pythagorean

[icecoldrocker]

what are the values for each note in the user scale page in global settings

hey thanks

[voip]

It is possible to set the Scale for each Program individually, and Pythagoras is already available as one of the choices in the dropdown menu. Out of interest, is the question posted intended for a customised version of the Pythagorean scale?

This might be of use: https://en.wikipedia.org/wiki/Pythagorean_tuning - the data from this source have been tabulated in column 2 of the table below, where 12-TET-dif is the difference, in cents, between a note's Pythagorean frequency and the frequency of the corresponding note in the Equally Tempered scale. In addition, I have measured the actual frequencies generated by the Kronos (which should be similar to the Nautilus) and created a data column called Kronos-dif, which gives the difference in cents between notes played using a blank Kronos init EXi Program, first with the Equally Tempered scale and then the Pythagorian scale, referenced to the key of C. The fourth column (Dif(2)-Dif(1)) is the difference between the two data sources (i.e. Wikipedia vs. actual measurements on the Kronos). It can be seen that the Kronos' implementation of the Pythagorean scale is roughly 4 cents higher than the Wikipedia page values, for each corresponding note played. I'm guessing that, had the Kronos's Pythagorean scale been referenced to the key of D, the Kronos-dif values would have essentially been the same as the 12-TET-dif data. It would be reasonable to expect that the Kronos and Nautilus are similar, in this regard, since they use the same basic sound engines. The frequencies measured when playing the Kronos in Equal Tempered Scale all corresponded to the last 0.1Hz of the expected frequencies, based on 440.0Hz concert pitch for the A note.

Code: Select all

Note|12-TET-dif |Kronos-dif|Dif(2)-
    |(cents)    |(cents)   |Dif(1)
--------------------------------
D      0.00      3.88       3.88
Eb    -9.78     -5.98       3.80
E      3.91      7.94       4.03
F     -5.87     -1.92       3.95
F#     7.82     12.05       4.23
G     -1.96      2.03       3.99
Ab   -11.73
G#    11.73     15.98       4.25
A      1.96      6.00       4.04
Bb    -7.82     -4.01       3.81
B      5.87     10.03       4.16
C     -3.91      0.00       3.91
C#     9.78     13.99       4.21

Ab and G# are the diminshed fifth and augmented fourth corresponding to the sixth interval on the 12 note Equally Tempered scale.

.