Search found 1099 matches

by Dave Keenan
Sat Sep 17, 2022 2:06 pm
Forum: The lounge
Topic: Truncated Integer-Limit Triangle (TILT)
Replies: 0
Views: 253

Truncated Integer-Limit Triangle (TILT)

[This is a draft of a section from a textbook chapter that Douglas Blumeyer and I are working on. I have placed it here temporarily because I want to refer to it from this feudal primes post .] DRAFT Truncated integer limit triangle (TILT) As we (Dave and Douglas) developed this tuning article serie...
by Dave Keenan
Sat Sep 03, 2022 6:55 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4612#p4612] By searching on "2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73" (wooden primes) in the OEIS, I found...
by Dave Keenan
Sat Sep 03, 2022 6:26 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4611#p4611] Here at last are the 6th-order-limit nobles as PC-vectors, in Stern-Brocot-tree reading-order of their medie...
by Dave Keenan
Sat Sep 03, 2022 4:01 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4610#p4610] We like to visualise the common factors among a set of rational pitches by displaying them on a prime lattic...
by Dave Keenan
Fri Sep 02, 2022 6:15 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4609#p4609] I've had some fun naming the orders of nobles on the Stern-Brocot tree. To get enough names, I've rationalis...
by Dave Keenan
Fri Sep 02, 2022 2:20 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4608#p4608] In RTT it is convenient that we have an obvious ordering of primes, so that unless we are told otherwise, a ...
by Dave Keenan
Fri Sep 02, 2022 10:40 am
Forum: The lounge
Topic: Listen to Merciful/Just cadences - a gem from Margo Schulter
Replies: 2
Views: 2462

Re: Listen to Merciful/Just cadences - a gem from Margo Schulter

I'm uploading these documents here as a backup. The originals are at http://www.bestii.com/~mschulter/ and can be seen/heard above.
by Dave Keenan
Thu Sep 01, 2022 9:20 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4607#p4607] Here's a 2D table of the small feudal integers we've been discussing. Only the units and fundamental-primes ...
by Dave Keenan
Thu Sep 01, 2022 4:13 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4606#p4606] I've been somewhat glossing over the idea of "units" — those integers of ℤ[ϕ] (and hence ℚ(√5)) th...
by Dave Keenan
Wed Aug 31, 2022 8:45 pm
Forum: The lounge
Topic: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]
Replies: 9
Views: 1673

Re: Noble frequency ratios as prime-count vectors in ℚ(√5) [superseded]

[Note: This thread is of historical interest only. Please see the updated version (using a better choice for the fundamental primes) at https://forum.sagittal.org/viewtopic.php?p=4605#p4605] Here is a table of the first 32 (superunison) noble numbers, working our way down the Stern-Brocot tree, sho...