... of ... reinforce ... On real acoustic instruments, none of the interval ratios will be *exact* (even the best tuners commit small errors, and often ...
... Yes, in whole numbers. My survey just looked at -- you would call it? -- the utonal chords? with fractions, where that pattern (not that I'm arguing it...
... Yes. ... Rarer? Meaning the total waveform repeats more rarely? ... What do you mean? C-e-a is a triad. Over? ... than ... Not really -- my work doesn't...
Paul, ... Reasonable. On a purely electronically-tuned instrument, I'd expect tuning errors small enough that beats would take several seconds to evolve, and...
Kelly, ... Do listen to Paul! He makes more sense than I do - even to me! :) ... And not only laymen. Many mathematicians see pattern as being the core...
... No. The number pattern is less commom. What exactly do you mean by waveform? ... Sorry. I should use other terminology, as I distinguish inversions from...
Hello Concerning c-e-a, Paul wrote that it is "best understood" as 5:4:3/1, whereas Yahya wrote that 12:15:20 is "most informative." Someone here (Carl?) wrote...
... to ... And Yahya makes more sense to me than just about anyone. ... what ... to ... math ... This is a key point, and an excellent amplification of your...
... Less common where? ... The pattern of compression and rarefaction of the air or the pattern of movement of the speaker cone or of your eardrum, as a...
... Not quite -- 1/(5:4:3). ... Sorry, I didn't mean to favor one over the other. In terms of actual psychoacoustics, I believe 1/(5:4:3) is most convenient...
... In my 'survey' of utonal chords, now debunked, where I looked at the patterns of integers in the three fractions. ... pattern ... of ... Ok. (I thought...
... 5:4:3/1, ... actual ... while ... If ... the ... inversion) ... seventh ... My piano tuner is my tuning system! I'm still rather 'asleep' to tuning system...
Hello! After calculating a bunch of difference tones for various chords (the usual JI, 5-limit ones I find on the piano), I saw something that interested me:...
Hi Paul. paul wrote>In the minor 9th chord C2-Eb3-D4...you mention as ... Ab2), ... and 45- 24 = 21. Relative to the chord in question, these notes would be a...
... a. ... do ... No, but neither of these chords are in root position, and in regard to what you wrote above, both are in closed position (i.e., close- ...
... Then there probably isn't anything close to 3:5:8:13 on there. ... Well, get yourself a piano tuning wrench and wake up! ... What tunings are you listening...
... How do you find JI chords on the piano if it's tuned by a standard piano tuner? ... I'm confused. 4:5:9 could be c-e-d', but where does the b come in? ... ...
... You're Right. ... of ... Excuse me. I meant major ninth chord. ... minor ... tertial ... outer ... Right. ... I'm defining 'chord' as having an outer...
... favorite ... So did you mean for a different set of numbers to go along with the letters, or a different set of letters to go along with the numbers? A C...
hi Paul. ... the ... numbers? ... a ... Actually, I was thinking of c-e-b-d', but haven't calculated the numbers for any quatrads yet. This actually brings up...
... But you mean 8:10:15:18, yes? ... You mean like as part of e-g#-b-d'? c-e-b-d' isn't a dominant seventh chord. ... In Partch's world, you're either playing...
... Yes. ... seventh > chord. I mean, e-b-d', alone, or even when it's part of c-e-b-d', reminds me of e-g#-b-d without the 3rd (gutted, and liking its...
... the ... I'm suprised you hear a g# rather than a g missing in c-e-b-d'. ... on ... If you're interested in harmonies up to a prime-limit of 7, probably the...
... I hear the absence of g# ...(as well as the 'turned around' minor seventh chord, with 6/5 on top).... it's hard to describe, but it's sort of my modas...
... Yes. Plomp and Levelt were the original authors of the relevant paper in this area, which Sethares and others took up in their way later. ... Searching the...
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