When I was exploring some alternate time signatures, I came across two references in the Wikipedia to "horogram patterns". Now, Google thinks this is a spelling error for hologram, and so searching for it doesn't turn up anything interesting.

Does anybody know what a horogram pattern is and how it relates to unusual time signatures?

  • 1
    see anaphoria.com/hrgm.PDF, google.com/… which I found by combining Kraig Grady (the composer associated with them in the wiki article) with horogram in my searches
    – Dave
    Oct 8 '14 at 13:22
  • elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm relates horograms to tuning
    – Dave
    Oct 8 '14 at 13:38
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    @Dave seems to have found the same links I'd have recommended. Be warned: "Horogram pattern" can send you off to similar mathematical structures applied to optical surfaces! By the way, a handy Google tip: enclose the desired word in quotes and you'll avoid the "autocorrect search term" annoyance. Oct 8 '14 at 13:45

Papers on Horogram Rhythms can be found at http://anaphoria.com/hrgm.PDF and at http://www.anaphoria.com/horo2.pdf with a discussion of a possibly better algorithm by Viggo Brun at http://anaphoria.com/ViggoRhythm.pdf

You use horograms to algorithmically generate long rhythmic and scalar patterns using the Golden Ratio (Phi).

Horagrams are diagrams consisting of concentric circles crossed by a set of radial lines. "Horagram" comes from the Latin "hora," hour. Just as you can see what time it is by observing the angle of the "little hand" on a conventional analog clock (or the shadow on a sundial if you are a medievalist), so you can tell what pitch is indicated by the angle of a radial line on a horagram. Source: 5- TO 9-TONE, OCTAVE-REPEATING SCALES: FROM WILSON'S GOLDEN HORAGRAMS OF THE SCALE TREE by David J. Finnamore

The complete explanation of Golden Horograms is far too complex to explain here so I suggest Finnamore's article above, which although it's talking about pitches could also be applied to meters.

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