User talk:Aura: Difference between revisions

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:::::: For the record, I'm doing this with 159edo in mind, and this is not a meantone temperament as the syntonic comma is not tempered out. I'm not keen on using too many numeric descriptors like "pental" or "septimal" or even "undecimal" for this particular idea, as at the end of the day, my goal is to build off of the SHEFKHED interval naming system for EDOs up to 160edo. I should also point out that not all Pythagorean intervals are Diatonic intervals- only those with an odd limit of 243 or less, therefore, I'm thinking that "Diatonic" is the label that ought to be privileged over "Pythagorean". On a semi-related note, my preferred major scale consists of the intervals 1/1, 9/8, 5/4, 4/3, 3/2, 27/16, 15/8, and 2/1, and I do in fact build directly off of this scale for my diatonic chords- yes, the grave fifth occurs between the sixth and the third, and for me, this serves to amplify the diatonic functions of the VIm chord, as this kind of tuning says "we're not done yet", especially in deceptive cadences. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:39, 1 September 2020 (UTC)

:::::: While I'm on this whole topic of Diatonic intervals, I should mention that I prefer the notes of all my scales to connect directly to the tonic by means of the intervals between the tonic and the other notes in the scale having a power of two in the numerator and or the denominator- that said, I still recognize that 6/5 doesn't meet this criteria when this interval occurs between the I and the IIIm scale degrees, and thus, my preferred minor scale consists of the intervals 1/1, 9/8, 77/64, 4/3, 3/2, 8/5, 16/9, and 2/1. It is for this reason- along with the fact that the 7-limit finds frequent use among barbershop quartets and the like as accidentals in otherwise diatonic keys- that I would classify 11/8, 16/11, 7/4, and 8/7 as "Paradiatonic" intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:09, 1 September 2020 (UTC)

:::::: Now, back to this discussion of notation, some will undoubtedly ask where this process of coming up with labels for scale steps of differing edos should stop, and I have an answer for that as well. There is a step-size limit at play in which the step size should be greater than 7 cents. This is because at a step size of 7 cents, the distance halfway between steps is 3.5 cents, which, from what I'm gathering, is below the average just noticeable difference between pitches. At step sizes of 7 cents and smaller, the steps will begin to bleed into one another and become indistinguishable from one another to even the best trained ears. Thus, any edo with a step size of 7 cents or less is ineligible for this kind of extensive process of labeling different ~~interval~~ sizes. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:51, 1 September 2020 (UTC)

:::::: Now, back to this discussion of notation, some will undoubtedly ask where this process of coming up with labels for scale steps of differing edos should stop, and I have an answer for that as well. There is a step-size limit at play in which the step size should be greater than 7 cents. This is because at a step size of 7 cents, the distance halfway between steps is 3.5 cents, which, from what I'm gathering, is below the average just noticeable difference between pitches. At step sizes of 7 cents and smaller, the steps will begin to bleed into one another and become indistinguishable from one another to even the best trained ears. Thus, any edo with a step size of 7 cents or less is ineligible for this kind of extensive process of labeling different step sizes. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:51, 1 September 2020 (UTC)

:::::: I can anticipate that some may object that I should draw the line for defining edo steps at something more substantial like 13.5 cents, but I while concur that an edo step size between 7.5 and 13.5 cents is not viable in the traditional musical sense as a step between consecutive notes, I do notice that it does have a usage as a comma pump, and therefore, it has musical value as an edo step size for purposes of modulation, especially for modulating Jacob-Collier-style between keys. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:49, 1 September 2020 (UTC)

:::::: One of the problems I have with notation that doesn't take these kinds of kleismatic differences into account is that without such distinctions, it's hard to determine which notes should have which tunings in order to accomplish a seamless modulation between keys on different circles of fifths, and I've honestly found that to be a significant problem with transcriptions of Jacob Collier's rendition of In the Bleak Midwinter in particular. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:33, 1 September 2020 (UTC)

