Guided NAFlutomat - Step 4. Temperament

This page provides one of the steps in the Guided version of NAFlutomat — a design tool for flute-crafting. The series of eight steps helps you set the most important inputs to the NAFlutomat tool and provides descriptions and explanations of those inputs.

Progress

1. Units (Imperial) ⇒ 2. Key of Flute (A4) ⇒ 3. Pitch Standard (A4=440) ⇒
4. Temperament ⇒ 5. Environment ⇒ 6. Bore Diameter ⇒
7. Wall Thickness ⇒ 8. Direction Holes ⇒ 9. NAFlutomat

Step 4. Temperament

Description

A tuning system is a rule that determines the frequencies of all the notes above the fundamental note (with all finger holes closed ).

The various rules for tuning systems and musical temperaments are a major rabbit hole topic. In brief:

• If you are designing a “concert-tuned” instrument that plays best with Western classical instruments such as guitars and pianos, choose Equal temperament.
• If you want to tune your flute in line with the majority of contemporary Native American flutes made today, choose Equal temperament.
• If you would like to explore a tuning that may sound better to your ear or other peoples' ears, consider one of the Harmonic temperaments or Pythagorean temperament.

Equal Temperament

Equal temperament (or equal-tempered tuning) is one very common musical temperament. It places each note so that the ratio of frequencies between neighboring notes is the same.

Equal temperament has several advantages. If you have an instrument tuned to equal temperament, you can transpose a melody from one key to another and the notes will have the same relative tuning when played on that instrument (i.e. the instrument does not need to be re-tuned for the transposed melody to sound the same as the original melody).

However, equal temperament involves compromises. The tuning that sounds best to most people's ears involves using frequency ratios between notes that are simple ratios, such as 2:1, 3:2, 4:3, 5:3, etc. The notes in an equal tempered scale are always slightly off from those ideal ratios, except for the octave interval, which is fixed at 2:1.

In Western countries, the term equal temperament by default means a 12-note scale. However, in other musical cultures the scale of notes within an octave could be divided into 24 musical tones (Arabian music, see [Marcus 1993]), 19 musical tones ([Mandelbaum 1961]  and [Bucht 2004] ), or 31 musical tones ([Keislar 1991]).

See the article Right in Tune.

Alternate Temperaments

The alternate temperaments let you design flutes where the primary notes have specific frequency ratios from the fundamental note. Both Harmonic temperaments use ratios from a “five-limit harmonic tuning” system where all the notes are related by ratios of small whole numbers. The Pythagorean tuning was one of the earliest tuning systems, dating back to our earliest written records in Ancient Mesopotamia (see Flutes of Gilgamesh and Ancient Mesopotamia).

Temperaments

Fingering	Harmonic-1		Harmonic-2		Pythagorean
	Ratio	Bias from Equal Temperament	Ratio	Bias from Equal Temperament	Ratio	Bias from Equal Temperament
	2:1	0 cents	2:1	0 cents	2:1	0 cents
	9:5	+18 cents	16:9	−4 cents	16:9	−4 cents
	8:5	+16 cents	8:5	+16 cents	128:81	−8 cents
	3:2	+2 cents	3:2	+2 cents	3:2	+2 cents
	4:3	−2 cents	4:3	−2 cents	4:3	−2 cents
	6:5	+16 cents	6:5	+16 cents	32:27	−6 cents
	1:1	0 cents	1:1	0 cents	1:1	0 cents