Pythagorean Tuning

More and more I get the impression that the pythagorean tuning and Pythagoras have not so much to do with each other.
One can easily think that this tuning was discovered or invented by him. No, it is definitely not so.

Pythagoras discovered, most sources agree, above all the constant relationship between the length of the strings of a lyre and the basic chords of music (1:2 for the octave, 2:3 for the fifth and 3:4 for the fourth). These numerical ratios are also fundamental to pure tuning.
The tuning system with the Pythagorean circle of fifths does not originate from Pythagoras. The sources are scanty, it is not clear to me where the circle of fifths comes from.

In the Middle Ages, this tuning was the generally valid and used tuning. At the beginning of the 16th century, in addition to the octave and fifth, the major third was also intoned purely in chordal combinations, and for keyboard instruments pythagorean temperament was increasingly replaced by meantone temperament.

Pythagoras in the forge is an ancient legend describing how Pythagoras discovered in a forge the euphony of hammers sounding together, the weights of which were in certain integer ratios. This observation had formed the starting point for experiments, which became the basis for the music-theoretical description of intervals. With the knowledge gained in this way, Pythagoras had founded the theory of music. The legend had the consequence that Pythagoras was called the inventor of “music” in the Roman Empire and in the Middle Ages, by which music theory was meant.

Pythagorean Tuning – Concert Pitch A4 = 432 Hz

Note nameHz
8.0000000
8.4279835
9.0000000
9.4814815
10.1250000
10.6666667
11.3906250
12.0000000
12.6419753
13.5000000
14.2222222
15.1875000
16.0000000
16.8559671
18.0000000
18.9629630
20.2500000
21.3333333
22.7812500
24.0000000
25.2839506
A027.0000000
A#0/Bb028.4444444
B030.3750000
C132.0000000
C#1/Db133.7119342
D136.0000000
D#1/Eb137.9259259
E140.5000000
F142.6666667
F#1/Gb145.5625000
G148.0000000
G#1/Ab150.5679012
A154.0000000
A#1/Bb156.8888889
B160.7500000
C264.0000000
C#2/Db267.4238683
D272.0000000
D#2/Eb275.8518519
E281.0000000
F285.3333333
F#2/Gb291.1250000
G296.0000000
G#2/Ab2101.1358025
A2108.0000000
A#2/Bb2113.7777778
B2121.5000000
C3128.0000000
C#3/Db3134.8477366
D3144.0000000
D#3/Eb3151.7037037
E3162.0000000
F3170.6666667
F#3/Gb3182.2500000
G3192.0000000
G#3/Ab3202.2716049
A3216.0000000
A#3/Bb3227.5555556
B3243.0000000
C4 (middle C)256.0000000
C#4/Db4269.6954733
D4288.0000000
D#4/Eb4303.4074074
E4324.0000000
F4341.3333333
F#4/Gb4364.5000000
G4384.0000000
G#4/Ab4404.5432099
A4 concert pitch432.0000000
A#4/Bb4455.1111111
B4486.0000000
C5512.0000000
C#5/Db5539.3909465
D5576.0000000
D#5/Eb5606.8148148
E5648.0000000
F5682.6666667
F#5/Gb5729.0000000
G5768.0000000
G#5/Ab5809.0864198
A5864.0000000
A#5/Bb5910.2222222
B5972.0000000
C61024.0000000
C#6/Db61078.7818930
D61152.0000000
D#6/Eb61213.6296296
E61296.0000000
F61365.3333333
F#6/Gb61458.0000000
G61536.0000000
G#6/Ab61618.1728395
A61728.0000000
A#6/Bb61820.4444444
B61944.0000000
C72048.0000000
C#7/Db72157.5637860
D72304.0000000
D#7/Eb72427.2592593
E72592.0000000
F72730.6666667
F#7/Gb72916.0000000
G73072.0000000
G#7/Ab73236.3456790
A73456.0000000
A#7/Bb73640.8888889
B73888.0000000
C84096.0000000
C#8/Db84315.1275720
D84608.0000000
D#8/Eb84854.5185185
E85184.0000000
F85461.3333333
F#8/Gb85832.0000000
G86144.0000000
G#8/Ab86472.6913580
A86912.0000000
A#8/Bb87281.7777778
B87776.0000000
C98192.0000000
C#9/Db98630.2551440
D99216.0000000
D#9/Eb99709.0370370
E910368.0000000
F910922.6666667
F#9/Gb911664.0000000
G912288.0000000

Scala Data

! pythagore.scl
!
Pythagorean 12-tone with whole tones divided arithmetically
12
!
256/243
9/8
32/27
81/64
4/3
729/512
3/2
128/81
27/16
16/9
243/128
2/1