User:Lhearne/Extra-Diatonic Intervals: Difference between revisions
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=== Intermediates === | === Intermediates === | ||
To provide native support for Semaphore, Pajara and Injera, intermediates are also added to the system. It should be noted immediately that intermediates are not as common to common microtonal interval naming as neutrals and though are a useful addition to this scheme, may be left out if desired. | To provide native support for Semaphore, Pajara and Injera, intermediates are also added to the system. It should be noted immediately that intermediates are not as common to common microtonal interval naming as neutrals and though are a useful addition to this scheme, may be left out if desired. The appendix includes the MOS scales and edos from 'lists of all edos and MOS Scales', but without any intermediates. | ||
‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths-seventh’ or ‘sinth’. | ‘2-3’ lies exactly half-way between M2 and m3 and divides the P4 in half. It may be read ‘second-third’ or ‘serd’. ‘6-7’, it’s octave-inverse lies exactly half-way between M6 and m7 and may be read ‘sixths-seventh’ or ‘sinth’. | ||
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Mavila[16] 8|7 can be writtten | Mavila[16] 8|7 can be writtten | ||
P1 A2 M2 m2 M3 m3 | P1 A2 M2 m2 M3 m3 A4 P4 A5 P5 d5 M6 m6 M7 m7 d7 P8. | ||
The primary interval names for 16edo are the same, but for the inclusion of intermediates: | The primary interval names for 16edo are the same, but for the inclusion of intermediates: | ||
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#* s4 (sub 4th) = P4 - septimal comma | #* s4 (sub 4th) = P4 - septimal comma | ||
#* S5 (super 5th) = P5 + septimal comma | #* S5 (super 5th) = P5 + septimal comma | ||
# If meantone comma alterations are used, S1 (supra unison) may be labelled at P1 + meantone comma and d8 (small octave) at P8 - meantone comma. If septimal comma alterations are used, S1 (super unison) may be labelled at P1 + septimal comma and s8 (sub octave) may be labelled at P8 - septimal comma. If both are needed, and after steps 13-16 are completed as desired the interval corresponding to a super or supra unison (equivalently, sub or small octave) is yet otherwise unlabeled then to ascertain whether S1 is a supra or super unison (or equivalently s8 a small or sub octave), for all degrees, the short hand for 'small' is to be 'sl' rather than 's', and for 'supra' is to be 'SR' rather than 'S'. | # If meantone comma alterations are used, S1 (supra unison) may be labelled at P1 + meantone comma and d8 (small octave) at P8 - meantone comma. If septimal comma alterations are used, S1 (super unison) may be labelled at P1 + septimal comma and s8 (sub octave) may be labelled at P8 - septimal comma. If both are needed and not equal, and after steps 13-16 are completed as desired the interval corresponding to a super or supra unison (equivalently, sub or small octave) is