Comparison of mode notation systems: Difference between revisions
Wikispaces>FREEZE No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
__FORCETOC__ | __FORCETOC__ | ||
= | =[[KiteGiedraitis|Kite Giedraitis]] method= | ||
== | ==Proposed method of naming all possible rank-2 scales== | ||
'''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely. | '''Mode numbers''' provide a way to name MOS, MODMOS and even non-MOS rank-2 scales and modes systematically. Like [[Modal_UDP_Notation|Modal UDP notation]], it starts with the convention of using ''some-temperament-name''[''some-number''] to create a generator-chain, and adds a way to number each mode uniquely. | ||
See [[ | See [[Naming Rank-2 Scales using Mode Numbers]]. | ||
=Jake Freivald method= | =[[Jake Freivald]] method= | ||
My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include | My goals for numbering the modes are to make it as simple as possible for people to identify and use the modes they're talking about. As such, desired characteristics include | ||
| Line 69: | Line 68: | ||
==Extending to non-MOS== | ==Extending to non-MOS== | ||
My suggestion is that (a) you still start with the step size that occurs the largest number of times, and (b) you still push the largest cluster of that as far out as possible | |||
If the scale is made of xL+ys+zM, and any two of x, y, or z are the same, and they're larger than the third number, then the scale starts with the larger of the steps -- just like meantone major starts with larger steps. In other words, if it's 3L+3s+2M, we start with L. If it's 2L+3s+3M, we start with M. | |||
(Note that the word "scale" is ambiguous in some of what follows. I don't think we'll get away from that in real life, so I'm just pushing on, even where it sounds weird.) | (Note that the word "scale" is ambiguous in some of what follows. I don't think we'll get away from that in real life, so I'm just pushing on, even where it sounds weird.) | ||
| Line 95: | Line 94: | ||
This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.) | This also works for Kite's question about meantone[8], which is LMsMLLML. There are more L's than any other step size, so the scale has to start with L. The L's are in equal clusters of two, so there's no obvious way to pick which one goes first: mode 1 must start with LL. So let's again pick the mode that has the longest string of non-L's to go after that first LL: Mode 1 of meantone[8] is LLMsMLLM. (That's C - D - E - F - F# - G - A - B - C, or something like it.) | ||
Let's try something harder: the rank-3 scale [[http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&limit=11&tuning=po | Let's try something harder: the rank-3 scale minerva[12], which I found through [http://x31eq.com/cgi-bin/scala.cgi?ets=12_31_22&limit=11&tuning=po Graham's temperament finder]. Since there are four step sizes, I'm going to label them LMms, where the capital M is larger than the small m. With steps of 113, 113, 87, 113, 87, 99, 113, 87, 113, 87, 113, and 73, that's LLmLmMLmLmLs, 6L+1M+4m+1s. L has to go first. There's a cluster of two L's in the string, and I push that as close to the end as possible: LmMLmLmLsLLm. Graham is showing mode 10 of this scale in his temperament finder. | ||
NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all. | NOTE: NO collapsing genchains. NO generator knowledge needed. No mapping knowledge (or indeed mapping at all) required. Extensible to higher ranks without problems. It doesn't matter whether the scale is a temperament at all. | ||
[[category:rank 2]] | |||