World music uses a wide variety of scales; our 12 increment western scale is only one among musical languages. And a bamboo flute can be tuned to whatever scale you desire.
notes on tuning from aloe's rev.net Music page. There is a lot more there.
It is said that the basis of music is the human voice. While this statement ignores older phenomena such as bird calls, it is largely true. Children learn to sing before they learn to play pianos and violins. Around the world, most song seems to be based on just intonation. (There may be exceptions.) Therefore, the first test of versatility is whether a tuning system can reasonably substitute for just intonation, by imitating commonly-used just intervals.
An underlying and recurring problem in music is establishing compatibility between tuning systems used in ensemble performances.
In choral music, the purest chords are provided by just intonation, providing the simplest mathematical relationship between notes. Pitches must be adjusted note by note, to correspond to the lead voice. Such constant adjustment is commonplace for a singer. It is also possible on some instruments, by exact placement of a finger along an unfretted viol string or movement of a trombone slide.
However, the majority of musical instruments are difficult to retune, including woodwinds with permanent holes, guitars with glued frets, organs with solid pipes, and pianos with 88 taut and interrelated strings. The value of these instruments depends on their ability to modulate between keys without retuning. Therefore, their tuning reflects a compromise between purity and versatility. In Western music, compromise usually results in 12-tone equal temperament: adding together pentatonic (black key) and heptatonic (white key) scales, so that semi-tones and chromatic intervals are made to coincide.
Although 12-tone music can provide a reasonably accurate expression of music from Bach to Bacharach, it cannot capture the subtlety of music designed to fit divergent theoretical contexts: African neutral intervals, enharmonic scales of ancient Greece, augmented intervals of Hungary, 17-note Arabic tuning, 22-note Indian tuning, quarter-tone compositions of Charles Ives, African-American blue notes, and Indonesian 5-tone slendro and 7-tone pelog scales (to name a few). Moreover, 12TET instruments cannot even produce a true 4:5:6:7 barbershop seventh chord, an American tradition.
Many non-Western systems are also mutually incompatible. Composers who want to combine scales from various countries risk writing music that cannot be played anywhere, by anyone.
http://www.mcgee-flutes.com/FluteMyths.htm
The "correct" stopper distance is one diameter of the head bore
Close, but not the complete story. The conventional stopper distance is one diameter of the head bore - about 19mm for the typical conical flute. But recognise it is a compromise, not a golden rule. A shorter distance - typically about 16mm - will enhance the third octave at the expense of the bottom octave. A greater distance - up to about 23mm - will enhance the bottom notes, at the risk of driving the top of the 2nd octave flat, and making the third octave hard to play and very flat. For Irish music, I recommend increasing the stopper distance until you find the highest note you normally play starts to tend flat.
A plain cylindrical flute can be in tune
Aw, wouldn't that be handy. We'd all be making and playing flutes from bamboo, electrical conduit, water pipe, rolled up newspapers, car exhausts and so on. Unfortunately, it isn't true - the head of a flute must contract for the octaves to be in tune. In a "cylindrical" flute like the Boehm, the contraction appears as a tapered head. In a conical flute, it is conspired to look like a cylinder. But it must be there.
You can force a simple cylindrical flute into tune, but recognise you are forcing it. That is taking processing power from you, and teaching you habits you will have to unlearn if you then get a well-bored flute. Only you can decide if that's an approach that is going to work for you.
The hole placement chart I use for festivals:
it is easy to lay out. Just get a big sheet of poster board, you will need some kind of stop edge along the bottom for the open end of the flute to bump again, to make using it easier. I get that by the luck of having my poster board fit just inside a framed cork / noteboard I had lying around.
At one end of the poster starting from the bottom edge, lay out a short flute, on the other end lay out a long flute. By that I mean make a mark up from the bottom of the paper at the mouth hole distance and measure back down from that for each finger hole distance.
My shortest hi D flute is 260 mm, so make your short one 250 mm
Your actual measurements (based on the percentages below) would be:
107.5
125
145
182.5
207.5
For the long side, the lo G I just tried to make is about 690 mm acoustic length
So try 700 mm for the long end.
301
350
406
476
511
581
For this range the poster paper had better be long or the lines will be too steep to be easy to use.
Once the 2 end ones are laid out, just draw connecting lines between the corresponding hole marks.
Making flutes: make the mouth hole first, cut tube to reach the root note you want, leave a bit flat (1/8th tone or less) as making finger holes will make the tube diameter effectively bigger and the acoustic length a bit shorter – there is interaction between holes.
Then put the foot of the flute (open end) on the bottom of the chart and slide the flute along the chart until the CENTER of the mouth hole lines up with the mouth hole line. Mark the finger holes (look as straight down on the chart as you can.
The measurements are shown as percentages of distance from >the mouthhole (acoustic length). All measurements are from hole centers, not edges.
Mouth hole - 43% 50%58% 68%73% 83% 100%