yet otherwise unlabeled then to ascertain whether S1 is a supra or super unison (or equivalently s8 a small or sub octave), for all degrees, the short hand for 'small' is to be 'sl' rather than 's', and for 'supra' is to be 'SR' rather than 'S'. | ||
# Remaining augmented (M + A) and diminished (m - A) intervals may be labelled 'A' and 'd'. | # Remaining augmented (M + A) and diminished (m - A) intervals may be labelled 'A' and 'd'. | ||
# If desired, augmentation and diminution may be iterated through the continued adding or subtracting of A, labelled by additional 'A' or 'd' prefixes respectively. | # If desired, augmentation and diminution may be iterated through the continued adding or subtracting of A, labelled by additional 'A' or 'd' prefixes respectively. | ||
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=== Primary interval names for edos === | === Primary interval names for edos === | ||
2edo: P1 P4/4-5/P5 P8 | 2edo: P1 P4/4-5/P5 P8 | ||
3edo: P1 3-4/P4 P5/5-6 P8 | 3edo: P1 3-4/P4 P5/5-6 P8 | ||
4edo: P1 2-3 P4/4-5/P5 6-7 P8 | 4edo: P1 2-3 P4/4-5/P5 6-7 P8 | ||
5edo: P1/1-2 2-3 3-4/P4 P5/5-6 6-7 7-8/P8 | 5edo: P1/1-2 2-3 3-4/P4 P5/5-6 6-7 7-8/P8 | ||
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Mavila[9] 4|4: P1 M2 M3 m3 P4 P5 M6 m6 m7 P8 | Mavila[9] 4|4: P1 M2 M3 m3 P4 P5 M6 m6 m7 P8 | ||
Mavila[16] 8|7: P1 A2 M2 m2 M3 m3 | Mavila[16] 8|7: P1 A2 M2 m2 M3 m3 A4 P4 A5 P5 d5 M6 m6 M7 m7 d7 P8 | ||
Meantone[5] 2|2: P1 M2 P4 P5 m7 P8 | Meantone[5] 2|2: P1 M2 P4 P5 m7 P8 | ||
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== Conclusion == | == Conclusion == | ||
Using only 'S' and 's' as qualifiers to M, m, P, A and d, along with N and intermediate degrees, a system is developed wherein for most edos below 50 intervals can be systematically named such that for primary interval names, 'S' and 's' raise and lower, respectively, by 1 step of an edo , whilst the intervals of many MOS scales may be consistently named across different tunings, taking the best of both Igliashon Jones' extra diatonic interval names and Sagispeak. One does not need to understand the comma associations to make use of the interval names. While the intervals of some MOS scales may hold consistent names in edos in an Ups and Downs based scheme, there are many common scales that do not in such a system, that do in this one, such as scales of Diminished and Augmented temperament. What's more, the use of neutrals and intermediates leads to quicker recognition of MOS scales that may be supported in edos. | Using only 'S' and 's' as qualifiers to M, m, P, A and d, along with N and intermediate degrees, a system is developed wherein for most edos below 50 intervals can be systematically named such that for primary interval names, 'S' and 's' raise and lower, respectively, by 1 step of an edo , whilst the intervals of many MOS scales may be consistently named across different tunings, taking the best of both Igliashon Jones' extra diatonic interval names and