September 22, 2008
The vast throngs of devoted readers of this blog may recall sometime back in mid-April when I waxed poetic over the TI-34 Explorer II calculator as a must-have tuning tool for on-the-go Tuning Geeks (you know who you are … both of you). As fate would have it, shortly after posting that effusive little review, my TI-34EII started to behave erratically. I'll spare you the details, but suffice it to say that sadly, after just a few years of use, my precious friend was laid to rest and tagged for the great recycle bin in the sky.
But the story doesn't end there, my friends. As the title of this blog entry suggests, I decided not to let this little setback destroy my penchant for typing little keys and viewing answers to everyday tuning problems on a hand-held device costing around twenty bucks. It occurred to me that in the several years that had passed since I had bought my first TI-34, probably something better had become available. I did some research online at the Texas Instruments website. It took a bit longer than I would have liked to find out if any other TI calculators featured the op1 op2 buttons of the 34IIE, these being the main reason the device is useful as a tuning calculator, but after downloading and searching through a few PDF documents, I found at last that my hunch was correct.
The TI-34 E has a big brother, the TI-34 MultiView, as shown here. It took only a moments deliberation for me to take the plunge and shell out $23.79 for this little gem at Staples. Don't let its vaguely-reminiscient-of-Fisher-Price exterior fool you; this is a serious ratio-computing powerhouse, fundamentally similar to the TI-34EII, but with more memory, a larger display, and some useful additional features.
To begin with, as the image here shows, the MultiView is capable of displaying ratios as integers above and below a horizontal line, instead of on the same line with a slash. It has a button dedicated to this purpose, labeled (n over d), allowing ratios to be entered this way. The arrow buttons must be used to navigate in four directions around the display, which has four lines where the TI-34 E only has two. The third row of keys from the top begins with a button dedicated to simplifying fractions, which the MultiView also does automatically unless you choose to turn off that function. I find this quite handy. A simple example; type in the following:
5 (n over d) 4 (right) × 5 (n over d) 4 (enter)
The display reads 25 over 16, as expected. Now, I know what you're thinking. What's the big deal? Well, what I find nice about this is that there is still space on the display to do another ratio calculation below this one, without scrolling this result out of view. And another advantage of this vertical notation is that it allows entering continued fractions, which usually figures into tuning theory as an algorithmic bridge between JI and ETs, but the technique can also be used as a simple trick for entering in ratio calculations such as the one above using only one operator key instead of two; as in:
5 (n over d) 4 (n over d) 5 (n over d) 4 (enter)
The answer again is 25 over 16. The format of the display when using this slick method is not as nice as above, but it's faster. Of course, all this talk about ratios should not distract us from what makes these TI calculators so useful for tuning in the first place — the op1 and op2 function calculating buttons — old friends to those of us familiar with the 34EII. Tuning Geeks may want to enter something such as the following to measure the interval ans in terms of x units, to three decimal places:
op1=round(x×(log(ans)÷log(2)),3)
Storing 1200 in memory for x gives a cents value calculation. If we take our answer 25 over 16 and press op1 with this function programmed, the MultiView outputs 772.627, the correct cents value. Yes, the 34IIE would have given this answer as well, but the four line display of the MultiView allows both the ratio and the cents value to be shown at once on the display, which I think you will agree is quite handy, especially when ratio calculations get complicated.
Obviously, with these kinds of formulas, you can plug in whatever values you want. The MultiView allows you to use not just five variables as in the 34EII, but a whopping seven variables! Count 'em: x y z t a b c. Add ans to that and you have 8 variables you can use in your op1 and op2 formulas. More math and trig functions are available in comparison to the 34EII as well.
But wait, there's more! One of the best features of the MultiView is its statistics data list view. This mode, entered by pressing the data key, allows entry of three lists of data L1(42), L2(42) and L3(42). The choice of 42 as a data limit per column may have something to do with Douglas Adams, but I like to think that it has something to do with tuning. 42 is a pretty fortuitous number of elements to have in a Tuning Calculator, considering that Harry Partch's famous Chromelodeon tuning was made up of 43 tones, so that if we just omit 1/1 from our list, we've got space for the whole shebang right there in one column!
