Örjan Hansson, September 2004
- Web site: http://ohw.se, E-mail: harpoh (at) ohw.se
- Page last updated: 2012-08-30
- Web location: http://ohw.se/hca/tuning/
It is only recently that I have started to tune my harmonicas on a regular basis. Previously, I did occasional adjustements of reeds that were clearly out of tune. But I often noticed that reeds that were badly out of tune (a semitone or more) could not be retuned. I have now learnt that this is due to a phenomenon called metal fatigue and that there is no idea to try to tune them. The only thing is to replace them, which, however, I find too difficult and time consuming. I simply replace the whole reed plate instead.
There is a large amount of information on harmonica tuning on the Internet which I have learnt a lot from. I highly recommend visiting Pat Missin’s Web site and reading his explanations and advice. In particular his text Altered States [Missin, 1996]. He has also a lot of links to other Web sites with relevant information. The books by Steve Baker [Baker, 1991] and Lee Oskar [Oskar, 1996] are also very informative.
The tuning procedure that I use follows closely Pat Missin’s recommendations, in particular the tuning scheme suggested by him. I have written an accompanying text Theory of harmonica tuning, which to a large extent is a rephrasing and summary of the information in Altered States. To this I have added some of my own ideas and experiences which will be summarized in the present text. There are some references [in square brackets] in this text which are listed in full at the end of Theory of harmonica tuning.
Nowadays, I enjoy more and more the sound of a well-tuned harmonica. And I realize that this is one of the factors that make professional players sound so good. As Pat Missin has put it: It is often said that the most important aspects of musical performance are the “three ts”: tuning, timing and tone.
2. Tuning scheme
The tuning scheme that I use for 10-hole diatonic (Richter) harmonicas (that is, blues harps) is called 19-limit Just Intonation (JI). As described in Theory of harmonica tuning, it is a variant of JI that gives reasonably good chords in both 2nd and 3rd position. The scheme can be summarized as a table (Table 8B in Theory of harmonica tuning).
This scheme is essentially that recommended by Pat Missin [Missin, 1996]. The 1st position tonic blow chord is in perfect JI. The tuning of the draw note in channels (holes) 6 and 10 makes it a a major whole tone and a perfect fifth in 2nd and 3rd position, respectively, that are in perfect JI. The tuning of the draw note in channels 5 and 9 is a compromise. It is a little too sharp for the flattened seventh chord in 2nd position and a little too flat for the minor third in 3rd position. However, a positive side effect is that the minor chord in 4-6 draw is accompanied by a difference tone equal to the root of the chord but two octaves down [Missin, 2004].
In addition to the above tuning scheme I use an octave stretching of 2 cent/octave. This means that 2 cent are added (subtracted) for each increase (decrease) of the notes by an octave. I also use a master tuning slightly higher than the standard A4 = 440 Hz, usually A4 = 443 Hz. These adjustments are described in Theory of harmonica tuning. and are easily done with the tuner I am using (see next section).
The tuning scheme in the previous section should be interpreted in the following way:
The numbers for the blow and draw notes in the different channels (holes) tell how many cent the note should differ from the corresponding note in 12-tone equal temperament (12TET). That is, how much they should differ from those on, for example, a (well-tuned) piano.
There are (hardware) instrument tuners with a moving needle that display the deviation in cent from 12TET when a note is played into its microphone. Thus, for a well-tuned harp, sounding a 1B (the blow note in hole 1) should result in no deviation, 2B should give a negative deviation of 14 cent, 3B shold give a positive 2 cent deviation, and so on.
3.1 Software tuner
I use a software tuner called Chromatia Tuner (version 3.1) that I highly recommend. The tuner is shareware and can be obtained from the maker FMJ-Soft. I have installed it on my laptop computer and use it with a Shure SM57 microphone connected to an SB Audigy 2NX external soundcard.
In addition to working as an ordinary (hardware) tuner, Chromatia can also apply octave stretching and it is easy to change the master tuning. However, it has an additional special feature that I find very conveniant: It is not restricted to 12TET but can easily be used with other tuning schemes. The tuner will then show deviations (in cent) from those other tuning schemes.
There are quite a number of alternative tuning schemes already included with the program. But one can also add custom ones in the form of text files that follow a simple format called Scala [Op de Coul, 2001]. I use Chromatia with the following Scala file which corresponds to the tuning scheme in the previous section.
! ji_hca19.scl by Orjan Hansson, 2004-07-17, 2006-12-27 ! Lines starting with an exclamation mark are ! treated as comments in Scala files. ! The following is a short description of the scale: 19 limit JI for hca (2nd and 3rd pos) ! ! Some comments left out. ! The following number tells how many notes ! there are in the scale: 7 ! ! Here follows the definitions of the notes in ! the scale. (Only numbers are read, the rest is ! treated as a comment.) ! 9/8 Major whole tone 5/4 Major third 171/128 Perfect fourth increased with 3 cent as a ! compromise between 2nd and 3rd pos 3/2 Perfect fifth 27/16 Major sixth increased with 22 cent 15/8 Major seventh 2/1 Octave
Chromatia will load this file upon start if it exists in the same directory as the executable. Then the deviations shown by the tuner will correspond to deviations with respect to this tuning scheme.
