Major second: Difference between revisions

A '''major second (M2)''' is an interval that spans one scale step in the [[5L 2s|diatonic]] scale with the major (wider) quality. It is generated by stacking 2 fifths [[octave reduction|octave reduced]], and depending on the specific tuning, it ranges from 171 to 240{{cent}} ([[7edo|1\7]] to [[5edo|1\5]]). It can be considered the large step of the diatonic scale.

The Pythagorean ([[3-limit]]) major second is [[9/8]], which is 204 cents in size and corresponds to the mos-based interval category of the diatonic major second. It is generated by [[stacking]] two just perfect fifths of [[3/2]]. There is also a Pythagorean diminished third of [[65536/59049]], which is about 180 cents in size. While called a "third", it is within the range of major seconds.

Other major seconds exist in higher [[prime limit|limits]], however, for example:

! colspan="2" | Delta-1

! colspan="2" | Delta-2

! colspan="2" | Delta-3

| 8/7

| 231{{c}}

| 15/13*

| 248{{c}}

| 22/19*

| 253{{c}}

| 9/8

| 204{{c}}

| 17/15

| 217{{c}}

| 23/20*

| 242{{c}}

| 10/9

| 182{{c}}

| 19/17

| 193{{c}}

| 25/22

| 221{{c}}

| 11/10*

| 165{{c}}

| 21/19

| 173{{c}}

| 26/23

| 212{{c}}

|  

|  

|  

|  

| 28/25

| 196{{c}}

|  

|  

|  

|  

| 29/26

| 189{{c}}

|  

|  

|  

|  

| 31/28

| 176{{c}}

|  

|  

|  

|  

| 32/29*

| 170{{c}}

== In edos ==

The following table lists the best tuning of 10/9, 9/8, and 8/7, as well as other major seconds if present, in various significant [[edo]]s.

! Edo

! 10/9

! 9/8

! 8/7

! Other major seconds

| 5

| colspan="3" | 240{{c}}

|  

| 7

| colspan="3" | 171{{c}}

|  

| 12

| colspan="3" | 200{{c}}

|  

| 15

| 160{{c}}

| colspan="2" |240{{c}}

|  

| 16

| *

| colspan="2" | 225{{c}}

|  

| 17

| colspan="3" | 212{{c}}

|  

| 19

| colspan="2" | 189{{c}}

| 253{{c}}

| 22

| 164{{c}}

| colspan="2" | 218{{c}}

|  

| 24

| colspan="2" | 200{{c}}

| 250{{c}}

| 25

| colspan="2" | 192{{c}}

| 240{{c}}

| 26

| colspan="2" | 185{{c}}

| 231c

| 27

| 178{{c}}

| colspan="2" | 222{{c}}

|  

| 29

| 166{{c}}

| 207{{c}}

| 248{{c}}

|  

| 31

| colspan="2" | 194{{c}}

| 232{{c}}

|  

| 34

| 176{{c}}

| 212{{c}}

| 247{{c}}

|  

| 41

| 176{{c}}

| 205{{c}}

| 234{{c}}

|  

| 53

| 181{{c}}

| 204{{c}}

| 226{{c}}

| 249{{c}} ≈ 15/13

== In mos scales ==

Being a small interval, major seconds generate a number of monosmall and monolarge [[mos]].

These tables start from the last monolarge mos generated by the interval range.

Scales with more than 12 notes are not included.

! colspan="3" | Mos