81/80
33/32
21/20
16/15
12/11
11/10
10/9
9/8
8/7
7/6
32/27
6/5
11/9
5/4
14/11
9/7
21/16
4/3
27/20
11/8
7/5
10/7
16/11
40/27
3/2
32/21
14/9
11/7
8/5
18/11
5/3
27/16
12/7
7/4
16/9
9/5
20/11
11/6
15/8
40/21
64/33
160/81
42 is also rather an appropriate choice for me personally, as my own work revolves around the use of 205ET as an adaptive system of 41ET, where 41 zones define the set of categorical intervals. With 42 elements, columns can contain lists of categorical JI intervals including both 1/1 and 2/1, and having multiple columns allows showing how 11-Limit and 13-Limit intervals overlap in the Wide and Narrow categories, how a pair of commas occupy the same category, and how a couple of 3-Limit intervals can be used in place of a couple of 5-Limit and 7-Limit intervals. In column 1, the list can contain the 11-Limit intervals. I list it below as a simple column without any line numbering or other formatting, showing the 11-Limit intervals in bold:
1/1
64/63
28/27
256/243
16/15
12/11
10/9
9/8
8/7
7/6
32/27
6/5
11/9
5/4
81/64
9/7
21/16
4/3
27/20
11/8
45/32
64/45
16/11
40/27
3/2
32/21
14/9
128/81
8/5
18/11
5/3
27/16
12/7
7/4
16/9
9/5
11/6
15/8
243/128
27/14
63/32
2/1
The second column can replace the 11-Limit intervals with 13-Limit, again shown in bold as follows:
1/1
64/63
28/27
256/243
16/15
13/12
10/9
9/8
8/7
7/6
32/27
6/5
16/13
5/4
81/64
9/7
21/16
4/3
27/20
18/13
45/32
64/45
13/9
40/27
3/2
32/21
14/9
128/81
8/5
13/8
5/3
27/16
12/7
7/4
16/9
9/5
24/13
15/8
243/128
27/14
63/32
2/1
The third column can show the Syntonic Comaa L1 / S8 in place of the 7-Limit comma Nm2 / WM7 of Archytas, and 3-Limit d5 / a4 options in place of the 5-Limit Sa4 / Ld5. Here the 13-Limits are kept in the list:
1/1
81/80
28/27
256/243
16/15
13/12
10/9
9/8
8/7
7/6
32/27
6/5
16/13
5/4
81/64
9/7
21/16
4/3
27/20
18/13
1024/729
729/512
13/9
40/27
3/2
32/21
14/9
128/81
8/5
13/8
5/3
27/16
12/7
7/4
16/9
9/5
24/13
15/8
243/128
27/14
160/81
2/1
Note that the notation here is actually pitch notation using ratios, rather than interval notation using colons — a minor quibble. The table below puts it all together, with added columns naming the intervals:
1 1/1 P1
2 64/63 Nm2 81/80 L1
3 28/27 Sm2
4 256/243 m2
5 16/15 Lm2
6 12/11 NM2 13/12 Wm2
7 10/9 SM2
8 9/8 M2
9 8/7 LM2
10 7/6 Sm3
11 32/27 m3
12 6/5 Lm3
13 11/9 Wm3 16/13 NM3
14 5/4 SM3
15 81/64 M3
16 9/7 LM3
17 21/16 S4
18 4/3 P4
19 27/20 L4
20 11/8 Sd5 18/13 Na4
21 45/32 Sa4 1024/729 d5
22 64/45 Ld5 729/512 a4
23 16/11 La4 13/9 Wd5
24 40/27 S5
25 3/2 P5
26 32/21 L5
27 14/9 Sm6
28 128/81 m6
29 8/5 Lm6
30 18/11 NM6 13/8 Wm6
31 5/3 SM6
32 27/16 M6
33 12/7 LM6
34 7/4 Sm7
35 16/9 m7
36 9/5 Lm7
37 11/6 Wm7 24/13 NM7
38 15/8 SM7
39 243/128 M7
40 27/14 LM7
41 63/32 WM7 160/81 S8
42 2/1 P8
Although the multi-column display mode is intended for statistical conversions which I haven't yet found useful for tuning purposes, possibly some further tuning mischief is yet to be discovered using those functions.
In summary, the MultiView is a considerable upgrade over the 34EII, at just a few dollars more. I leave you now so that you may travel to your nearest Staples and buy one with the money you will save on gasoline by riding there on your bicycle.
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