Linus: Difference between revisions

The name '''winwood''' is proposed for the rank three 13-limit temperament tempering out the valerisma 137858491849/137438953472 (13^10 * 2^-37), the higherlovesma 578509309952/576650390625 (7^10 * 2^9 * 5^-10 * 3^-10), and the rollwithitsma 39135393/39062500 (11^5 * 3^5 * 5^-10 * 2^-2). As a consequence of the latter two, it also tempers out the kalisma (9801/9800).

Winwood has a period of 1/10 of an octave, and so it is named by analogy with blackwood and whitewood (and is also a tribute to Steve Winwood, [http://www.keyboardmag.com/lessons/1251/synth-soloing-in-the-style-of-steve-winwood/50240 whose signature sound] involves the use of very narrow pulse waves. This particular type of waveform amplifies the higher harmonics a lot and might make it easier to hear consonances involving them, making it a promising option for microtonal work). Unlike blackwood and whitewood, winwood's accuracy is quite high owing to the small size of the commas it tempers out.

Tempering out the valerisma means that [[16/13|16:13]] is represented by exactly 360 cents, tempering out the higherlovesma means that [[15/14|15:14]] is represented by exactly 120 cents, and tempering out the rollwithitsma means that [[33/25|33:25]] is represented by exactly 480 cents. Thus these intervals form circles of 10, 10, and 5, respectively. Because the kalisma is also tempered out, 99:70 and its inversion are both represented by the 600 cent tritone.

Good tunings for winwood include [[80edo|80edo]], [[130edo|130edo]], and [[270edo|270edo]]; there may be others.

[[Category:winwood]]

[[Category:13-limit]]