Myna temperament (7-limit 4p&27p or 11-limit 31p&58p) is one that might be a good test case for different notation strategies. With the mapping [<1 -1 0 1 -3] <0 10 9 7 25]>, it's going to need many different sizes of accidentals to fill the gaps between the fifths, and it doesn't get any better if you use the 4-note MOS for the nominals in place of a chain of fifths. So I tried the strategy of notating the simplest JI representation of a tempered interval. This seems to be working out well for the simpler, most common JI intervals, e.g.
[+1, -1> 5/3 B
[-2, +9> 5/4 F
[-1, +7> 7/4 C
When you get to [+1, -2>, the simplest representation is 7/5, which requires a schisma accent if you write it in Sagittal as G , but A is an alternative that doesn't require an accent. We can ignore the schisma accent if we're using fewer than 89 notes, since 32805/32768 maps to [-23, +89>. This strategy works reasonably well for 7-limit myna until you get to +/- 24, where [-6, +24> is represented as 81/70 and [+7, -24> as 140/81; the JI calculator spreadsheet gives F and B as the Athenian approximations for these pitches. The biggest problem with this approach is that you get redundant symbols for the same tempered comma, e.g.
[-1, +4> 36/35 D
[+5, -16> 49/27 C = C [+6, -20> [-1, +4>
Adding 11-limit intervals gives simpler notations for some notes, e.g.
[-3, +15> 11/6 C
[-6, +24> 55/48 E
On the other hand, some intervals like [-4, +18> bring in Sagittal symbols that are less commonly seen than the 7-limit notation.
[-4, +18> 25/16 A
[-4, +18> 11/7 A
Based on these options, I chose a single symbol for each comma. The choice of for [-1, +4> instead of or was motivated by flag addition: + = .
[+15, -58> 896/891
[-8, +31> 81/80
[+7, -27> 64/63
[-1, +4> 55/54
[-9, +35> 33/32
[-2, +8> 25/24
[-10, +39> 135/128
The one interval that has a couple of options is [+6, -23>, which I'm notating as 28/27: it can be represented approximately as (Athenian) or (Promethean). Since I'm not using any other Promethean symbols, I chose to use and ignore the schisma accent. So what I ended up with looks like a reasonable notation for myna temperament. Notating temperaments as JI is a good starting point, but you can get better results with some careful observation.
myna temperament notation
- herman.miller
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myna temperament notation
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- Dave Keenan
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Re: myna temperament notation
Good work there, Herman! I'm sorry I can't spare the time to investigate enough to suggest any alternatives.
It certainly underscores the point that linear temperament notations are still more art than science.
It certainly underscores the point that linear temperament notations are still more art than science.