Major 4ths & 5ths

[Conrad Hoffsommer]

At 12:06 2/10/2004 -0700, you wrote:
>  Hi Davids,
>Knowing Paul, I think that he is trying to discribe the different intervals
>found ( dread ) in historical temperments.  Not Equal.
>Joe Goss



Just to confuse everybody...

The following is a list of theoretical interval sizes based on their 
relationships along the harmonic series.

Musically, things are different.
m2 = 100¢,
M2 = 200¢
Aug2/m3 = 300¢
M3/Dim IV = 400¢
IV = 500¢
etc.

         Mathematics of Intervals

RatioNameSize in ¢
Adjacent intervals:
1/2Octave1200
2/3Fifth 702
3/4Fourth 498
4/5Major third 386
5/6Minor third 316
6/7Small m3 267
7/8Maximum tone 231
8/9Major Tone 204
9/10Minor Tone 182
10/11                  Minimum Tone            165
11/123/4 Tone 151
15/16Just diatonic semitone 112
Single skip intervals
3/5M6 884
5/7Small Tritone 583
7/9large M3 435
9/11Neutral third 347
Double skip intervals
4/7Harmonic m7 969
5/8m6 814
7/10Large tritone 617

12th root of 2 = 1:1.05946       = Temp. semitone     100
1200th root of 2 = 1:1.00057779  = cent               1

Comma - the difference between two sets of just intervals or combinations 
of just intervals.
Diesis - difference between # & b tuned on the same key

Pythagorean (ditonic) comma     23.5¢

Syntonic comma          22  ¢
- 81/80 - the difference between Pythagorean M3 and Just M3.
    & also  "      "         "    Just m3 and Pythagorean m3
Enharmonic diesis       41  ¢



Conrad Hoffsommer - Music Technician
Luther College, 700 College Dr., Decorah, Iowa 52101-1045
Vox-(563)-387-1204 // Fax (563)-387-1076

- Education is what you get from reading the small print. Experience is 
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