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 :::::: For the record, I'm doing this with 159edo in mind, and this is not a meantone temperament as the syntonic comma is not tempered out.  I'm not keen on using too many numeric descriptors like "pental" or "septimal" or even "undecimal" for this particular idea, as at the end of the day, my goal is to build off of the SHEFKHED interval naming system for EDOs up to 160edo.  I should also point out that not all Pythagorean intervals are Diatonic intervals- only those with an odd limit of 243 or less, therefore, I'm thinking that "Diatonic" is the label that ought to be privileged over "Pythagorean".  On a semi-related note, my preferred major scale consists of the intervals 1/1, 9/8, 5/4, 4/3, 3/2, 27/16, 15/8, and 2/1, and I do in fact build directly off of this scale for my diatonic chords- yes, the grave fifth occurs between the sixth and the third, and for me, this serves to amplify the diatonic functions of the VIm chord, as this kind of tuning says "we're not done yet", especially in deceptive cadences. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:39, 1 September 2020 (UTC)
 :::::: While I'm on this whole topic of Diatonic intervals, I should mention that I prefer the notes of all my scales to connect directly to the tonic by means of the intervals between the tonic and the other notes in the scale having a power of two in the numerator and or the denominator- that said, I still recognize that 6/5 doesn't meet this criteria when this interval occurs between the I and the IIIm scale degrees, and thus, my preferred minor scale consists of the intervals 1/1, 9/8, 77/64, 4/3, 3/2, 8/5, 16/9, and 2/1.  It is for this reason- along with the fact that the 7-limit finds frequent use among barbershop quartets and the like as accidentals in otherwise diatonic keys- that I would classify 11/8, 16/11, 7/4, and 8/7 as "Paradiatonic" intervals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:09, 1 September 2020 (UTC)
-:::::: Now, back to this discussion of notation, some will undoubtedly ask where this process of coming up with labels for scale steps of differing edos should stop, and I have an answer for that as well.  There is a step-size limit at play in which the step size should be greater than 7 cents.  This is because at a step size of 7 cents, the distance halfway between steps is 3.5 cents, which, from what I'm gathering, is below the average just noticeable difference between pitches.  At step sizes of 7 cents and smaller, the steps will begin to bleed into one another and become indistinguishable from one another to even the best trained ears.  Thus, any edo with a step size of 7 cents or less is ineligible for this kind of extensive process of labeling different interval sizes. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:51, 1 September 2020 (UTC)
+:::::: Now, back to this discussion of notation, some will undoubtedly ask where this process of coming up with labels for scale steps of differing edos should stop, and I have an answer for that as well.  There is a step-size limit at play in which the step size should be greater than 7 cents.  This is because at a step size of 7 cents, the distance halfway between steps is 3.5 cents, which, from what I'm gathering, is below the average just noticeable difference between pitches.  At step sizes of 7 cents and smaller, the steps will begin to bleed into one another and become indistinguishable from one another to even the best trained ears.  Thus, any edo with a step size of 7 cents or less is ineligible for this kind of extensive process of labeling different step sizes. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:51, 1 September 2020 (UTC)
 :::::: I can anticipate that some may object that I should draw the line for defining edo steps at something more substantial like 13.5 cents, but I while concur that an edo step size between 7.5 and 13.5 cents is not viable in the traditional musical sense as a step between consecutive notes, I do notice that it does have a usage as a comma pump, and therefore, it has musical value as an edo step size for purposes of modulation, especially for modulating Jacob-Collier-style between keys. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:49, 1 September 2020 (UTC)
 :::::: One of the problems I have with notation that doesn't take these kinds of kleismatic differences into account is that without such distinctions, it's hard to determine which notes should have which tunings in order to accomplish a seamless modulation between keys on different circles of fifths, and I've honestly found that to be a significant problem with transcriptions of Jacob Collier's rendition of In the Bleak Midwinter in particular. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:33, 1 September 2020 (UTC)