Here are some Scala files that I have written for harmonica tuning:
- ji_hca01.scl: JI for hca (1st pos)
- ji_hca02.scl: JI for hca (2nd pos)
- ji_hca03.scl: JI for hca (3rd pos)
- ji_hca19.scl: 19-limit JI for hca (2nd and 3rd pos) (the one I currently use)
- ji_hca23.scl: JI for hca (2nd and 3rd pos) (an alternative to the above)
- ji_hnm02.scl: JI for nat minor hca (2nd pos)
The files have been packed into a zip-file which can be downloaded from here.
3.2 Chromatia settings
I use Chromatia with the following settings (Options/Tuning):
- Scale root key
- This should be set to the key of the harmonica.
- Octave stretch
- I use 2 cent/octave.
- Master tuning
- Usually, harmonicas are tuned a little sharp, for example to A4 = 443 Hz (12 cent above 440 Hz). When using Chromatia with tuning schemes other than 12TET, it is very important to set the master tuning to the desired frequency of the scale root key. For a C major diatonic harmonica, one should set C4 to 263 Hz (9 semitones of 12TET below A4 = 443 Hz). For a natural minor harp played in 2nd position one should set the scale root key and master tuning to that of the 2nd position root note (if the above Scala file is used).
I find it conveniant to keep track of what I am doing with the help of an Excel spreadsheet. Thus, I first go through all the reeds in a pair of reed plates and write down how much each one deviates from the tuning scheme. Then I select those reeds that show significant deviations (1 Hz or more) and adjust them each in turn until the tuning is satisfactory. Finally, I write down the deviations of those reeds that I have retuned.
One reason for the 1-Hz criterion is that this corresponds to the so called just noticeable frequency difference for human hearing up to about 1 kHz (it becomes larger at higher frequencies) [Hall, 1991, p.97]. As noted in Theory of harmonica tuning, 1 Hz corresponds to 4 cent at A4 = 440 Hz but only half as much for each increase with an octave. (At A3 = 220 Hz, 1 Hz is 8 cent; at A5 = 880 Hz it is 2 cent.) Indeed, it is possible to detect smaller frequency differences by carefully listening to beats when playing intervals. For example, an octave mistuned by 1 Hz results in a beating
rate of one per second. However, in practice it is difficult to achieve an accuracy
better than 1 Hz with the tuning procedure described below.
4.1 Activating the reeds
In the beginning I found it quite difficult to get consistent readings on the tuner. The needle was jumping back and forth and repeating the measurement several times gave different results each time. First one must learn to blow (draw) in a very relaxed way
and with a steady air flow. Second, it is important not to bend the notes. This can be quite difficult for certain notes, presumably because of resonance phenomena in the vocal tract. (Personally I have difficulties with notes around Bb5 which easily bend down.)
Another thing I experienced was that the frequency of a reed tended to decrease the more I blewed on it. This is probably due to two things [Epping, 1999a]: First, as the reed gets warmer its resonance frequency drops a little. Second, and most important, extended blowing will make it moist, due to condensation of water from the breath. And the larger effective mass will lower the frequency of the reed (see next section).
The above problem does not occur with the draw reeds. Therefore, I decided to activate the blow reeds also by drawing on them. This can be done with the following simple device. Since most of my harmonicas are from the Hohner MS series, I use a a spare plastic MS comb on which I have put Scotch tape on the complete blow (upper) side.
Then I press the reed plate (blow or draw) with my thumbs against the draw (lower) side of the comb with the reeds facing down. It is then an easy matter to activate both draw and blow reeds by drawing in the appropriate hole. I put my thumbs on the reeds next to, and on each side of, the reed I am working on. In this way I can have my mouth quite wide open (important for relaxed playing) and yet only activate one reed at a time.
Of course, if only draw reeds are going to be tuned, it is unnecessary to detach the reed plates since the draw reeds are easily accessible even whith the plates mounted on the comb.
4.2 Tuning the reeds
To change the resonance frequency of a reed one could either remove mass from it (by scraping or grinding) or add mass to it (for example by adding a small drop of solder). An analogy with an oscillating mass at the end of a spring is useful here: The resonance frequency is proportional to the square-root of (k/m) where k is the spring constant (related to its stiffness) and m is the mass attached to the end. Thus, increasing the mass will lower the frequency while a higher frequency will result if the mass is decreased. A harmonica reed responds in a similar way to changes of the mass at the tip (the free end). The stiffness (k) of the reed can also be affected: If ones removes material from the reed close to its root (towards the end where it is attached to the reed plate with a nail), k will decrease and so will the frequency [Baker, 1991, p.55; Oskar, 1996, p.9].
I find it practical to use an electrical rotating grinding tool. There are several types available, for example those manufactured by Dremel or Black & Decker. Mine is a Co-Tech multipurpose tool which is quite cheap (200 SEK) but works satisfactorily. I use it with a small conical grinding stone at its slowest speed (15000 rpm).
A tool like this is very effective and one has to be extremely careful. A slight touch with the tool on the reed to make a mark 1 mm wide and 2 mm long is sufficient to change the frequency of the order of 10 cent.
The reed needs to be supported when one is working on it with a grinding tool. For this I use the thin brass plate that comes with the Lee Oskar Tool Kit (a razor blade or something similar may also do). I insert the plate under the reed to be tuned and over adjacent reeds to protect them from accidental damage.