tag:blogger.com,1999:blog-2688138290971915830.post2877811486792942724..comments2024-03-25T21:35:47.298-07:00Comments on Interdependent Science: Seventh ChordsJimKhttp://www.blogger.com/profile/16167191806249119508noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-2688138290971915830.post-19568444702034347572018-06-08T13:11:47.189-07:002018-06-08T13:11:47.189-07:00and here is an 8x24x24 mesh: https://app.box.com/s...and here is an 8x24x24 mesh: https://app.box.com/shared/static/5rl2ii4ab1kgzb9x8s6h0gfwc29o3rsi.mp3JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-85148515688156029172018-06-07T19:10:19.253-07:002018-06-07T19:10:19.253-07:00I created another version, where the toroidal mesh...I created another version, where the toroidal mesh is two dimensional, 40x40, instead. The longer distance allow for a greater range of fluctuation. https://app.box.com/shared/static/b1ms0dx1e94im3j1vw2ggd8ag74a66zv.mp3<br />JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-61488496032918069912018-06-07T17:06:26.295-07:002018-06-07T17:06:26.295-07:00ooops I think I got emic and etic backwards! That&...ooops I think I got emic and etic backwards! That's what I get for trying to look smart! https://en.wikipedia.org/wiki/Emic_and_eticJimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-27235186352832513472018-06-07T17:03:44.401-07:002018-06-07T17:03:44.401-07:00yeah exactly I am a 5-limit fan rather than 3- or ...yeah exactly I am a 5-limit fan rather than 3- or 7-limit! These days I am less interesting in the "emic" approach of overtone ratios etc., though of course that is always at the foundation. I am more interested in an "etic" angle, looking at the network generated by some primitive intervals in a pitch set, and how that network can be a basis for structure and pattern. <br />JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-58603708241015016642018-06-07T15:52:54.013-07:002018-06-07T15:52:54.013-07:00You could generate a 12-scale out of 53TET the Pyt...You could generate a 12-scale out of 53TET the Pythagorean way by clocking out 12 stacked fifths (keep adding 31 modulo 53) from a tonic at 0, i.e. 0, 31, 62, 93, 124, 155, 186, 217, 248, 279, 310, 341 to give you 0, 31, 9, 40, 18, 49, 27, 5, 36, 14, 45 and 23. Re-ordered this is 0, 5, 9, 14, 18, 23, 27, 31, 36, 40, 45, 49.<br />That would give you minor/major third at 14 and 18 and minor/major 7th at 45 and 49.<br />But you appear to be using 5/4 as a frequency ratio (as opposed to Pythagorean 81/64) to get your major third at, as you say, 17. If that's from using direct frequency harmonics, an actual 'seventh harmonic' approach would give you 42 (for a minor 7th) and you'd need to go up to the 15th harmonic for a major 7th at step 48 out of 53.<br />But I feel that - however you generate your scale (you need at least 10-tonicity to introduce a minor third and at least 11-tonicity to begin distinguishing major and minor 7ths) - three major thirds will always overshoot both 7ths (ending up too close to the octave to call) and three minor thirds will always undershoot and plonk you into the sixth's 'sphere of influence'.<br /><em><strong>On the other hand</strong></em>, he said boldly, that 'sixth' sound has often been used - musically - as a subdominant preparation for a cadential dominant (7th!) approach for resolution. So, functionally, yer 333 could arguably be a kind of a 7th. Everybody wins!LemoUtanhttps://www.blogger.com/profile/11110031436968511583noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-31103218603613235162018-06-07T13:04:01.417-07:002018-06-07T13:04:01.417-07:00In this experiment, I just used whatever necessary...In this experiment, I just used whatever necessary inversions to fit all the chords into a single octave span.JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-31853137992724439212018-06-07T13:02:16.884-07:002018-06-07T13:02:16.884-07:00I guess a major seventh in 53TET should be a major...I guess a major seventh in 53TET should be a major third on top of a perfect fifth, i.e. 17+31 = 48. The eight seventh chords I am proposing will have their sevenths at 42, 45, 48, and 51 steps above the root. JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-55643396386162541612018-06-07T12:58:51.860-07:002018-06-07T12:58:51.860-07:00In 53TET, a minor third is 14 steps and a major th...In 53TET, a minor third is 14 steps and a major third is 17 steps. I don't know what an "actual 7th" ought to be! I don't know music theory at all - this exploration I'm doing is a kind of attempt to understand music theory in a way that works for me. I am slowly discovering that the work needed is much more reshaping my way of thinking rather than reshaping music theory! But I seem to be a tough nut! <br /><br />A sixth is probably a minor third below an octave, so that's 53-14=39 in 53TET. 14+14+14 is 42 so that's a decent bit higher than the sixth. 17+17+17=51, a bit short of an octave. So maybe 53TET is rich enough that all eight seventh chords can be heard unambiguously. Of course hearing them is going to depend on context. My toroidal mesh is a mathematical way to create some context. I offer it as an invitation to some brave musical competent to find meaningful musical context for these various microtonal sevenths!JimKhttps://www.blogger.com/profile/16167191806249119508noreply@blogger.comtag:blogger.com,1999:blog-2688138290971915830.post-79943369815557613052018-06-07T10:58:23.001-07:002018-06-07T10:58:23.001-07:00I recently had a similar go at thirteenth chords a...I recently had a similar go at <a href="https://mi.doh.so/2018/05/unlucky-4-sum.html" rel="nofollow">thirteenth chords</a> and concluded there were really only 28 - for various reasons, including the requirement that the highest note in the thirdy-stack actually <em>be</em> a thirteenth (including being a minor thirteenth).<br /><br />For 7ths, although there are - as you say - eight ways to stack thirds, two of 'em might thus be considered illegitimate (4+4+4 athletically skips right over the actual 7th and 3+3+3+3 replaces it with a 6th).<br /><br />Bearing this in mind, I'd find enumerating essentially distinct 13ths (including inversions thereof) built from stacked major and minor thirds within 53TET rather terrifying! :)LemoUtanhttps://www.blogger.com/profile/11110031436968511583noreply@blogger.com