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Equal Beating Tunings of Essentially Tempered Chords
I've been recently spending quite a bit of time listening to these chords with the woodwinds section available in the latest Logic Express. When I reached the essentially tempered chords, realizing that they can't be tuned beatless, wondered if they could be tuned such that each interval has the same beat. Turns out in many cases they can, and have rational solutions. In my opinion they sound better this way. There's a fairly straightforward way of solving this for an arbitrary number of notes. Some of you probably already know of it.
As a concrete example, the Marvel chord 1/1-5/4-7/5-14/9 can be tempered as 1/1-121/97-136/97-151/97. With 220 Hz as 1/1, all intervals will beat at about 2.3 Hz. That's calculated based on the idea that the ratio of each pair of fractions approximates 5/4, 9/8, 10/9, and 9/7 respectively.
Is there already a page for an idea like this? If not, would someone please direct me to the best place to start one?
- BryceHathaway November 06, 2015, 03:31:13 PM UTC-0800
15-limit or 19-limit?
- xenwolf October 19, 2011, 12:32:32 AM UTC-0700
is it 7-limit or 19-limit?
- xenwolf October 19, 2011, 12:30:09 AM UTC-0700
thank you, Gene :-)
- xenwolf October 19, 2011, 12:21:49 AM UTC-0700
Are we sticking to only codimension 1 here? Because if not, 1/1-7/6-11/8-8/5 deserves a shoutout, perhaps even 1/1-7/6-11/8-8/5-15/8-11/10-9/7-3/2.
Maybe in the future it would be nice to have a 2D table organizing everything by limit and codimension.
- mbattaglia1 September 17, 2011, 01:46:26 AM UTC-0700
I forgot to add "orwell tetrad" to the list, though the page around for while.
- genewardsmith September 17, 2011, 02:13:05 PM UTC-0700