This plugin for renoise(tm), which is a music tracker,
- calculates the consonance value as described by Werner Brefeld (see references)
- determines the interval of dyads for up to 24 halftones of the twelve-tone system
- displays emotional effects for intervals between 0 and 12 halftones
- calculates cents for intervals
The main design objectives for this plugin are to aid musical composition training in general as well as to compensate for lack of ear training.
Currently, English and German languages are supported.
In addition to the features above, a rudimentary detection of a few counterpoint violations is available and will be indicated in the status bar at the bottom of the analysis window.
- Consecutive fifths
- Consecutive octaves
- Fifth - fourth - fifth
- Leaps not followed by counter-movement in seconds (>=+7~-1|2 or >=-7~+1|2)
- Checking for unwanted dissonances in a composition
- Training of musical composition
- Optimizing a synthesizer settings like tuning, etc.
Concerning the latter, assuming the arbitrary notes A-3, C#-4, B-3, A-4 and F-5, the consonance values for equal temperament would be
Switching from equal temperament to Kirnberger III tuning on F, the consonance values would be
The consonance value for A-4 to F-5 were significantly improved.
Roughly explained, the consonance value is an approximation to the expected level of consonance or dissonance, basically calculated by
having a/ b as the frequency ratios, in its lowest terms, either of the pure intervals or of a chosen tuning, and v as the volume percentage. Volume differences are dissected into separate chords, as outlined in the references, thus v in this case is the same for each interval.
The consonance value is calculated separately for each two-tone as well as for each chord. Concerning the chords, the calculation is performed for the actual chord as well as for a "virtual" lingering chord, which takes notes previously played into account, at least the ones for which there are no notes in the respective column of the actual chord. Pls. refer to the example below for more details. The feature of lingering chords is only available if no note lines are left out.
As an example let's assume eight notes selected from the Moonlight Sonata as shown in the first screenshot from renoise(tm) below. The selection itself does not affect which notes are considered for the analysis. The position of the edit cursor is taken as reference. The selection is only for illustrative purposes.
If you start the tool e.g. from the editor position in line 38, the display will be as shown in the second screenshot. It is highly recommended to assign a keyboard shortcut to the tool for quick access. The corresponding entry in renoise(tm) can be found under "Global/Tools/Interval Calculator".
In the upper left corner there is a possibility to switch between the features mentioned above. In the case of the consonance value (abbreviated as "sonance"), the picture is as shown in the third screenshot.
Another example concerning the calculation of the consonance value, showing an augmented triad and the dominant seventh chord:
Yet another example concerning the calculation of the consonance value, this time for the Pythagorean tuning on D, showing the imperfect fifth or wolf fifth with a significantly higher dissonance of 18.17 instead of 2.45.
Due to the nature of the calculation of the consonance value, the irrational numbers of the equal temperament cannot be used, therefore the frequency ratios are approximated as described by Frieder Stolzenburg (see references). The hearing threshold, which can be configured in the settings, can be used to fine-tune the approximation.
For the Pythagorean tuning the same approximation is used, based on frequencies derived from the pitch level and the tuning note. The hearing threshold is also considered when calculating the ratios.
The pure interval tuning is not a tuning, of course, and does not take anything into account, no pitch, no tuning note, no hearing threshold.
| View | Purpose | Lines might be omitted | Limitations | Approximate max. size (4k, 200% scaling) |
|---|---|---|---|---|
| Condensed | Excerpt | Yes (prioritizing having at least one interval for each column) | If lines omitted: Counterpoint, effect display, lingering chords not available | 12 note columns x 8 rows |
| Compact | Overview | No | None | 24 note columns x 24 rows |
As I have no idea how to get either the scaling factor or the current window size and it's not possible to set relative sizes on top elements, the hard-coded sizes are best-effort estimations. If you experience issues, pls. let me know.
The fist setting is the type of the view, representing the different features outline above. Furthermore, the tuning, the tuning note and the language can be selected. Pls. note the limitations concerning tunings (see below). The sonance thresholds are used to control the colors for displaying the consonance values. The left rotary controls the threshold between light green for strong consonance and dark green for imperfect consonance, the rotary in the middle then the threshold to slight dissonance and finally, the right rotary the threshold to the strong dissonance.
Furthermore, the hearing threshold can be configured, as outlined in the tuning chapter above. Furthermore, the damping factor can be used to fine-tune the calculation of the lingering chord. The calculation basically calculates a new volume by taking the original volume times the damping factor to the power of the number of note lines, which is equal to the distance of the lingering note relative to the actual chord. Furthermore, the pitch level (= Kammerton-Frequenz) can be configured.
Lastly, the rightmost section can also be used to optimize the display of the note matrix
- by selecting the maximum number of lines to be displayed
- as well as the search depth, which can be used to limit the search range, which might become handy in case of sparsely distributed note lines
- The number of tracks to be considered
My special thanks go to Werner Brefeld for his elaboration of the consonance value calculation (in German only) and his willing and extensive support regarding questions, and for cross-reading this documentation,
and to Frieder Stolzenburg for allowing to use his approximation implementation as a reference.
Stolzenburg, Frieder
Harmony Perception by Periodicity Detection (March 2015)
Journal of Mathematics and Music.
9.10.1080/17459737.2015.1033024.
- The calculation of consonance value is only an approximation
- "OFF" notes are not considered calculating the consonance value for lingering chords
- No guarantee is given for correctness (not intended for professional/ critical use)
- Specific renoise(tm) effects like pitch level, etc. are not considered
Download current release at the release page