Sagispeak. One does not need to understand the comma associations to make use of the interval names. While the intervals of some MOS scales may hold consistent names in edos in an Ups and Downs based scheme, there are many common scales that do not in such a system, that do in this one, such as scales of Diminished and Augmented temperament. What's more, the use of neutrals and intermediates leads to quicker recognition of MOS scales that may be supported in edos. | ||
== Appendix == | |||
=== Primary interval names for edos, without intermediates === | |||
2edo: P1 P4/P5 P8 | |||
3edo: P1 P4 P5 P8 | |||
4edo: P1 SM2/sm3 P4/P5 SM6/sm7 P8 | |||
5edo: P1/m2 M2/m3 M3/P4 P5/m6 M6/m7 M7/P8 | |||
6edo: P1 SM2 sm3/s4 P4/P5 S5/sM6 sm7 P8 | |||
7edo: P1 N2 N3 P4 P5 N6 N7 P8 | |||
8edo: P1 m3 M2 P4 4-5 P5 m7 M6 P8 | |||
9edo: P1 M2 M3 m3 P4 P5 M6 m6 m7 P8 | |||
10edo: P1/m2 N2 M2/m3 N3 M3/P4 4-5 P5/m6 N6 M6/m7 N7 M7/P8 | |||
11edo: P1 M2 M3 N3 m3 P4 P5 M6 N6 m6 m7 P8 | |||
12edo: P1 m2 M2 m3 M3 P4 A4/d5 P5 m6 M6 m7 M7 P8 | |||
13edo: P1 N2 m3 M2 N3 P4 N5 N4 P5 N6 m7 M6 N7 P8 | |||
14edo: P1 S1/sm2 N2 SM2/sm3 N3 SM3/s4 P4 SA4/sd5 P5 S5/sm6 N6 SM6/sm7 N7 SM7/s8 P8 | |||
15edo: P1/m2 S1/Sm2 sM2 M2/m3 Sm3 sM3 M3/P4 S4 s5 P5/m6 Sm6 sM6 M6/m7 Sm7 sM7/s8 M7/P8 | |||
16edo: P1 d1 M2 m2 M3 m3 A4 P4 d4/A5 P5 d5 M6 m6 M7 m7 A8 P8 | |||
17edo: P1 N1 N2 M2 m3 N3 M3 P4 N4 N5 P5 m6 N6 M6 m7 N7 N8 P8 | |||
19edo: P1 S1/sm2 m2 M2 SM2/sm3 m3 M3 SM3/s4 P4 A4 d5 P5 S5/sm6 m6 M6 SM6/sm7 m7 M7/s8 P8 | |||
21edo: P1 S1 sm2 N2 SM2 sm3 N3 SM3 s4 P4 SA4 sd5 P5 S5 sm6 N6 SM6 sm7 N7 SM7 d8 P8 | |||
22edo: P1 m2 Sm2 sM2 M2 m3 Sm3 sM3 M3 P4 S4 4-5 s5 P5 m6 Sm6 sM6 M6 m7 Sm7 sM7 M7 P8 | |||
23edo: P1 d1 A2 M2 m2 d2/A3 M3 m3 d3 A4 P4 d4 A5 P5 d5 A6 M6 m6 d6/A7 M7 m7 d7 A8 P8 | |||
24edo: P1 S1/sm2 m2 N2 M2 SM2/sm3 m3 N3 M3 SM3/s4 P4 N4 A4/d5 N5 P5 S5/sm6 m6 N6 M6 SM6/sm7 m7 N7 M7 SM7/s8 P8 | |||
26edo: P1 A2 d2 m2 M2 A2 d3 m3 M3 A3 d4 P4 A4 AA4/dd5 d5 P5 A5 d6 m6 M6 A6 d7 m7 M7 A7 d8 P8 | |||
27edo: P1 m2 Sm2 N2 sM2 M2 m3 Sm3 N3 sM3 M3 P4 N4 d6 A3 N5 P5 m6 Sm6 N6 sM6 M6 m7 Sm7 N7 sM7 M7 P8 | |||
28edo: P1 sA1 1-2 Sm2 N2 sM2 2-3 Sm3 N3 sM3 3-4 S4 N4 sA4 4-5 Sd5 N5 s5 5-6 Sm6 N6 sM6 6-7 Sm7 N7 sM7 7-8 Sd8 P8 | |||
29edo: P1 S1 m2 Sm2 sM2 M2 SM2/sm3 m3 Sm3 sM3 M3 SM3/s4 P4 S4 d5 A4 s5 P5 S5/sm6 m6 Sm6 sM6 M6 SM6/sm7 m7 Sm7 sM7 M7 s8 P8 | |||
31edo: P1 N1 sm2 m2 N2 M2 SM2 sm3 m3 N3 M3 SM3 s4 P4 N4 A4 d5 N4 P5 S5 sm6 m6 N6 M6 SM6 sm7 m7 N7 M7 SM7 N8 P8 | |||
34edo: P1 1-2 m2 Sm2 N2 sM2 M2 2-3 m3 Sm3 N3 sM3 M3 3-4 P4 S4 N4 4-5 N5 s5 P5 5-6 m6 Sm6 N6 sM6 M6 6-7 m7 Sm7 N7 sM7 M7 7-8 P8 | |||
38edo: P1 S1 A1 sm2 m2 N2 M2 SM2 A2/d3 sm3 m3 N3 M3 SM3 d4 s4 P4 N4 A4 4-5 d5 N5 P5 S5 A5 sm6 m6 N6 M6 SM6 A6/d7 sm7 m7 N7 M7 SM7 d8 s8 P8 | |||
41edo: P1 N1 sm2 m2 Sm2 N2 sM2 M2 SM2 sm3 m3 Sm3 N3 sM3 M3 SM3 s4 P4 S4 N4 d5 A4 N5 sM5 P5 S5 sm6 m6 Sm6 N6 sM6 M6 SM6 sm7 m7 Sm7 N7 sM7 M7 SM7 N8 P8 | |||
43edo: P1 S1 1-2 A1/sm2 m2 dd3 AA1 M2 SM2/d3 2-3 A2/sm3 m3 dd4 AA2 M3 SM3/d4 3-4 A3/s4 P4 dd5 AA3 A4 d5 dd6 AA4 P5 S5/A6 5-6 A5/sm6 m6 dd7 AA5 M6 SM6/d7 6-7 A6/sm7 m7 dd8 AA6 M7 SM7/d8 7-8 s8 P8 | |||
