User talk:Lhearne: Difference between revisions

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:::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment. I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]], and I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists because 159edo is still among the EDOs we need to make a well-ordered interval naming system for, and I can tell you that both the schisma and the monzisma are tempered out in that EDO, thus eliminating virtually all of the commas in that chain. I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations. Therefore, I think we need to find better candidates than these. Even if the five-limit comma we end up choosing is virtually unknown to the community at large, I still think something like this is likely to be the better option in the end- after all I just found {{monzo| -99 61 1 }} by digging through combinations of the schisma that the monzisma, and that comma is definitely not well known to the community. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:07, 9 February 2021 (UTC)

::::::::::::::::::: Ok cool I see now. So the pythagorean axis is still the basis. I worried about using M and m for 4th and 5th where is means something different, but since it isn't defined at all for 4th and 5ths, I think that might be ok, though I still worry that the difference between major and minor fourths and fifths to augmented and diminished fourths and fifths would not be the same as for 2nds, 3rds, 6ths, and 7ths. The logic I was using from the diatonic system was that A - P = P - d = A - M = m - d = A1 = 2187/2048, where 1sts, 4ths, 5ths, and 8ths use P and 2nds, 3rds, 6ths, and 7ths use M and m. Although M4 - m4 = (33/32)^2 is similar in size to 2187/2048, the rastma separates them, and we are not tempering it in the naming system. What's more, major and minor come from the specific interval sizes of each generic interval of the diatonic scale. This is an integral basis to extended diatonic interval names. Another idea I had was to call 11/8 a neutral fourth, where for neutrals, using your N and n, which I like actually, we would have

n - P = P - N = n - m = M - N = U1 = 33/32, whilst retaining A - P = P - d = A - M = m - d = A1 = 2187/2048. the problem with this is that most people didn't really think of 11/8 as a neutral fourth, but I quite like to.

::::::::::::::::::: regarding the disachisma, don't worry, your suggestion of the septimal kleisma was not what led me to suggest the diaschisma. The diaschisma is actually useful for intervals of 2.5 the same way the rastma is for intervals of 2.11. I thought that if defined based 2.3 and now extended to support 2.11, we should also aim to support 2.5, 2.7, and 2.13. The magic comma - the small dieses, is analogous to the Nexus comma in this way. 5 5/4 major thirds represents a tempered 3/2. 25/24 is important in 2.5, and in many 5-limit temperaments, not as a type of Augmented unison, as it can be defined as ccA1, but as a type of minor second, in Magic[7] and Hanson[7], for example. 225/224 then connects this to the 7-limit, but we don't need 225/224 if we have the diaschisma.

::::::::::::::::::: Magic[7] 6|0 is our 'diatonic' scale -

::::::::::::::::::: 6/5 5/4 3/2 25/16 15/8 48/25 2/1

::::::::::::::::::: Cm3 cM3 P5 ccA5 cM7 CCd8 P8

::::::::::::::::::: and perhaps Magic[10] 6|3 is more analogous to the alpharabian harmonic scale -

::::::::::::::::::: 25/24 6/5 5/4 32/25 3/2 25/16 8/5 15/8 48/25 2/1

::::::::::::::::::: ccA1 Cm3 cM3 CCd4 P5 ccA5 Cm6 cM7 CCd8 P8, which could be:

::::::::::::::::::: diaschisma-narrow min 2, classic minor 3, diaschisma-Wide Major 3, Perfect 5, diaschisma-narrow minor 6, classic minor 6, classic Major 7, diaschisma-Wide Major 7, Perfect 8.

::::::::::::::::::: the diaschismic intervals are like 5-limit super and sub intervals, and when 225/224 is tempered out they are equivalent, but we need it because 225/224 is not always tempered out, and these intervals are relatively simple. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 03:40, 11 February 2021 (UTC)

