[HN Gopher] The Tonnetz
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       The Tonnetz
        
       Author : mci
       Score  : 38 points
       Date   : 2025-10-18 07:30 UTC (4 days ago)
        
 (HTM) web link (thetonnetz.com)
 (TXT) w3m dump (thetonnetz.com)
        
       | mci wrote:
       | A recent blog post on thatsmaths.com was about Tonenetz, a
       | diagram of harmonic relationships of notes. Tonenetz means 'tone
       | network' in German :-)
        
         | gus_massa wrote:
         | Do you have a link to the post in thatsmaths?
        
           | mitchbob wrote:
           | https://thatsmaths.com/2025/10/16/music-and-maths-are-
           | inextr...
        
             | pasteldream wrote:
             | > the defects of this tuning method became evident and the
             | more flexible "well-tempered" tuning scheme was devised.
             | This ensures that the ratio of pitch between every two
             | adjacent notes is precisely the same.
             | 
             | The author seems to have confused well-temperament and
             | equal temperament.
             | 
             | It is also odd that he calls just intonation a
             | "simplification" of Pythagorean tuning.
        
       | tshaddox wrote:
       | I first became aware of this concept many years on Gary Garrett's
       | blog, where he primarily refers to it as "the lattice." His
       | introduction to the concept gives a brief history:
       | 
       | https://www.garygarrett.me/?p=342
       | 
       | More introduction to the lattice:
       | 
       | https://www.garygarrett.me/?p=995
       | 
       | https://www.garygarrett.me/?p=1632
       | 
       | https://www.garygarrett.me/?p=1696
       | 
       | Some comparison audio between equal temperament and just
       | intonation:
       | 
       | https://www.garygarrett.me/?p=1812
       | 
       | Some songs with lattice animations:
       | 
       | https://www.garygarrett.me/?p=103
       | 
       | https://www.garygarrett.me/?p=1253
       | 
       | I also like this book which Gary recommends, although it's very
       | challenging and I never made it all the way through:
       | 
       | https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...
        
       | juancroldan wrote:
       | As an indie music composer, this kind of unusual tone arrangement
       | is great for creativity, thanks! I noticed that the same triangle
       | will play different chords from time to time, is that on purpose?
        
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