46edo: P1 S1 sm2 m2 Sm2 A1 d3 sM2 M2 SM2 sm3 m3 Sm3 A2 d4 sM3 M3 SM3 s4 P4 S4 sd5 d5 Sd5/sA4 A4 SA4 s5 P5 S5 sm6 m6 Sm6 A4 d7 sM6 M6 SM6 sm7 m7 Sm7 A6 d8 sM7 M7 SM7 s8 P8 | |||
=== Interval names for MOS scales === | |||
Augmented[6] 1|0 (3): P1 Sm3 sM3 P5 Sm6 sM7 P8 | |||
Augmented[9] 1|1 (3): P1 Sm2 Sm3 sM3 P4 P5 Sm6 SM6 sM7 P8 | |||
Augmented[12] 2|1 (3): P1 Sm2 M2 Sm3 sM3 P4 sA4 P5 Sm6 Sm7 SM6 sM7 P8 | |||
Augmented[15] 2|2 (3): P1 Sm2 sM2 M2 Sm3 sM3 P4 Sd5 sA4 P5 Sm6 Sm7 SM6 m7 sM7 P8 | |||
Blackwood[10] 1|0 (5): P1/m2 sM2 M2/m3 sM3 M3/P4 s5 P5/m6 sM6 M6/m7 sM7 M7/P8 | |||
Blackwood[15] 1|1 (5): P1/m2 S1/Sm2 sM2 M2/m3 Sm3 sM3 M3/P4 S4 s5 P5/m6 Sm6 sM6 M6/m7 Sm7 sM7/s8 M7/P8 | |||
Diminished[8] 1|0 (4): P1 sM2 Sm3 P4 4-5 Sm6 sM6 sM7 P8 | |||
Diminished[12] 1|1 (4): P1 Sm2 sM2 Sm3 sM3 P4 4-5 P5 Sm6 sM6 Sm7 sM7 P8 | |||
Injera[12] 3|2 (2): P1 sm2 M2 sm3 SM3 P4 4-5 P5 sm6 M6 m7 SM7 P8 | |||
Injera[14] 3|3 (2): P1 sm2 M2 sm3 m3 SM3 P4 4-5 P5 sm6 M6 SM6 m7 SM7 P8 | |||
Machine[5] 2|2: P1 M2 M3 m6 m7 P8 | |||
Machine[6] 3|2: P1 M2 M3 A4 m6 m7 P8 | |||
Machine[11] 5|5: P1 d3 M2 d4 M3 d5 A4 m6 A5 m7 A6 P8 | |||
Mavila[7] 3|3: P1 M2 m3 P4 P5 M6 m7 P8 | |||
Mavila[9] 4|4: P1 M2 M3 m3 P4 P5 M6 m6 m7 P8 | |||
Mavila[16] 8|7: P1 A2 M2 m2 M3 m3 A4 P4 A5 P5 d5 M6 m6 M7 m7 d7 P8 | |||
Meantone[5] 2|2: P1 M2 P4 P5 m7 P8 | |||
Meantone[7] 3|3: P1 M2 m3 P4 P5 M6 m7 P8 | |||
Meantone[12] 6|5: P1 m2 M2 m3 M3 P4 A4 P5 m6 M6 m7 M7 P8 | |||
Meantone[19] 9|9: P1 A1 m2 M2 A2 m3 M3 d4 P4 A4 d5 P5 A5 m6 M6 d7 m7 M7 d8 P8 | |||
Miracle[10] 5|4: P1 Sm2 SM2 N3 s4 sA4 S5 N6 sm7 sM7 P8 | |||
Miracle[11] 5|5: P1 Sm2 SM2 N3 s4 Sd5 sA4 S5 N6 sm7 sM7 P8 | |||
Negri[9] 4|4: P1 Sm2 SM2/sm3 sM3 P4 P5 Sm6 SM6/sm7 sM7 P8 | |||
Negri[10] 4|4: P1 Sm2 SM2/sm3 sM3 P4 A4 P5 Sm6 SM6/sm7 sM7 P8 | |||
Neutral[7] 3|3: P1 N2 N3 P4 P5 N6 N7 P8 | |||
Neutral[10] 5|4: P1 N2 M2 N3 P4 N4 P5 N6 m7 N7 P8 | |||
Neutral[17] 8|8: P1 N1 N2 M2 m3 N3 M3 P4 N4 N5 P5 m6 N6 M6 m7 N7 N8 P8 | |||
Pajara[10] 2|2 (2): P1 Sm2 M2 sM3 P4 4-5 P5 Sm6 m7 sM7 P8 | |||
Pajara[12] 3|2 (2): P1 Sm2 M2 Sm3 sM3 P4 4-5 P5 Sm6 sM6 m7 sM7 P8 | |||
Porcupine[7] 3|3: P1 sM2 Sm3 P4 P5 sM6 Sm7 P8 | |||
Porcupine[8] 4|3: P1 sM2 Sm3 P4 s5 P5 sM6 Sm7 P8 | |||
Porcupine[15] 7|7: P1 S1 sM2 M2 Sm3 sM3 P4 S4 s5 P5 Sm6 sM6 m7 Sm7 s8 P8 | |||
Semaphore[5] 2|2: P1 SM2/sm3 P4 P5 SM6/sm7 P8 | |||
Semaphore[9] 4|4: P1 M2 SM2/sm3 SM3/s4 P4 P5 S5/sm6 SM6/sm7 m7 P8 | |||
Slendric[5] 2|3: P1 SM2 s4 S5 sm7 P8 | |||
Slendric[6] 3|2: P1 SM2 s4 P5 S5 sm7 P8 | |||
Slendric[11] 5|5: P1 S1 SM2 sm3 s4 P4 P5 S5 SM6 sm7 s8 P8 | |||
Superpyth[7] 3|3: P1 M2 m3 P4 P5 M6 m7 P8 | |||
Superpyth[12] 6|5: P1 m2 M2 m3 M3 P4 A4 P5 m6 M6 m7 M7 P8 | |||
Superpyth[17] 8|8: P1 m2 A1 M2 m3 d4 M3 P4 d5 A4 P5 m6 A5 M6 m7 d8 M7 P8 | |||
Tetracot[6] 3|2: P1 sM2 N3 S4 N6 Sm7 P8 | |||
Tetracot[7] 4|2: P1 sM2 N3 S4 P5 N6 Sm7 P8 | |||
Tetracot[13] 6|6: P1 N2 sM2 Sm3 N3 P4 S4 s5 P5 N6 sM6 Sm7 N7 P8 | |||