79edo: Difference between revisions
→Music: Added music |
→Theory: these are a part of existing temperament so i am revoking my own names and naming them this |
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It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for [[Orwellismic_temperaments#Sentinel-11-limit|sentinel temperament]]. 79 is the 22nd prime EDO number. | It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for [[Orwellismic_temperaments#Sentinel-11-limit|sentinel temperament]]. 79 is the 22nd prime EDO number. | ||
79edo adequately represents the | 79edo adequately represents the [[Decaononic|way of playing]] where a tone is considered to be [[10/9]] instead of [[9/8]]. In [[12edo]] and meantones close to it used predominantly in Western music), when the difference betweein 10/9 and 9/8 is tempered out, what really happens is that the 9/8 only note is used, and 10/9 is raised to be equal to 9/8. 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A maximum evenness variant of such scale can be generated by naively stacking 6 [[12edo]] diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament. | ||
A maximum evenness variant of such scale can be generated by naively stacking 6 [[12edo]] diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. | |||
== Scales == | == Scales == | ||
* | * Bluebirds[7] - also [[glacial]] | ||
* | * Bluebirds[46] | ||
== Music == | == Music == | ||
Revision as of 19:06, 30 May 2023
| ← 78edo | 79edo | 80edo → |
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.22 | -6.57 | +3.33 | -6.44 | -4.48 | -5.08 | +5.40 | +1.37 | +6.28 | +0.11 | -5.49 |
| Relative (%) | -21.2 | -43.2 | +21.9 | -42.4 | -29.5 | -33.5 | +35.6 | +9.0 | +41.4 | +0.7 | -36.1 | |
| Steps (reduced) |
125 (46) |
183 (25) |
222 (64) |
250 (13) |
273 (36) |
292 (55) |
309 (72) |
323 (7) |
336 (20) |
347 (31) |
357 (41) | |
It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for sentinel temperament. 79 is the 22nd prime EDO number.
79edo adequately represents the way of playing where a tone is considered to be 10/9 instead of 9/8. In 12edo and meantones close to it used predominantly in Western music), when the difference betweein 10/9 and 9/8 is tempered out, what really happens is that the 9/8 only note is used, and 10/9 is raised to be equal to 9/8. 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A maximum evenness variant of such scale can be generated by naively stacking 6 12edo diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. From a regular temperament theory perspective, these scales are a part of the bluebirds temperament.
Scales
- Bluebirds[7] - also glacial
- Bluebirds[46]
Music
- Silence and Secrecy (Julian Malerman)