User talk:Godtone: Difference between revisions

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::: 15/8 is a pretty different case to 16/15 IMO, and one of the reasons for preferring 15/14 and 17/16 over 16/15 is because they represent better intervals for ''stepping upwards'' while 16/15 represents a good interval for ''stepping downwards'', plus personal preference as aforementioned. Also consider that 15/8 can be expressed as (3/2)(5/4), both already existing in the list of superparticulars, while 16/15 = (4/3)/(5/4) and so is again implicit in existing superparticulars. This means that the lower superparticulars can be used to emphasize/help evidence these subtler intervals' existences in a chord. In other words, I believe prioritising the accuracy of the simpler superparticulars is worth sacrificing the accuracy of ''some'' more complex ones but that specific complex superparticulars of interest should ideally especially be represented with accuracy. For example, for stepping up, 15/14 is a pleasing wider minor second to me with a nice ring to it, and 17/16 a darker, more shimmery and slightly more familiar alternative. And it isn't that I don't take finer distinctions more seriously, just that, in the context of approximate systems, you (IMO) kind of compromise their 'seriousness' (with respect to JI) anyway, and I see simplification as a good thing. Also, IMO, 16/15's power of 2 isn't very easy to hear unless there are more tones emphasizing the 16 and I think this applies more generally for intervals whose numerators are powers of 2 greater than 8. Oh and out of curiosity, what is the largest (in cents) comma you're comfortable with (intentionally) tempering? [[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 21:57, 20 December 2020 (UTC)

:::: Well, I can indeed hear 16/15's power of two with just the two notes involved- particularly when the notes are set up high. I've done the experiments with Audacity using nearly pure tones, and 16/15 is the interval that strikes me as being the most natural for a leading tone in either direction. It may be true that I do compromise the seriousness of JI in some respects when it comes to those smaller commas, but the largest comma I'm comfortable with intentionally and directly tempering out for sure (outside of the 12edo-based systems that I'm actually quite familiar with) is the keenanisma, which is only about 4.503 cents, and even then, that is situational. When it comes to commas regarding fifths, I'd have to say Mercator's comma- which is about 3.615 cents wide- is the best, as it's the smallest 3-limit comma that can be tempered out for an EDO while still ending up with a reasonable step size. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:34, 20 December 2020 (UTC)

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	::: 15/8 is a pretty different case to 16/15 IMO, and one of the reasons for preferring 15/14 and 17/16 over 16/15 is because they represent better intervals for ''stepping upwards'' while 16/15 represents a good interval for ''stepping downwards'', plus personal preference as aforementioned. Also consider that 15/8 can be expressed as (3/2)(5/4), both already existing in the list of superparticulars, while 16/15 = (4/3)/(5/4) and so is again implicit in existing superparticulars. This means that the lower superparticulars can be used to emphasize/help evidence these subtler intervals' existences in a chord. In other words, I believe prioritising the accuracy of the simpler superparticulars is worth sacrificing the accuracy of ''some'' more complex ones but that specific complex superparticulars of interest should ideally especially be represented with accuracy. For example, for stepping up, 15/14 is a pleasing wider minor second to me with a nice ring to it, and 17/16 a darker, more shimmery and slightly more familiar alternative. And it isn't that I don't take finer distinctions more seriously, just that, in the context of approximate systems, you (IMO) kind of compromise their 'seriousness' (with respect to JI) anyway, and I see simplification as a good thing. Also, IMO, 16/15's power of 2 isn't very easy to hear unless there are more tones emphasizing the 16 and I think this applies more generally for intervals whose numerators are powers of 2 greater than 8. Oh and out of curiosity, what is the largest (in cents) comma you're comfortable with (intentionally) tempering? [[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 21:57, 20 December 2020 (UTC)		::: 15/8 is a pretty different case to 16/15 IMO, and one of the reasons for preferring 15/14 and 17/16 over 16/15 is because they represent better intervals for ''stepping upwards'' while 16/15 represents a good interval for ''stepping downwards'', plus personal preference as aforementioned. Also consider that 15/8 can be expressed as (3/2)(5/4), both already existing in the list of superparticulars, while 16/15 = (4/3)/(5/4) and so is again implicit in existing superparticulars. This means that the lower superparticulars can be used to emphasize/help evidence these subtler intervals' existences in a chord. In other words, I believe prioritising the accuracy of the simpler superparticulars is worth sacrificing the accuracy of ''some'' more complex ones but that specific complex superparticulars of interest should ideally especially be represented with accuracy. For example, for stepping up, 15/14 is a pleasing wider minor second to me with a nice ring to it, and 17/16 a darker, more shimmery and slightly more familiar alternative. And it isn't that I don't take finer distinctions more seriously, just that, in the context of approximate systems, you (IMO) kind of compromise their 'seriousness' (with respect to JI) anyway, and I see simplification as a good thing. Also, IMO, 16/15's power of 2 isn't very easy to hear unless there are more tones emphasizing the 16 and I think this applies more generally for intervals whose numerators are powers of 2 greater than 8. Oh and out of curiosity, what is the largest (in cents) comma you're comfortable with (intentionally) tempering? [[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 21:57, 20 December 2020 (UTC)

			:::: Well, I can indeed hear 16/15's power of two with just the two notes involved- particularly when the notes are set up high. I've done the experiments with Audacity using nearly pure tones, and 16/15 is the interval that strikes me as being the most natural for a leading tone in either direction. It may be true that I do compromise the seriousness of JI in some respects when it comes to those smaller commas, but the largest comma I'm comfortable with intentionally and directly tempering out for sure (outside of the 12edo-based systems that I'm actually quite familiar with) is the keenanisma, which is only about 4.503 cents, and even then, that is situational. When it comes to commas regarding fifths, I'd have to say Mercator's comma- which is about 3.615 cents wide- is the best, as it's the smallest 3-limit comma that can be tempered out for an EDO while still ending up with a reasonable step size. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 22:34, 20 December 2020 (UTC)