# DIMI temperament

DIMI-A and DIMI-O are generating individual notes with counter circuits. The idea is to divide frequencies down from a single ultrasonic oscillator. When the divider ratios are large enough, it is possible to approximate an equal temperament scale.

Bigger ratios would demand more TTL chips, so as a compromise, DIMIs use ratios that can be presented with less than 12 bits, preferably less than 8. In addition to this, ratios where you are counting should not have more than eight ‘1’s, so they can be detected with a single eight-input NAND port. This limits usable ratios to around 300, which is not enough to achieve perfect estimation for an equally tempered scale.

Typical DIMI-A divider circuit has two 7493 TTL counter circuits in series. They count the numbers up every time a clock pulse is received at N11 pin 14. Selected outputs are wired to a 7430 NAND gate. This sets the value the circuit is counting to. In this case, it is 1100 0100, which in the 10 decimal system corresponds to 196. When this number is reached, the feedback connection from the output through inverter gate will reset counters. Counting will then restart from zero.

The ratios (confirmed from hardware) on DIMI-A are the following:

- C# 350
- D 330
- D# 312
- E 294
- F 277
- F# 261
- G 247
- G# 233
- A 220
- A# 208
- B 196
- C 185

According to schematics, DIMI-O uses the same ratios but with one note offset, so ratio 350 is used for C while 185 is used for B. It is worth noting that ratios 185/196 are mentioned in other sources as the lowest ratios, giving more or less perfect semitone (1.0594595 vs. ‘perfect’ 1.059463094) [1, 2]. My guess is that for this reason, the DIMI-A temperament has been built on top of this ratio.

Ratios giving a more or less perfect approximation of an equal temperament are a bit larger, between 508 and 959 [1]. Ratios this high would require additional gates.

If I’m crunching numbers correctly in Excel, even if we decide to keep 185/196 ratios as a starting point, temperament can be improved. An improved temperament would be:

**C# 349**- D 330
**D# 311**- E 294
- F 277
**F# 262**- G 247
- G# 233
- A 220
- A# 208
- B 196
- C 185

More detailed tables illustrating the DIMI-A temperament can be found here. As seen, the tuning of C#, D#, and F# seems off. Tweaking those ratios will bring the sum of all deviations down considerably. From these datasets, you can also see that tuning DIMI-A using C as a reference will give you the best results (while using F# would result in all other notes being far off).

DIMIs will generate all necessary clock frequencies from the same main oscillator that is used to generate note frequencies. Therefore, the main oscillator is tuned much higher than note generators require. On DIMI-A, the main oscillator frequency is around ~12.4 MHz, which is divided down by four before being fed to the note generator divider circuit. Octaves of different notes are generated by dividing note generator outputs by 2^n.

## References

- https://electro-music.com/forum/phpbb-files/harmonic_logs_781.pdf
- https://electro-music.com/forum/topic-65094.html