User talk:Xenwolf: Difference between revisions

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== 311 EDO huge table ==

311 EDO is a one-of-a-kind extremely consistent system to the point it can be said to be the first true melodic model of the harmonic series itself. Therefore to understand the structure of the harmonic series (at least in the 41-limit add-73) without making it impractical, it would be useful to use 311 EDO, and 311 EDO is a great alternative to cents for this reason (which requires smaller numbers and only round numbers) because of being distinctly consistent in the [[23-odd-limit]] and consistent in the 41-prime-limited 77-odd-limit with prime harmonic 73 included as the only prime over 41 and under 81 which is more in tune than out of tune (which is to say its step error is less than a quarter), but furthermore, because of it fitting the way 311 EDO maps the harmonic series by filling a gap and because of it being an odd prime with less error than all previous primes. 311 EDO is therefore a natural system to inspect when looking at ways of modelling higher-limit systems and has important connections with many simpler systems. Just one example would be [[Canousmic_temperaments#Superlimmal|Superlimmal]], the 29-limit 80&311 temperament. Another reason it is a one-of-a-kind system is that in terms of having rooted harmonics with less than 25% error each, I did a search before in Python 3 and there is nothing that beats it until over 20 thousand, meaning it is simultaneously the first and last EDO to truly approximate the harmonic series, and the fact it does it up to a very large subset of the 77-odd-limit makes it worth inspecting the structure of for anyone wishing to learn medium-to-high-complexity tempered JI/odd-limits. Sorry if I've overstressed my point. Also the other table has been there for as long as I remember, and I felt it was both incomplete and messy so I wanted a table from a more systematic approach.

311 EDO is a one-of-a-kind extremely consistent system to the point it can be said to be the first true melodic model of the harmonic series itself. Therefore to understand the structure of the harmonic series (at least in the 41-limit add-73) without making it impractical, it would be useful to use 311 EDO, and 311 EDO is a great alternative to cents for this reason (which requires smaller numbers and only round numbers) because of being distinctly consistent in the [[23-odd-limit]] and consistent in the 41-prime-limited 77-odd-limit with prime harmonic 73 included as the only prime over 41 and under 81 which is more in tune than out of tune (which is to say its step error is less than a quarter), but furthermore, because of it fitting the way 311 EDO maps the harmonic series by filling a gap and because of it being an odd prime with less error than all previous primes. 311 EDO is therefore a natural system to inspect when looking at ways of modelling higher-limit systems and has important connections with many simpler systems. Just one example would be [[Canousmic_temperaments#Superlimmal|Superlimmal]], the 29-limit 80&311 temperament. Another reason it is a one-of-a-kind system is that in terms of having rooted harmonics with less than 25% error each, I did a search before in Python 3 and there is nothing that beats it until over 20 thousand, meaning it is simultaneously the first and last EDO to truly approximate the harmonic series, and the fact it does it up to a very large subset of the 77-odd-limit makes it worth inspecting the structure of for anyone wishing to learn medium-to-high-complexity tempered JI/odd-limits. Sorry if I've overstressed my point. Also the other table has been there for as long as I remember, and I felt it was both incomplete and messy so I wanted a table from a more systematic approach. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:17, 27 December 2021 (UTC)

Revision as of 23:17, 27 December 2021 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,289 edits →311 EDO huge table: new section ← Older edit		Revision as of 23:17, 27 December 2021 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,289 edits m →311 EDO huge table Newer edit →
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	== 311 EDO huge table ==		== 311 EDO huge table ==

	311 EDO is a one-of-a-kind extremely consistent system to the point it can be said to be the first true melodic model of the harmonic series itself. Therefore to understand the structure of the harmonic series (at least in the 41-limit add-73) without making it impractical, it would be useful to use 311 EDO, and 311 EDO is a great alternative to cents for this reason (which requires smaller numbers and only round numbers) because of being distinctly consistent in the [[23-odd-limit]] and consistent in the 41-prime-limited 77-odd-limit with prime harmonic 73 included as the only prime over 41 and under 81 which is more in tune than out of tune (which is to say its step error is less than a quarter), but furthermore, because of it fitting the way 311 EDO maps the harmonic series by filling a gap and because of it being an odd prime with less error than all previous primes. 311 EDO is therefore a natural system to inspect when looking at ways of modelling higher-limit systems and has important connections with many simpler systems. Just one example would be [[Canousmic_temperaments#Superlimmal\|Superlimmal]], the 29-limit 80&311 temperament. Another reason it is a one-of-a-kind system is that in terms of having rooted harmonics with less than 25% error each, I did a search before in Python 3 and there is nothing that beats it until over 20 thousand, meaning it is simultaneously the first and last EDO to truly approximate the harmonic series, and the fact it does it up to a very large subset of the 77-odd-limit makes it worth inspecting the structure of for anyone wishing to learn medium-to-high-complexity tempered JI/odd-limits. Sorry if I've overstressed my point. Also the other table has been there for as long as I remember, and I felt it was both incomplete and messy so I wanted a table from a more systematic approach.		311 EDO is a one-of-a-kind extremely consistent system to the point it can be said to be the first true melodic model of the harmonic series itself. Therefore to understand the structure of the harmonic series (at least in the 41-limit add-73) without making it impractical, it would be useful to use 311 EDO, and 311 EDO is a great alternative to cents for this reason (which requires smaller numbers and only round numbers) because of being distinctly consistent in the [[23-odd-limit]] and consistent in the 41-prime-limited 77-odd-limit with prime harmonic 73 included as the only prime over 41 and under 81 which is more in tune than out of tune (which is to say its step error is less than a quarter), but furthermore, because of it fitting the way 311 EDO maps the harmonic series by filling a gap and because of it being an odd prime with less error than all previous primes. 311 EDO is therefore a natural system to inspect when looking at ways of modelling higher-limit systems and has important connections with many simpler systems. Just one example would be [[Canousmic_temperaments#Superlimmal\|Superlimmal]], the 29-limit 80&311 temperament. Another reason it is a one-of-a-kind system is that in terms of having rooted harmonics with less than 25% error each, I did a search before in Python 3 and there is nothing that beats it until over 20 thousand, meaning it is simultaneously the first and last EDO to truly approximate the harmonic series, and the fact it does it up to a very large subset of the 77-odd-limit makes it worth inspecting the structure of for anyone wishing to learn medium-to-high-complexity tempered JI/odd-limits. Sorry if I've overstressed my point. Also the other table has been there for as long as I remember, and I felt it was both incomplete and messy so I wanted a table from a more systematic approach. --[[User:Godtone\|Godtone]] ([[User talk:Godtone\|talk]]) 23:17, 27 December 2021 (UTC)