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Maths vs. Music - Tuning and harmony
#29
RE: Is there a real chance that there is a multiverse?
(September 10, 2016 at 4:48 pm)Alex K Wrote: And last but not least, a comparison of an A major triad in pure tuning with the exact ratios 5/4 for the third and 3/2 for the fifth, and in equal tuning with 2^4/12 and 2^7/12 for the third and fifth.

https://dl.dropboxusercontent.com/u/4685...arison.mp3

It plays the exact ratios for 2 seconds, then the equal temperament for 2 seconds, then repeat. Equal temperament really sounds wrong when contrasted directly with the exact ratios...

The effect is maybe more subtle, but still very noticeable when everything is taken one octave lower, i.e. based on 220 hz.

https://dl.dropboxusercontent.com/u/4685...rison2.mp3

Well done.

if you really want to hear the difference, I recommend playing a simple cadence: I ii V I in major or i iv V i in minor.  The difference becomes very obvious then.

The problem is that you are (i think) using sin waves: it's such a pure sound that it sounds like single notes rather than chords.  I've considered writing a computer program that will let you choose how you derive each note by linking it to previous ones; for example, you could say, "Use the B that is the major 3rd of that G chord we used last bar," or "Use the B that is the perfect 5th above the e-minor (iii) chord that we modulated to" or whatever.  Ultimately, I'd like to do this with entire pieces of MIDI-recorded music, like say a Beethoven Sonata.  But the problem is that MIDI pitches are only adjustable in cents, making the MIDI system useless. So I'd have to collect the data using MIDI, and then do the math to adjust all the pitches and generate my own .wav files. So you could have the entire piece in a kind of "dynamic just tuning," something that I think nobody has attempted yet.

I think it's the kind of project that could land me a professorship somewhere, no?
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Messages In This Thread
Maths vs. Music - Tuning and harmony - by Thumpalumpacus - September 9, 2016 at 12:46 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 12, 2016 at 5:58 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 12, 2016 at 9:17 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 12, 2016 at 9:26 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 13, 2016 at 5:09 am
RE: Maths vs. Music - Tuning and harmony - by Alex K - September 13, 2016 at 5:14 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 13, 2016 at 7:04 am
RE: Is there a real chance that there is a multiverse? - by bennyboy - September 10, 2016 at 7:47 pm
RE: Maths vs. Music - Tuning and harmony - by Alex K - September 12, 2016 at 5:30 am
RE: Maths vs. Music - Tuning and harmony - by bennyboy - September 12, 2016 at 6:03 am
RE: Maths vs. Music - Tuning and harmony - by Alex K - September 12, 2016 at 6:20 am

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