@@ Line 131: / Line 131: @@
 :::::::::::::::::: Anyhow, now that we've hopefully narrowed down the comma selection in terms of what to use to define a well-ordered system, let's take a look at the available 5-limit commas, seeing as that seems to be where you're most focused at the moment.  I will say that a number of the common 5-limit commas are likely to be pulled down by combinations of the [[schisma]] and the [[monzisma]], and I'm pretty sure it would be a bad idea to use them as commas for well-ordered interval lists because 159edo is still among the EDOs we need to make a well-ordered interval naming system for, and I can tell you that both the schisma and the monzisma are tempered out in that EDO, thus eliminating virtually all of the commas in that chain.  I think you may need to run an algorithm to find most of the commas that need to be eliminated as candidates based on the resulting list, though I can already tell you that the [[counterschisma]], the [[tricot comma]], [[Mercator's comma]], the [[vulture comma]], the [[amity comma]], the [[kleisma]] and the [[semicomma]] are on that avoid list based on my own personal calculations.  Therefore, I think we need to find better candidates than these.  Even if the five-limit comma we end up choosing is virtually unknown to the community at large, I still think something like this is likely to be the better option in the end- after all I just found {{monzo| -99 61 1 }} by digging through combinations of the schisma that the monzisma, and that comma is definitely not well known to the community. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:07, 9 February 2021 (UTC)
+::::::::::::::::::: Ok cool I see now. So the pythagorean axis is still the basis. I worried about using M and m for 4th and 5th where is means something different, but since it isn't defined at all for 4th and 5ths, I think that might be ok, though I still worry that the difference between major and minor fourths and fifths to augmented and diminished fourths and fifths would not be the same as for 2nds, 3rds, 6ths, and 7ths. The logic I was using from the diatonic system was that A - P = P - d = A - M = m - d = A1 = 2187/2048, where 1sts, 4ths, 5ths, and 8ths use P and 2nds, 3rds, 6ths, and 7ths use M and m. Although M4 - m4 = (33/32)^2 is similar in size to 2187/2048, the rastma separates them, and we are not tempering it in the naming system. What's more, major and minor come from the specific interval sizes of each generic interval of the diatonic scale. This is an integral basis to extended diatonic interval names. Another idea I had was to call 11/8 a neutral fourth, where for neutrals, using your N and n, which I like actually, we would have
+n - P = P - N = n - m = M - N = U1 = 33/32, whilst retaining A - P = P - d = A - M = m - d = A1 = 2187/2048. the problem with this is that most people didn't really think of 11/8 as a neutral fourth, but I quite like to.
+::::::::::::::::::: regarding the disachisma, don't worry, your suggestion of the septimal kleisma was not what led me to suggest the diaschisma. The diaschisma is actually useful for intervals of 2.5 the same way the rastma is for intervals of 2.11. I thought that if defined based 2.3 and now extended to support 2.11, we should also aim to support 2.5, 2.7, and 2.13. The magic comma - the small dieses, is analogous to the Nexus comma in this way. 5 5/4 major thirds represents a tempered 3/2. 25/24 is important in 2.5, and in many 5-limit temperaments, not as a type of Augmented unison, as it can be defined as ccA1, but as a type of minor second, in Magic[7] and Hanson[7], for example. 225/224 then connects this to the 7-limit, but we don't need 225/224 if we have the diaschisma.
+::::::::::::::::::: Magic[7] 6|0 is our 'diatonic' scale -
+::::::::::::::::::: 6/5 5/4 3/2 25/16 15/8 48/25 2/1
+::::::::::::::::::: Cm3 cM3 P5 ccA5 cM7 CCd8 P8
+::::::::::::::::::: and perhaps Magic[10] 6|3 is more analogous to the alpharabian harmonic scale -
+::::::::::::::::::: 25/24 6/5 5/4 32/25 3/2 25/16 8/5 15/8 48/25 2/1
+::::::::::::::::::: ccA1 Cm3 cM3 CCd4 P5 ccA5 Cm6 cM7 CCd8 P8, which could be:
+::::::::::::::::::: diaschisma-narrow min 2, classic minor 3, diaschisma-Wide Major 3, Perfect 5, diaschisma-narrow minor 6, classic minor 6, classic Major 7, diaschisma-Wide Major 7, Perfect 8.
+::::::::::::::::::: the diaschismic intervals are like 5-limit super and sub intervals, and when 225/224 is tempered out they are equivalent, but we need it because 225/224 is not always tempered out, and these intervals are relatively simple. --[[User:Lhearne|Lhearne]] ([[User talk:Lhearne|talk]]) 03:40, 11 February 2021 (UTC)