Monthly Archives: June 2011

Transposition via Reference Frequency on a Chromatic Tuner

UPDATE: The beta version of DaTuner (DaTunerBeta) on the market has a transposition option as of 14/08/2011.  This will be released soon in the pro version.

I have had requests to enable transposition in DaTuner, but it has really been there the whole time except not really obvious or easy to use. The thing is, the reference frequency in DaTuner has a range of 220Hz (A3) all the way up to 880Hz (A5). The reference frequency is not only useful for orchestra tuning, but also for transposition. I have corresponded with a user of DaTuner about this and they didn’t agree, so here is my logic.

1.) Transposition, by definition, is the shifting up or down of the scale without changing the mathematical relationship between notes.
2.) Example: a transposition of +1 semitone would mean that A would become A#, A# would become B, and so on.
3.) Mathematically, the frequency relationship between semitones is exponential. Each semitone’s frequency can be expressed as (2^(1/12) * previous frequency.)
4.) Moving the reference frequency changes at which frequency A4 starts. The relationship between A4 to A#4, B, etc, does not change. Therefore, transposition can be accomplished by simply moving the reference frequency up or down by x semitones. I know that it is not easy to do this in your head, and soon DaTuner will have support for transposition, but this is a stop-gap poor-mans solution.

Here is a table of the reference frequencies to use to accomplish a transposition of a certain number of semitones in DaTuner, or any other chromatic tuner with a wide reference frequency range.

Semitones (up) Reference Freq(Hz) Note at 440Hz
-12 880 A
-11 830.61 A#/Bb
-10 783.99 B
-9 739.99 C
-8 698.46 C#/Db
-7 659.26 D
-6 622.25 D#/Eb
-5 587.33 E
-4 554.37 F
-3 523.25 F#/Gb
-2 493.88 G
-1 466.16 G#/Ab
0 440 A
1 415.3 A#/Bb
2 392 B
3 369.99 C
4 349.23 C#/Db
5 329.63 D
6 311.13 D#/Eb
7 293.66 E
8 277.18 F
9 261.63 F#/Gb
10 246.94 G
11 233.08 G#/Ab
12 220 A