Douglas Blumeyer's RTT How-To: Difference between revisions

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[[File:Shape_of_scale_of_movements_on_axes.png|thumb|left|200px|'''Figure 3e.''' the basic shape the scaled axes make between neighbor maps (maps with only 1 difference between their terms)]]

Our example ET will be 40. We'll start out at the map {{map|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (we'll be calling it a '''simple map''' here, though elsewhere you may find it called a "[[patent val]]"<ref>~~My first concern with “patent” map is that "patent", as an adjective, is unfamiliar~~ to ~~most people, unless it relates to those documents called patents. Calling them "obvious maps" would have been better than "patent maps".~~

Our example ET will be 40. We'll start out at the map {{map|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (we'll be calling it a '''simple map''' here, though elsewhere you may find it called a "[[patent val]]"<ref>See my proposal to rename this object here: https://en.xen.wiki/w/Talk:Patent_val</ref>).

~~ ~~

The second concern is that they are not always obvious. If it were, there would be no contention about it. This name suggests a positive value judgment (and dismissive value judgement on other maps) which we think is inappropriate. A name like “patent” or "obvious" map may lead too many people concerned with accurate tuning to accept this ~~map when if they'd known better they may have preferred the map with the most accurate tuning overall, i.e. the “best” map~~. ~~The classic example of a best map which is not the patent map is 17c at the 5-limit~~.

~~ ~~

These concerns arose in recent public discussion I was involved in, and it was agreed at that time that "naive" was an apt replacement for "patent". But through further discussion, we decided that this would have the opposite problem: where "patent" had excessively positive connotations, "naive" would have had inappropriately negative connotations, and might run the risk of discouraging people from using them despite such maps being relatively good. So we concluded that a word with more neutral connotations was appropriate, and so we're going with "simple". These maps may not always be obvious, but they are always simple to calculate.

~~ ~~

The simple map sets octaves pure, and then for each other prime harmonic individually, chooses the nearest mapping (the one with least error). That's clearly simple, and it's good, but it's not necessarily best. On the other hand, the best map is not strictly defined yet, but it would have a more elaborate definition, involving a consideration of errors in the ratios ''between'' primes, not only in the primes themselves.</ref>).

From here, let’s move by a single step on the 5-axis by adding 1 to the 5-term of our map, from 93 to 94, therefore moving to the map {{map|40 63 94}}. This map is found directly to the left. This makes sense because the orientation of the 5-axis is horizontal, and the positive direction points out from the origin toward the left, so increases to the 5-term move us in that direction.

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 [[File:Shape_of_scale_of_movements_on_axes.png|thumb|left|200px|'''Figure 3e.''' the basic shape the scaled axes make between neighbor maps (maps with only 1 difference between their terms)]]
-Our example ET will be 40. We'll start out at the map {{map|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (we'll be calling it a '''simple map''' here, though elsewhere you may find it called a "[[patent val]]"<ref>My first concern with “patent” map is that "patent", as an adjective, is unfamiliar to most people, unless it relates to those documents called patents. Calling them "obvious maps" would have been better than "patent maps".
+Our example ET will be 40. We'll start out at the map {{map|40 63 93}}. This map is a default of sorts for 40-ET, because it’s the map where all three terms are as close as possible to JI when prime 2 is exact (we'll be calling it a '''simple map''' here, though elsewhere you may find it called a "[[patent val]]"<ref>See my proposal to rename this object here: https://en.xen.wiki/w/Talk:Patent_val</ref>).
-<br><br>
-The second concern is that they are not always obvious. If it were, there would be no contention about it. This name suggests a positive value judgment (and dismissive value judgement on other maps) which we think is inappropriate. A name like “patent” or "obvious" map may lead too many people concerned with accurate tuning to accept this map when if they'd known better they may have preferred the map with the most accurate tuning overall, i.e. the “best” map. The classic example of a best map which is not the patent map is 17c at the 5-limit.
-<br><br>
-These concerns arose in recent public discussion I was involved in, and it was agreed at that time that "naive" was an apt replacement for "patent". But through further discussion, we decided that this would have the opposite problem: where "patent" had excessively positive connotations, "naive" would have had inappropriately negative connotations, and might run the risk of discouraging people from using them despite such maps being relatively good. So we concluded that a word with more neutral connotations was appropriate, and so we're going with "simple". These maps may not always be obvious, but they are always simple to calculate.
-<br><br>
-The simple map sets octaves pure, and then for each other prime harmonic individually, chooses the nearest mapping (the one with least error). That's clearly simple, and it's good, but it's not necessarily best. On the other hand, the best map is not strictly defined yet, but it would have a more elaborate definition, involving a consideration of errors in the ratios ''between'' primes, not only in the primes themselves.</ref>).
 From here, let’s move by a single step on the 5-axis by adding 1 to the 5-term of our map, from 93 to 94, therefore moving to the map {{map|40 63 94}}. This map is found directly to the left. This makes sense because the orientation of the 5-axis is horizontal, and the positive direction points out from the origin toward the left, so increases to the 5-term move us in that direction.