International Organization for Numerical Musical Tuning

Guidelines for
Tuning Specifications

The following table shows some of the most common examples of ways to declare a tuning.


Not Endorsed
 
Endorsed
 
Standard
Equal Temperament or Equally Tempered
ET or 12-ET
EDO or 12-EDO
ED2 or 12-ED2
C or Scale of C
C Major
Ionian
Natural Scale
C - D - E - F - G - A - B - C
1st - 2nd - 3rd - 4th - 5th - 6th - 7th - 8th
Unison - Major Second - Major Third - Perfect Fourth - Perfect Fifth - Major Sixth - Major Seventh - Octave
Tonic (key note) - Supertonic - Major mediant - Subdominant - Dominant - Major submediant - Leading tone - Tonic
whole, whole, half, whole, whole, whole, half
W - W - H - W - W - W - H
L - L - s - L - L - L - s
two identical tetrachords separated by a whole tone
0 - 200 - 400 - 500 - 700 - 900 - 1100 - 1200 cents
and any other logarithmic units of measurement (like savarts)
440 Hz
 
 
 
 
 
 
 
 
image: 7 tones of the 12-tone equal tempered scale written as q/p-th root of 2
image: 7 tones of the 12-tone equal tempered scale written exponentially as 2 to the power p/q
2^(0/12) , 2^(2/12) , 2^(4/12) , 2^(5/12) , 2^(7/12) , 2^(9/12) @ 440 Hz , 2^(11/12) , 2^(12/12) = IoE
image: 7 tones of the 12-tone equal tempered scale written as fractions of exponents of the numbers 2 and 2^(19/12) instead of 3
 
 
Harmonic and Harmonic Series
Just Intonation
n-limit JI
Rational Tuning
Pythagorean
Circle/Cycle/Spiral of Fifths
256 Hz - 288 Hz - 324 Hz - 341.333 Hz - 384 Hz - 432 Hz - 486 Hz - 512 Hz
432 Hz
 
 
 
1–1 @ 256 Hz , 8–9 , 4–5 , 3–4 , 2–3 , 3–5 , 8―15 , 1–2 = IoE
1|1 @ 256 Hz , 8|9 , 4|5 , 3|4 , 2|3 , 3|5 , 8|15 , 1|2 = IoE
1:1 @ 256 Hz , 8:9 , 4:5 , 3:4 , 2:3 , 3:5 , 8:15 , 1:2 = IoE
1/1 @ 256 Hz , 9/8 , 5/4 , 4/3 , 3/2 , 5/3 , 15/8 , 2/1 = IoE
24/24 @ 256 Hz , 27/24 , 30/24 , 32/24 , 36/24 , 40/24 , 45/24 , 48/24 = IoE
24 @ 256 Hz , 27 , 30 , 32 , 36 , 40 , 45 , 48 = IoE
1 @ 256 Hz, 2⁻³×3² , 2⁻²×5 , 2²×3⁻¹ , 2⁻¹×3 , 3⁻¹×5 , 2⁻³×3×5 , 2 = IoE
|0 0 0> @ 256 Hz , |−3 2 0> , |−2 0 1> , |2 −1 0> , |−1 1 0> , |0 −1 1> , |−3 1 1> , |1 0 0> = IoE
2⁰—3⁰ , 2³—3² , 2⁶—3⁴ , 3¹—2² , 2¹—3¹ = G , 2⁴—3³ @ 432 Hz , 2⁷—3⁵ , 3⁰—2¹ = IoE
 
Lucy Tuning
MOS
 
image: the 7 tones of the so-called “C Major” scale in Lucy tuning, written as 2 to the power of a fraction involving 1 in the numerator and the mathematical constant Pi in the denominator
image: the 8 tones of ring #8 derived from the horogram generated by the ratios 0/1 and 1/2, written as the interval of equivalence 2 to the power of fractions involving the golden ratio phi
 
and any alterations or combinations of the above.
and any other combinations of the above, where
G stands for "Generator" (it is not a "note name"), and
IoE stands for "Interval of Equivalence", meaning the sonic entity believed to represent the same quality on a different level, whose role as a sonic distance divided and multiplied by every member of the series is to expand the scale both descending and ascending.