Comparing Note Spectra of 3 New Flutes (Xindi)

About the instruments

The 3 instruments used in this comparison are made based on a flute design created by a Chinese physicist and dramatist Din, Xi-Lin in 1935. He called it Xindi, literally “new flute” compared to traditional Chinese dizi. In 2020, a friend of mine and I started to re-designed and made Xindi using an open source software Woodwind Instrument Designer (WIDesigner), machines such as a wood lathe and a drill press, tools such as reamers and calipers. Until now we developed 2 major versions of the re-designed Xindi which the 3 instruments here belong.

Besides from the major difference between bore and tonehole sizes, in the original Din version, there are 11 toneholes generating the 12 tones of the equal temperament. It creates heavy pressure for players with only 10 fingers; therefore in flute B we canceled the hole which was supposed to be covered by the root of left hand index finger, making it a flute with 10 toneholes. The result is that tone C in the temperament requires the use of cross fingerings. Cross fingerings are optional with the 11-toneholes version, and below I will discuss this impact on the note spectrum.

I will use the scientific pitch notation to label pitch, that is, A4 as a pitch of 442 Hz and A5 as 884 Hz etc. The Xindi has a pitch range from D4 to approximately A6. In this report I choose some, not all pitches they have to describe my findings.

Predicting Note Spectrum with WIDesigner

WIDesigner provides a function “graph the spectrum of selected note in the current tuning tab.” As an example, the note D4’s spectrum of fl. B is shown below. The green part of the loop gain shows the prediction done by the program of frequencies which might appear when playing in this fingering. We can see the target frequency matches the green part which means this flute is supposed to produce this note easily and correctly. I will use this function to compare with some of the note spectra recorded for this report.

Findings

Compared to fl. A and B which have similar bore/tonehole profiles, fl. C has a relatively weaker loudness on the fundamental D4 frequency, which also means the higher harmonics constitutes the timbre more than the former two flutes. Not only D4, this phenomenon can be observed in other pitches as well. For another example, G6 stands out because it is near the highest pitch a Xindi can play.

Though the G6 fundamental frequency loudness are all high in three flutes, fl. C seems to own more loudness in the higher harmonic series. I think the effect of smaller bore and larger toneholes affect this much. Predictions from WIDesigner also show this tendency.

Loop gain with fl. C has more green parts on higher frequencies though they do not correspond with the harmonic series. In fact, if you make the program plot the spectrum of G6’s first 7 or more harmonics, you gain all part red on higher frequencies as shown below.

For the purpose of predicting spectrum, this helps little.

2. Different fingerings of a pitch cause different note spectra.

a. Regular C5 vs. cross fingering C5

The following shows the note spectrum of regular C5 and cross fingering C5 on fl. A, B, and C. Fl. B for the sake of 10 toneholes only has the cross fingering version.

Similarities within separate groups of fingerings are recognizable. C5 with regular fingering seems to own more well-defined harmonic series than with cross fingering. Also note that the second harmonic is stronger than the first harmonic in regular fingering, but in cross fingering the second harmonic become obviously weaker and its frequency not so well-defined. In my listening experience I also feel the notes with cross fingering have thinner timbre than other regular ones. Similar phenomenon can also be observed in WIDesigner’s note spectrum taking fl. C as an example:

b. D5 with/without opening the hole closest to the embouchure hole

The note D5 and D6 for Xindi have two usable fingerings, one closing all toneholes, another opening just the tonehole closest to the embouchure hole. The opening one hole version results in a little rise in pitch that can be unnoticeable, but the difference lies in the timbre. In this report I use the all-closed version on fl. B and C and the 1-opened version on fl. A to play D5/D6. Despite not showing the difference within one flute, the result of comparing between flutes has so far reached to certain insight.

For fl. B and C there seems to be another harmonic series added to the whole palette. There are harmonic series of D5 (589.99 Hz) and D4 (294.99 Hz) recognizable in these two. Fl. A does not show clearly other note’s spectrum besides D5. In my experience the all-closed version retains more low frequency sounds and the 1-opend results in a brighter timbre.

3. Differences caused by the flute material may be observed through note spectrum.

The Tatabuballi is a wood with high density and the Thorny Bamboo is rather loose. This may result in the difference shown below.

Using note A5 as an example, fl. A shows higher proportions of upper harmonic series than fl. B. Although I cannot completely exclude the factor of design differences, for example toneholes of fl. A are slightly bigger than fl. B, they are very similar in bore profiles. Also, results given in WIDesigner do not differ much.

WIDesigner so far does not include functions to manipulate difference in instrument materials. The two predicted spectra shown here do not differ much, therefore I suppose the difference seen in real spectra may be affected by the material difference. Further researches are needed.