{"id":647,"date":"2013-01-14T10:53:56","date_gmt":"2013-01-14T18:53:56","guid":{"rendered":"http:\/\/www.garygarrett.me\/?page_id=647"},"modified":"2014-04-20T19:19:37","modified_gmt":"2014-04-21T02:19:37","slug":"for-allaudin-and-friends","status":"publish","type":"page","link":"https:\/\/www.garygarrett.me\/?page_id=647","title":{"rendered":"For Friends of the Lattice"},"content":{"rendered":"

This is a repository for videos of particular interest to fans of the lattice and just intonation.<\/p>\n

In these videos, red represents the bass, yellow the melody, and orange the harmonies. The videos show motion of the notes on a 5-limit lattice, with a few 7-limit notes added.<\/p>\n

The notes are named\u00a0in the following way:<\/p>\n

Start with the basic just major scale, 1 thru 7 (1\/1, 9\/8, 5\/4, 4\/3, 3\/2, 5\/3, 15\/8)<\/p>\n

+ is up a Didymic comma (~22 cents)<\/p>\n

– is down a Didymic comma<\/p>\n

# is up a chromatic semitone (~70 cents)<\/p>\n

b is down a chromatic semitone<\/p>\n

7 is down ~49 cents, the difference between the septimal notes and their nearby JI namesakes. For example, a b7 (9:5) is at 1018 cents, and a 7b7 (7:4) is at 969, 49 cents flatter.<\/p>\n

Thanks to composer\u00a0Ben Johnston<\/a>\u00a0for +, -, and 7. I haven’t found a use for reciprocal sevens (yet), so I don’t have them on my lattice. If I add them, I’ll use Johnston’s upside-down 7 for the accidental, and they’ll be 49 cents sharp of their namesake.<\/p>\n

This system gives every note in the 7-limit lattice\u00a0a unique name, and defines its exact pitch.<\/p>\n

————————————————————<\/p>\n

These videos do the best job yet of comparing equal temperament with just intonation.<\/p>\n

The piece is example 22.10 in Harmonic Experience<\/a>. It is a one-minute tour of the lattice, an illustration of how music can move short distances in harmonic space and remain sensible to the ear while being very adventurous. I think it’s a beautiful composition. I got to know it very well in the making of the videos.<\/p>\n

The first video features W.A. Mathieu playing the piece on his excellently tuned piano. This is perfect equal temperament.<\/p>\n

For the second piece, I retuned the piano to the actual lattice pitches. There are 28 distinct notes in this soundtrack. I used the original track as a template for dynamics and timing, created a set of midi files that were restricted to 12-note regions of the lattice, mixed them down separately and recombined them.<\/p>\n

Going back and forth between these videos gives a great feel for what each tuning brings to the party.<\/p>\n

The notation is my usual, with letter names instead of numbers.\u00a0Works well, as long as it’s written in the key of C.<\/p>\n