to have chosen to solve his equations using Ln, using the change-of-base formula Log2(x) = Ln(x)/Ln2.
I’m writing music in 19-TET, and it’s a pity that you left it out. It has an almost-perfect minor third and a better major third.
He did say that you could use these expanded fractions to create other scales by privileging something other than the perfect fifth. It’s not really practical to explore all of them in a video...
Does the 19-TET have a worse perfect 5th? Is that why it didn't get appear in the continued fraction series?
@@somasundaramsankaranarayan4592 19-TET is a meantone temperament with a flat 5th but a virtually perfect minor third. Here is a piece I wrote in 19-TET: ruclips.net/video/L8zkQp4egp0/видео.html
Merci, an Al Gore Rhythm comment.
Good bye!!
You mispronounced "ln"; ln is called the natural logarithm.
Are you Einstein?
Too much math.